From 9b477f1702cea4dead022bab2ef5b79d066f2b0b Mon Sep 17 00:00:00 2001 From: mapcrafter2048 Date: Tue, 1 Oct 2024 20:56:02 +0530 Subject: [PATCH 01/11] Added the implementation for bijection method binary to decimal and euler method --- maths/bisection_method.ts | 27 +++++++++++++++++++++++++++ maths/decimal_convert.ts | 20 ++++++++++++++++++++ maths/euler_method.ts | 25 +++++++++++++++++++++++++ 3 files changed, 72 insertions(+) create mode 100644 maths/bisection_method.ts create mode 100644 maths/decimal_convert.ts create mode 100644 maths/euler_method.ts diff --git a/maths/bisection_method.ts b/maths/bisection_method.ts new file mode 100644 index 00000000..ec3e7235 --- /dev/null +++ b/maths/bisection_method.ts @@ -0,0 +1,27 @@ +/** + * @function bisectionMethod + * @description Bisection method is a root-finding method that applies to any continuous function for which one knows two values with opposite signs. + * @param {number} a - The first value + * @param {number} b - The second value + * @param {number} e - The error value + * @param {Function} f - The function + * @return {number} - The root of the function + * @see [BisectionMethod](https://en.wikipedia.org/wiki/Bisection_method) + * @example bisectionMethod(1, 2, 0.01, (x) => x**2 - 2) = 1.4140625 + * @example bisectionMethod(1, 2, 0.01, (x) => x**2 - 3) = 1.732421875 + */ + +export const bisectionMethod = (a: number, b: number, e: number, f: Function): number => { + let c = a + while ((b - a) >= e) { + c = (a + b) / 2 + if (f(c) === 0.0) { + break + } else if (f(c) * f(a) < 0) { + b = c + } else { + a = c + } + } + return c +} \ No newline at end of file diff --git a/maths/decimal_convert.ts b/maths/decimal_convert.ts new file mode 100644 index 00000000..2413378e --- /dev/null +++ b/maths/decimal_convert.ts @@ -0,0 +1,20 @@ +/** + * @function decimalConvert + * @description Convert the binary to decimal. + * @param {string} binary - The input binary + * @return {number} - Decimal of binary. + * @see [DecimalConvert](https://www.programiz.com/javascript/examples/binary-decimal) + * @example decimalConvert(1100) = 12 + * @example decimalConvert(1110) = 14 + */ + +export const decimalConvert = (binary: string): number => { + let decimal = 0 + let binaryArr = binary.split('').reverse() + + for (let i = 0; i < binaryArr.length; i++) { + decimal += parseInt(binaryArr[i]) * Math.pow(2, i) + } + + return decimal +} diff --git a/maths/euler_method.ts b/maths/euler_method.ts new file mode 100644 index 00000000..bc4c4b7c --- /dev/null +++ b/maths/euler_method.ts @@ -0,0 +1,25 @@ +/** + * @function eulerMethod + * @description Euler's method is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. + * @param {number} x0 - The initial value of x + * @param {number} y0 - The initial value of y + * @param {number} h - The step size + * @param {number} n - The number of iterations + * @param {Function} f - The function + * @return {number} - The value of y at x + * @see [EulerMethod](https://en.wikipedia.org/wiki/Euler_method) + * @example eulerMethod(0, 1, 0.1, 10, (x, y) => x + y) = 2.5937424601 + * @example eulerMethod(0, 1, 0.1, 10, (x, y) => x * y) = 1.7715614317 + */ + +export const eulerMethod = (x0: number, y0: number, h: number, n: number, f: Function): number => { + let x = x0 + let y = y0 + + for (let i = 1; i <= n; i++) { + y = y + h * f(x, y) + x = x + h + } + + return y +} \ No newline at end of file From a358ea671faf54e14c6e34221c2e9ec6ca3784e2 Mon Sep 17 00:00:00 2001 From: mapcrafter2048 Date: Wed, 2 Oct 2024 09:01:55 +0530 Subject: [PATCH 02/11] Added the implementation of the edmondkarp along with tests --- graph/edmondkarp.ts | 76 +++++++++++++++++++++++++++++++ graph/test/edmondkarp_test.ts | 84 +++++++++++++++++++++++++++++++++++ 2 files changed, 160 insertions(+) create mode 100644 graph/edmondkarp.ts create mode 100644 graph/test/edmondkarp_test.ts diff --git a/graph/edmondkarp.ts b/graph/edmondkarp.ts new file mode 100644 index 00000000..0ff3ffb0 --- /dev/null +++ b/graph/edmondkarp.ts @@ -0,0 +1,76 @@ +/** + * @function edmondkarp + * @description Compute the maximum flow from a source node to a sink node. The input graph is in adjacency list form. It is a multidimensional array of edges. graph[i] holds the edges for the i'th node. Each edge is a 3-tuple where the 0'th item is the destination node, the 1'th item is the edge weight, and the 2'nd item is the edge capacity. + * @Complexity_Analysis + * Time complexity: O(V*E^2) where V is the number of vertices and E is the number of edges + * Space Complexity: O(V) where V is the number of vertices + * @param {[number, number, number][][]} graph - The graph in adjacency list form + * @param {number} source - The source node + * @param {number} sink - The sink node + * @return {number} - The maximum flow from the source node to the sink node + * @see https://en.wikipedia.org/wiki/Edmonds%E2%80%93Karp_algorithm + */ + +function edmondkarp(graph: [number, number, number][][], source: number, sink: number): number { + // Initialize capacity and flow matrices with zeros and build capacity matrix from graph + const n = graph.length; + const capacity = Array.from({ length: n }, () => Array(n).fill(0)); + const flow = Array.from({ length: n }, () => Array(n).fill(0)); + + // Build capacity matrix + for (let u = 0; u < n; u++) { + for (const [v, , cap] of graph[u]) { + capacity[u][v] = cap; + } + } + + // Breadth-first search + const bfs = (parent: number[]): boolean => { + const visited = Array(n).fill(false); + const queue: number[] = []; + queue.push(source); + visited[source] = true; + + // Find an augmenting path from source to sink by doing a BFS traversal + while (queue.length > 0) { + // Dequeue + const u = queue.shift()!; + // Enqueue all adjacent unvisited vertices with available capacity + for (let v = 0; v < n; v++) { + // If there is available capacity and the vertex has not been visited + if (!visited[v] && capacity[u][v] - flow[u][v] > 0) { + queue.push(v); + visited[v] = true; + parent[v] = u; + // If we reach the sink, we have found the augmenting path + if (v === sink) { + return true; + } + } + } + } + return false; + }; + + let maxFlow = 0; + const parent = Array(n).fill(-1); + + while (bfs(parent)) { + let pathFlow = Infinity; + // Find the maximum flow through the path found + for (let v = sink; v !== source; v = parent[v]) { + const u = parent[v]; + pathFlow = Math.min(pathFlow, capacity[u][v] - flow[u][v]); + } + // Update the flow matrix + for (let v = sink; v !== source; v = parent[v]) { + const u = parent[v]; + flow[u][v] += pathFlow; + flow[v][u] -= pathFlow; + } + + maxFlow += pathFlow; + } + + return maxFlow; +} \ No newline at end of file diff --git a/graph/test/edmondkarp_test.ts b/graph/test/edmondkarp_test.ts new file mode 100644 index 00000000..08b5909e --- /dev/null +++ b/graph/test/edmondkarp_test.ts @@ -0,0 +1,84 @@ +import { edmondsKarp } from '../edmondsKarp' + +describe('edmondsKarp', () => { + const init_flow_network = (N: number): number[][] => { + const graph = Array.from({ length: N }, () => Array(N).fill(0)); + return graph; + } + + const add_capacity = ( + graph: number[][], + u: number, + v: number, + capacity: number + ) => { + graph[u][v] = capacity; + } + + it('should return the correct maximum flow value for basic graph', () => { + const graph = init_flow_network(6); + add_capacity(graph, 0, 1, 16); + add_capacity(graph, 0, 2, 13); + add_capacity(graph, 1, 2, 10); + add_capacity(graph, 1, 3, 12); + add_capacity(graph, 2, 1, 4); + add_capacity(graph, 2, 4, 14); + add_capacity(graph, 3, 2, 9); + add_capacity(graph, 3, 5, 20); + add_capacity(graph, 4, 3, 7); + add_capacity(graph, 4, 5, 4); + expect(edmondsKarp(graph, 0, 5)).toBe(23); + }); + + it('should return the correct maximum flow value for single element graph', () => { + const graph = init_flow_network(1); + expect(edmondsKarp(graph, 0, 0)).toBe(0); + }); + + const linear_flow_network = init_flow_network(4); + add_capacity(linear_flow_network, 0, 1, 10); + add_capacity(linear_flow_network, 1, 2, 5); + add_capacity(linear_flow_network, 2, 3, 15); + test.each([ + [0, 3, 5], + [0, 2, 5], + [1, 3, 5], + [1, 2, 5], + ])( + 'correct result for linear flow network with source node %i and sink node %i', + (source, sink, maxFlow) => { + expect(edmondsKarp(linear_flow_network, source, sink)).toBe(maxFlow); + } + ); + + const disconnected_flow_network = init_flow_network(4); + add_capacity(disconnected_flow_network, 0, 1, 10); + add_capacity(disconnected_flow_network, 2, 3, 5); + test.each([ + [0, 3, 0], + [1, 2, 0], + [2, 3, 5], + ])( + 'correct result for disconnected flow network with source node %i and sink node %i', + (source, sink, maxFlow) => { + expect(edmondsKarp(disconnected_flow_network, source, sink)).toBe(maxFlow); + } + ); + + const cyclic_flow_network = init_flow_network(5); + add_capacity(cyclic_flow_network, 0, 1, 10); + add_capacity(cyclic_flow_network, 1, 2, 5); + add_capacity(cyclic_flow_network, 2, 0, 7); + add_capacity(cyclic_flow_network, 2, 3, 10); + add_capacity(cyclic_flow_network, 3, 4, 10); + test.each([ + [0, 4, 10], + [1, 4, 10], + [2, 4, 10], + ])( + 'correct result for cyclic flow network with source node %i and sink node %i', + (source, sink, maxFlow) => { + expect(edmondsKarp(cyclic_flow_network, source, sink)).toBe(maxFlow); + } + ); +}); From b560c2e9d2348022a07a1fed825fb40e12b4cd1b Mon Sep 17 00:00:00 2001 From: Aadish Jain <121042282+mapcrafter2048@users.noreply.github.com> Date: Thu, 3 Oct 2024 23:27:12 +0530 Subject: [PATCH 03/11] Update graph/edmondkarp.ts MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Co-authored-by: Lars Müller <34514239+appgurueu@users.noreply.github.com> --- graph/edmondkarp.ts | 1 - 1 file changed, 1 deletion(-) diff --git a/graph/edmondkarp.ts b/graph/edmondkarp.ts index 0ff3ffb0..81f47b0e 100644 --- a/graph/edmondkarp.ts +++ b/graph/edmondkarp.ts @@ -1,5 +1,4 @@ /** - * @function edmondkarp * @description Compute the maximum flow from a source node to a sink node. The input graph is in adjacency list form. It is a multidimensional array of edges. graph[i] holds the edges for the i'th node. Each edge is a 3-tuple where the 0'th item is the destination node, the 1'th item is the edge weight, and the 2'nd item is the edge capacity. * @Complexity_Analysis * Time complexity: O(V*E^2) where V is the number of vertices and E is the number of edges From 13ba5a34ecb0c9bcd3ccdba9d2f14fcce1901945 Mon Sep 17 00:00:00 2001 From: Aadish Jain <121042282+mapcrafter2048@users.noreply.github.com> Date: Thu, 3 Oct 2024 23:39:03 +0530 Subject: [PATCH 04/11] Update edmondkarp.ts --- graph/edmondkarp.ts | 106 ++++++++++++++++++++++++++------------------ 1 file changed, 64 insertions(+), 42 deletions(-) diff --git a/graph/edmondkarp.ts b/graph/edmondkarp.ts index 81f47b0e..8aa4511d 100644 --- a/graph/edmondkarp.ts +++ b/graph/edmondkarp.ts @@ -1,75 +1,97 @@ /** - * @description Compute the maximum flow from a source node to a sink node. The input graph is in adjacency list form. It is a multidimensional array of edges. graph[i] holds the edges for the i'th node. Each edge is a 3-tuple where the 0'th item is the destination node, the 1'th item is the edge weight, and the 2'nd item is the edge capacity. + * @function edmondkarp + * @description Compute the maximum flow from a source node to a sink node. The input graph is in adjacency list form. It is a multidimensional array of edges. graph[i] holds the edges for the i'th node. Each edge is a 2-tuple where the 0'th item is the destination node, and the 1'st item is the edge capacity. * @Complexity_Analysis - * Time complexity: O(V*E^2) where V is the number of vertices and E is the number of edges - * Space Complexity: O(V) where V is the number of vertices - * @param {[number, number, number][][]} graph - The graph in adjacency list form + * Time complexity: O(V * E^2) where V is the number of vertices and E is the number of edges + * Space Complexity: O(V^2) where V is the number of vertices + * @param {[number, number][][]} graph - The graph in adjacency list form * @param {number} source - The source node * @param {number} sink - The sink node * @return {number} - The maximum flow from the source node to the sink node * @see https://en.wikipedia.org/wiki/Edmonds%E2%80%93Karp_algorithm */ -function edmondkarp(graph: [number, number, number][][], source: number, sink: number): number { - // Initialize capacity and flow matrices with zeros and build capacity matrix from graph +function edmondkarp(graph: [number, number][][], source: number, sink: number): number { const n = graph.length; - const capacity = Array.from({ length: n }, () => Array(n).fill(0)); - const flow = Array.from({ length: n }, () => Array(n).fill(0)); - // Build capacity matrix + // Residual graph in adjacency list form + const residualGraph: Map = new Map(); for (let u = 0; u < n; u++) { - for (const [v, , cap] of graph[u]) { - capacity[u][v] = cap; + residualGraph.set(u, []); + for (const [v, capacity] of graph[u]) { + residualGraph.get(u)?.push([v, capacity]); + if (!residualGraph.has(v)) { + residualGraph.set(v, []); + } } } - // Breadth-first search - const bfs = (parent: number[]): boolean => { + const parent = Array(n).fill(null); + let maxFlow = 0; + + // Level-order BFS using two level arrays + const bfs = (): boolean => { const visited = Array(n).fill(false); - const queue: number[] = []; - queue.push(source); + const currentLevel: number[] = []; + const nextLevel: number[] = []; + currentLevel.push(source); visited[source] = true; - // Find an augmenting path from source to sink by doing a BFS traversal - while (queue.length > 0) { - // Dequeue - const u = queue.shift()!; - // Enqueue all adjacent unvisited vertices with available capacity - for (let v = 0; v < n; v++) { - // If there is available capacity and the vertex has not been visited - if (!visited[v] && capacity[u][v] - flow[u][v] > 0) { - queue.push(v); - visited[v] = true; - parent[v] = u; - // If we reach the sink, we have found the augmenting path - if (v === sink) { - return true; + while (currentLevel.length > 0) { + nextLevel.length = 0; + + for (const u of currentLevel) { + for (const [v, capacity] of residualGraph.get(u)!) { + if (!visited[v] && capacity > 0) { + parent[v] = u; + visited[v] = true; + + // If we reach the sink, we have found an augmenting path + if (v === sink) { + return true; + } + + nextLevel.push(v); } } } + + currentLevel.length = 0; + currentLevel.push(...nextLevel); } + return false; }; - let maxFlow = 0; - const parent = Array(n).fill(-1); - - while (bfs(parent)) { + while (bfs()) { let pathFlow = Infinity; + // Find the maximum flow through the path found - for (let v = sink; v !== source; v = parent[v]) { - const u = parent[v]; - pathFlow = Math.min(pathFlow, capacity[u][v] - flow[u][v]); + for (let v = sink; v !== source; v = parent[v]!) { + const u = parent[v]!; + const edge = residualGraph.get(u)!.find(([dest]) => dest === v)!; + pathFlow = Math.min(pathFlow, edge[1]); } - // Update the flow matrix - for (let v = sink; v !== source; v = parent[v]) { - const u = parent[v]; - flow[u][v] += pathFlow; - flow[v][u] -= pathFlow; + + // Update the residual graph + for (let v = sink; v !== source; v = parent[v]!) { + const u = parent[v]!; + + // Update forward edge + const edgeIndex = residualGraph.get(u)!.findIndex(([dest]) => dest === v); + residualGraph.get(u)![edgeIndex][1] -= pathFlow; + + // Update backward edge + const reverseEdge = residualGraph.get(v)!.find(([dest]) => dest === u); + if (reverseEdge) { + reverseEdge[1] += pathFlow; + } else { + residualGraph.get(v)!.push([u, pathFlow]); + } } maxFlow += pathFlow; } return maxFlow; -} \ No newline at end of file +} From ab770c32f36ddb76cfbdaffc2f98630fdd0cb4e3 Mon Sep 17 00:00:00 2001 From: Aadish Jain <121042282+mapcrafter2048@users.noreply.github.com> Date: Thu, 3 Oct 2024 23:40:32 +0530 Subject: [PATCH 05/11] Update graph/edmondkarp.ts MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Co-authored-by: Lars Müller <34514239+appgurueu@users.noreply.github.com> --- graph/edmondkarp.ts | 1 - 1 file changed, 1 deletion(-) diff --git a/graph/edmondkarp.ts b/graph/edmondkarp.ts index 8aa4511d..ef51de73 100644 --- a/graph/edmondkarp.ts +++ b/graph/edmondkarp.ts @@ -1,5 +1,4 @@ /** - * @function edmondkarp * @description Compute the maximum flow from a source node to a sink node. The input graph is in adjacency list form. It is a multidimensional array of edges. graph[i] holds the edges for the i'th node. Each edge is a 2-tuple where the 0'th item is the destination node, and the 1'st item is the edge capacity. * @Complexity_Analysis * Time complexity: O(V * E^2) where V is the number of vertices and E is the number of edges From 6fed73dadb3b08704818d48a42ece1a25aa3c2f6 Mon Sep 17 00:00:00 2001 From: mapcrafter2048 Date: Mon, 7 Oct 2024 21:05:05 +0530 Subject: [PATCH 06/11] Implement the furhter changes to make the algorithm more refined --- graph/edmondkarp.ts | 76 -------------------------- graph/edmonds_karp.ts | 96 +++++++++++++++++++++++++++++++++ graph/test/edmondkarp_test.ts | 84 ----------------------------- graph/test/edmonds_karp.test.ts | 82 ++++++++++++++++++++++++++++ 4 files changed, 178 insertions(+), 160 deletions(-) delete mode 100644 graph/edmondkarp.ts create mode 100644 graph/edmonds_karp.ts delete mode 100644 graph/test/edmondkarp_test.ts create mode 100644 graph/test/edmonds_karp.test.ts diff --git a/graph/edmondkarp.ts b/graph/edmondkarp.ts deleted file mode 100644 index 0ff3ffb0..00000000 --- a/graph/edmondkarp.ts +++ /dev/null @@ -1,76 +0,0 @@ -/** - * @function edmondkarp - * @description Compute the maximum flow from a source node to a sink node. The input graph is in adjacency list form. It is a multidimensional array of edges. graph[i] holds the edges for the i'th node. Each edge is a 3-tuple where the 0'th item is the destination node, the 1'th item is the edge weight, and the 2'nd item is the edge capacity. - * @Complexity_Analysis - * Time complexity: O(V*E^2) where V is the number of vertices and E is the number of edges - * Space Complexity: O(V) where V is the number of vertices - * @param {[number, number, number][][]} graph - The graph in adjacency list form - * @param {number} source - The source node - * @param {number} sink - The sink node - * @return {number} - The maximum flow from the source node to the sink node - * @see https://en.wikipedia.org/wiki/Edmonds%E2%80%93Karp_algorithm - */ - -function edmondkarp(graph: [number, number, number][][], source: number, sink: number): number { - // Initialize capacity and flow matrices with zeros and build capacity matrix from graph - const n = graph.length; - const capacity = Array.from({ length: n }, () => Array(n).fill(0)); - const flow = Array.from({ length: n }, () => Array(n).fill(0)); - - // Build capacity matrix - for (let u = 0; u < n; u++) { - for (const [v, , cap] of graph[u]) { - capacity[u][v] = cap; - } - } - - // Breadth-first search - const bfs = (parent: number[]): boolean => { - const visited = Array(n).fill(false); - const queue: number[] = []; - queue.push(source); - visited[source] = true; - - // Find an augmenting path from source to sink by doing a BFS traversal - while (queue.length > 0) { - // Dequeue - const u = queue.shift()!; - // Enqueue all adjacent unvisited vertices with available capacity - for (let v = 0; v < n; v++) { - // If there is available capacity and the vertex has not been visited - if (!visited[v] && capacity[u][v] - flow[u][v] > 0) { - queue.push(v); - visited[v] = true; - parent[v] = u; - // If we reach the sink, we have found the augmenting path - if (v === sink) { - return true; - } - } - } - } - return false; - }; - - let maxFlow = 0; - const parent = Array(n).fill(-1); - - while (bfs(parent)) { - let pathFlow = Infinity; - // Find the maximum flow through the path found - for (let v = sink; v !== source; v = parent[v]) { - const u = parent[v]; - pathFlow = Math.min(pathFlow, capacity[u][v] - flow[u][v]); - } - // Update the flow matrix - for (let v = sink; v !== source; v = parent[v]) { - const u = parent[v]; - flow[u][v] += pathFlow; - flow[v][u] -= pathFlow; - } - - maxFlow += pathFlow; - } - - return maxFlow; -} \ No newline at end of file diff --git a/graph/edmonds_karp.ts b/graph/edmonds_karp.ts new file mode 100644 index 00000000..75fa163a --- /dev/null +++ b/graph/edmonds_karp.ts @@ -0,0 +1,96 @@ +/** + * @function edmondsKarp + * @description Compute the maximum flow from a source node to a sink node using the Edmonds-Karp algorithm. + * @Complexity_Analysis + * Time complexity: O(V * E^2) where V is the number of vertices and E is the number of edges. + * Space Complexity: O(E) due to residual graph representation. + * @param {[number, number][][]} graph - The graph in adjacency list form. + * @param {number} source - The source node. + * @param {number} sink - The sink node. + * @return {number} - The maximum flow from the source node to the sink node. + * @see https://en.wikipedia.org/wiki/Edmonds%E2%80%93Karp_algorithm + */ + +export default function edmondsKarp( + graph: [number, number][][], + source: number, + sink: number +): number { + const n = graph.length + + // Initialize residual graph + const residualGraph: [number, number][][] = Array.from( + { length: n }, + () => [] + ) + + // Build residual graph from the original graph + for (let u = 0; u < n; u++) { + for (const [v, cap] of graph[u]) { + if (cap > 0) { + residualGraph[u].push([v, cap]) // Forward edge + residualGraph[v].push([u, 0]) // Reverse edge with 0 capacity + } + } + } + + const findAugmentingPath = (parent: (number | null)[]): number => { + const visited = Array(n).fill(false) + const queue: number[] = [] + queue.push(source) + visited[source] = true + parent[source] = null + + while (queue.length > 0) { + const u = queue.shift()! + for (const [v, cap] of residualGraph[u]) { + if (!visited[v] && cap > 0) { + parent[v] = u + visited[v] = true + if (v === sink) { + // Return the bottleneck capacity along the path + let pathFlow = Infinity + let current = v + while (parent[current] !== null) { + const prev = parent[current]! + const edgeCap = residualGraph[prev].find( + ([node]) => node === current + )![1] + pathFlow = Math.min(pathFlow, edgeCap) + current = prev + } + return pathFlow + } + queue.push(v) + } + } + } + return 0 + } + + let maxFlow = 0 + const parent = Array(n).fill(null) + + while (true) { + const pathFlow = findAugmentingPath(parent) + if (pathFlow === 0) break // No augmenting path found + + // Update the capacities and reverse capacities in the residual graph + let v = sink + while (parent[v] !== null) { + const u = parent[v]! + // Update capacity of the forward edge + const forwardEdge = residualGraph[u].find(([node]) => node === v)! + forwardEdge[1] -= pathFlow + // Update capacity of the reverse edge + const reverseEdge = residualGraph[v].find(([node]) => node === u)! + reverseEdge[1] += pathFlow + + v = u + } + + maxFlow += pathFlow + } + + return maxFlow +} diff --git a/graph/test/edmondkarp_test.ts b/graph/test/edmondkarp_test.ts deleted file mode 100644 index 08b5909e..00000000 --- a/graph/test/edmondkarp_test.ts +++ /dev/null @@ -1,84 +0,0 @@ -import { edmondsKarp } from '../edmondsKarp' - -describe('edmondsKarp', () => { - const init_flow_network = (N: number): number[][] => { - const graph = Array.from({ length: N }, () => Array(N).fill(0)); - return graph; - } - - const add_capacity = ( - graph: number[][], - u: number, - v: number, - capacity: number - ) => { - graph[u][v] = capacity; - } - - it('should return the correct maximum flow value for basic graph', () => { - const graph = init_flow_network(6); - add_capacity(graph, 0, 1, 16); - add_capacity(graph, 0, 2, 13); - add_capacity(graph, 1, 2, 10); - add_capacity(graph, 1, 3, 12); - add_capacity(graph, 2, 1, 4); - add_capacity(graph, 2, 4, 14); - add_capacity(graph, 3, 2, 9); - add_capacity(graph, 3, 5, 20); - add_capacity(graph, 4, 3, 7); - add_capacity(graph, 4, 5, 4); - expect(edmondsKarp(graph, 0, 5)).toBe(23); - }); - - it('should return the correct maximum flow value for single element graph', () => { - const graph = init_flow_network(1); - expect(edmondsKarp(graph, 0, 0)).toBe(0); - }); - - const linear_flow_network = init_flow_network(4); - add_capacity(linear_flow_network, 0, 1, 10); - add_capacity(linear_flow_network, 1, 2, 5); - add_capacity(linear_flow_network, 2, 3, 15); - test.each([ - [0, 3, 5], - [0, 2, 5], - [1, 3, 5], - [1, 2, 5], - ])( - 'correct result for linear flow network with source node %i and sink node %i', - (source, sink, maxFlow) => { - expect(edmondsKarp(linear_flow_network, source, sink)).toBe(maxFlow); - } - ); - - const disconnected_flow_network = init_flow_network(4); - add_capacity(disconnected_flow_network, 0, 1, 10); - add_capacity(disconnected_flow_network, 2, 3, 5); - test.each([ - [0, 3, 0], - [1, 2, 0], - [2, 3, 5], - ])( - 'correct result for disconnected flow network with source node %i and sink node %i', - (source, sink, maxFlow) => { - expect(edmondsKarp(disconnected_flow_network, source, sink)).toBe(maxFlow); - } - ); - - const cyclic_flow_network = init_flow_network(5); - add_capacity(cyclic_flow_network, 0, 1, 10); - add_capacity(cyclic_flow_network, 1, 2, 5); - add_capacity(cyclic_flow_network, 2, 0, 7); - add_capacity(cyclic_flow_network, 2, 3, 10); - add_capacity(cyclic_flow_network, 3, 4, 10); - test.each([ - [0, 4, 10], - [1, 4, 10], - [2, 4, 10], - ])( - 'correct result for cyclic flow network with source node %i and sink node %i', - (source, sink, maxFlow) => { - expect(edmondsKarp(cyclic_flow_network, source, sink)).toBe(maxFlow); - } - ); -}); diff --git a/graph/test/edmonds_karp.test.ts b/graph/test/edmonds_karp.test.ts new file mode 100644 index 00000000..22711ab9 --- /dev/null +++ b/graph/test/edmonds_karp.test.ts @@ -0,0 +1,82 @@ +import edmondsKarp from '../edmonds_karp' + +describe('Edmonds-Karp Algorithm', () => { + it('should find the maximum flow in a simple graph', () => { + const graph: [number, number][][] = [ + [ + [1, 3], + [2, 2] + ], // Node 0: Edges to node 1 (capacity 3), and node 2 (capacity 2) + [[3, 2]], // Node 1: Edge to node 3 (capacity 2) + [[3, 3]], // Node 2: Edge to node 3 (capacity 3) + [] // Node 3: No outgoing edges + ] + const source = 0 + const sink = 3 + const maxFlow = edmondsKarp(graph, source, sink) + expect(maxFlow).toBe(4) + }) + + it('should find the maximum flow in a more complex graph', () => { + const graph: [number, number][][] = [ + [ + [1, 10], + [2, 10] + ], // Node 0: Edges to node 1 and node 2 (both capacity 10) + [ + [3, 4], + [4, 8] + ], // Node 1: Edges to node 3 (capacity 4), and node 4 (capacity 8) + [[4, 9]], // Node 2: Edge to node 4 (capacity 9) + [[5, 10]], // Node 3: Edge to node 5 (capacity 10) + [[5, 10]], // Node 4: Edge to node 5 (capacity 10) + [] // Node 5: No outgoing edges (sink) + ] + const source = 0 + const sink = 5 + const maxFlow = edmondsKarp(graph, source, sink) + expect(maxFlow).toBe(14) + }) + + it('should return 0 when there is no path from source to sink', () => { + const graph: [number, number][][] = [ + [], // Node 0: No outgoing edges + [], // Node 1: No outgoing edges + [] // Node 2: No outgoing edges (sink) + ] + const source = 0 + const sink = 2 + const maxFlow = edmondsKarp(graph, source, sink) + expect(maxFlow).toBe(0) + }) + + it('should handle graphs with no edges', () => { + const graph: [number, number][][] = [ + [], // Node 0: No outgoing edges + [], // Node 1: No outgoing edges + [] // Node 2: No outgoing edges + ] + const source = 0 + const sink = 2 + const maxFlow = edmondsKarp(graph, source, sink) + expect(maxFlow).toBe(0) + }) + + it('should handle graphs with self-loops', () => { + const graph: [number, number][][] = [ + [ + [0, 10], + [1, 10] + ], // Node 0: Self-loop with capacity 10, and edge to node 1 (capacity 10) + [ + [1, 10], + [2, 10] + ], // Node 1: Self-loop and edge to node 2 + [] // Node 2: No outgoing edges (sink) + ] + const source = 0 + const sink = 2 + const maxFlow = edmondsKarp(graph, source, sink) + expect(maxFlow).toBe(10) + }) +}) From b5daf9f1b7543e73617e7aeb8dbdc90d309a5b85 Mon Sep 17 00:00:00 2001 From: Aadish Jain <121042282+mapcrafter2048@users.noreply.github.com> Date: Mon, 7 Oct 2024 23:14:21 +0530 Subject: [PATCH 07/11] Updated the test cases Updated the test cases --- graph/test/edmondkarp_test.ts | 84 --------------------------------- graph/test/edmonds_karp.test.ts | 82 ++++++++++++++++++++++++++++++++ 2 files changed, 82 insertions(+), 84 deletions(-) delete mode 100644 graph/test/edmondkarp_test.ts create mode 100644 graph/test/edmonds_karp.test.ts diff --git a/graph/test/edmondkarp_test.ts b/graph/test/edmondkarp_test.ts deleted file mode 100644 index 08b5909e..00000000 --- a/graph/test/edmondkarp_test.ts +++ /dev/null @@ -1,84 +0,0 @@ -import { edmondsKarp } from '../edmondsKarp' - -describe('edmondsKarp', () => { - const init_flow_network = (N: number): number[][] => { - const graph = Array.from({ length: N }, () => Array(N).fill(0)); - return graph; - } - - const add_capacity = ( - graph: number[][], - u: number, - v: number, - capacity: number - ) => { - graph[u][v] = capacity; - } - - it('should return the correct maximum flow value for basic graph', () => { - const graph = init_flow_network(6); - add_capacity(graph, 0, 1, 16); - add_capacity(graph, 0, 2, 13); - add_capacity(graph, 1, 2, 10); - add_capacity(graph, 1, 3, 12); - add_capacity(graph, 2, 1, 4); - add_capacity(graph, 2, 4, 14); - add_capacity(graph, 3, 2, 9); - add_capacity(graph, 3, 5, 20); - add_capacity(graph, 4, 3, 7); - add_capacity(graph, 4, 5, 4); - expect(edmondsKarp(graph, 0, 5)).toBe(23); - }); - - it('should return the correct maximum flow value for single element graph', () => { - const graph = init_flow_network(1); - expect(edmondsKarp(graph, 0, 0)).toBe(0); - }); - - const linear_flow_network = init_flow_network(4); - add_capacity(linear_flow_network, 0, 1, 10); - add_capacity(linear_flow_network, 1, 2, 5); - add_capacity(linear_flow_network, 2, 3, 15); - test.each([ - [0, 3, 5], - [0, 2, 5], - [1, 3, 5], - [1, 2, 5], - ])( - 'correct result for linear flow network with source node %i and sink node %i', - (source, sink, maxFlow) => { - expect(edmondsKarp(linear_flow_network, source, sink)).toBe(maxFlow); - } - ); - - const disconnected_flow_network = init_flow_network(4); - add_capacity(disconnected_flow_network, 0, 1, 10); - add_capacity(disconnected_flow_network, 2, 3, 5); - test.each([ - [0, 3, 0], - [1, 2, 0], - [2, 3, 5], - ])( - 'correct result for disconnected flow network with source node %i and sink node %i', - (source, sink, maxFlow) => { - expect(edmondsKarp(disconnected_flow_network, source, sink)).toBe(maxFlow); - } - ); - - const cyclic_flow_network = init_flow_network(5); - add_capacity(cyclic_flow_network, 0, 1, 10); - add_capacity(cyclic_flow_network, 1, 2, 5); - add_capacity(cyclic_flow_network, 2, 0, 7); - add_capacity(cyclic_flow_network, 2, 3, 10); - add_capacity(cyclic_flow_network, 3, 4, 10); - test.each([ - [0, 4, 10], - [1, 4, 10], - [2, 4, 10], - ])( - 'correct result for cyclic flow network with source node %i and sink node %i', - (source, sink, maxFlow) => { - expect(edmondsKarp(cyclic_flow_network, source, sink)).toBe(maxFlow); - } - ); -}); diff --git a/graph/test/edmonds_karp.test.ts b/graph/test/edmonds_karp.test.ts new file mode 100644 index 00000000..22711ab9 --- /dev/null +++ b/graph/test/edmonds_karp.test.ts @@ -0,0 +1,82 @@ +import edmondsKarp from '../edmonds_karp' + +describe('Edmonds-Karp Algorithm', () => { + it('should find the maximum flow in a simple graph', () => { + const graph: [number, number][][] = [ + [ + [1, 3], + [2, 2] + ], // Node 0: Edges to node 1 (capacity 3), and node 2 (capacity 2) + [[3, 2]], // Node 1: Edge to node 3 (capacity 2) + [[3, 3]], // Node 2: Edge to node 3 (capacity 3) + [] // Node 3: No outgoing edges + ] + const source = 0 + const sink = 3 + const maxFlow = edmondsKarp(graph, source, sink) + expect(maxFlow).toBe(4) + }) + + it('should find the maximum flow in a more complex graph', () => { + const graph: [number, number][][] = [ + [ + [1, 10], + [2, 10] + ], // Node 0: Edges to node 1 and node 2 (both capacity 10) + [ + [3, 4], + [4, 8] + ], // Node 1: Edges to node 3 (capacity 4), and node 4 (capacity 8) + [[4, 9]], // Node 2: Edge to node 4 (capacity 9) + [[5, 10]], // Node 3: Edge to node 5 (capacity 10) + [[5, 10]], // Node 4: Edge to node 5 (capacity 10) + [] // Node 5: No outgoing edges (sink) + ] + const source = 0 + const sink = 5 + const maxFlow = edmondsKarp(graph, source, sink) + expect(maxFlow).toBe(14) + }) + + it('should return 0 when there is no path from source to sink', () => { + const graph: [number, number][][] = [ + [], // Node 0: No outgoing edges + [], // Node 1: No outgoing edges + [] // Node 2: No outgoing edges (sink) + ] + const source = 0 + const sink = 2 + const maxFlow = edmondsKarp(graph, source, sink) + expect(maxFlow).toBe(0) + }) + + it('should handle graphs with no edges', () => { + const graph: [number, number][][] = [ + [], // Node 0: No outgoing edges + [], // Node 1: No outgoing edges + [] // Node 2: No outgoing edges + ] + const source = 0 + const sink = 2 + const maxFlow = edmondsKarp(graph, source, sink) + expect(maxFlow).toBe(0) + }) + + it('should handle graphs with self-loops', () => { + const graph: [number, number][][] = [ + [ + [0, 10], + [1, 10] + ], // Node 0: Self-loop with capacity 10, and edge to node 1 (capacity 10) + [ + [1, 10], + [2, 10] + ], // Node 1: Self-loop and edge to node 2 + [] // Node 2: No outgoing edges (sink) + ] + const source = 0 + const sink = 2 + const maxFlow = edmondsKarp(graph, source, sink) + expect(maxFlow).toBe(10) + }) +}) From 4b5f2b54f1049c1127ce28d01840a3f483b0a710 Mon Sep 17 00:00:00 2001 From: Aadish Jain <121042282+mapcrafter2048@users.noreply.github.com> Date: Mon, 7 Oct 2024 23:15:30 +0530 Subject: [PATCH 08/11] Updated the code and rewrite some functions Updated the code and rewrite some functions --- graph/edmondkarp.ts | 96 ------------------------------------------- graph/edmonds_karp.ts | 96 +++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 96 insertions(+), 96 deletions(-) delete mode 100644 graph/edmondkarp.ts create mode 100644 graph/edmonds_karp.ts diff --git a/graph/edmondkarp.ts b/graph/edmondkarp.ts deleted file mode 100644 index ef51de73..00000000 --- a/graph/edmondkarp.ts +++ /dev/null @@ -1,96 +0,0 @@ -/** - * @description Compute the maximum flow from a source node to a sink node. The input graph is in adjacency list form. It is a multidimensional array of edges. graph[i] holds the edges for the i'th node. Each edge is a 2-tuple where the 0'th item is the destination node, and the 1'st item is the edge capacity. - * @Complexity_Analysis - * Time complexity: O(V * E^2) where V is the number of vertices and E is the number of edges - * Space Complexity: O(V^2) where V is the number of vertices - * @param {[number, number][][]} graph - The graph in adjacency list form - * @param {number} source - The source node - * @param {number} sink - The sink node - * @return {number} - The maximum flow from the source node to the sink node - * @see https://en.wikipedia.org/wiki/Edmonds%E2%80%93Karp_algorithm - */ - -function edmondkarp(graph: [number, number][][], source: number, sink: number): number { - const n = graph.length; - - // Residual graph in adjacency list form - const residualGraph: Map = new Map(); - for (let u = 0; u < n; u++) { - residualGraph.set(u, []); - for (const [v, capacity] of graph[u]) { - residualGraph.get(u)?.push([v, capacity]); - if (!residualGraph.has(v)) { - residualGraph.set(v, []); - } - } - } - - const parent = Array(n).fill(null); - let maxFlow = 0; - - // Level-order BFS using two level arrays - const bfs = (): boolean => { - const visited = Array(n).fill(false); - const currentLevel: number[] = []; - const nextLevel: number[] = []; - currentLevel.push(source); - visited[source] = true; - - while (currentLevel.length > 0) { - nextLevel.length = 0; - - for (const u of currentLevel) { - for (const [v, capacity] of residualGraph.get(u)!) { - if (!visited[v] && capacity > 0) { - parent[v] = u; - visited[v] = true; - - // If we reach the sink, we have found an augmenting path - if (v === sink) { - return true; - } - - nextLevel.push(v); - } - } - } - - currentLevel.length = 0; - currentLevel.push(...nextLevel); - } - - return false; - }; - - while (bfs()) { - let pathFlow = Infinity; - - // Find the maximum flow through the path found - for (let v = sink; v !== source; v = parent[v]!) { - const u = parent[v]!; - const edge = residualGraph.get(u)!.find(([dest]) => dest === v)!; - pathFlow = Math.min(pathFlow, edge[1]); - } - - // Update the residual graph - for (let v = sink; v !== source; v = parent[v]!) { - const u = parent[v]!; - - // Update forward edge - const edgeIndex = residualGraph.get(u)!.findIndex(([dest]) => dest === v); - residualGraph.get(u)![edgeIndex][1] -= pathFlow; - - // Update backward edge - const reverseEdge = residualGraph.get(v)!.find(([dest]) => dest === u); - if (reverseEdge) { - reverseEdge[1] += pathFlow; - } else { - residualGraph.get(v)!.push([u, pathFlow]); - } - } - - maxFlow += pathFlow; - } - - return maxFlow; -} diff --git a/graph/edmonds_karp.ts b/graph/edmonds_karp.ts new file mode 100644 index 00000000..75fa163a --- /dev/null +++ b/graph/edmonds_karp.ts @@ -0,0 +1,96 @@ +/** + * @function edmondsKarp + * @description Compute the maximum flow from a source node to a sink node using the Edmonds-Karp algorithm. + * @Complexity_Analysis + * Time complexity: O(V * E^2) where V is the number of vertices and E is the number of edges. + * Space Complexity: O(E) due to residual graph representation. + * @param {[number, number][][]} graph - The graph in adjacency list form. + * @param {number} source - The source node. + * @param {number} sink - The sink node. + * @return {number} - The maximum flow from the source node to the sink node. + * @see https://en.wikipedia.org/wiki/Edmonds%E2%80%93Karp_algorithm + */ + +export default function edmondsKarp( + graph: [number, number][][], + source: number, + sink: number +): number { + const n = graph.length + + // Initialize residual graph + const residualGraph: [number, number][][] = Array.from( + { length: n }, + () => [] + ) + + // Build residual graph from the original graph + for (let u = 0; u < n; u++) { + for (const [v, cap] of graph[u]) { + if (cap > 0) { + residualGraph[u].push([v, cap]) // Forward edge + residualGraph[v].push([u, 0]) // Reverse edge with 0 capacity + } + } + } + + const findAugmentingPath = (parent: (number | null)[]): number => { + const visited = Array(n).fill(false) + const queue: number[] = [] + queue.push(source) + visited[source] = true + parent[source] = null + + while (queue.length > 0) { + const u = queue.shift()! + for (const [v, cap] of residualGraph[u]) { + if (!visited[v] && cap > 0) { + parent[v] = u + visited[v] = true + if (v === sink) { + // Return the bottleneck capacity along the path + let pathFlow = Infinity + let current = v + while (parent[current] !== null) { + const prev = parent[current]! + const edgeCap = residualGraph[prev].find( + ([node]) => node === current + )![1] + pathFlow = Math.min(pathFlow, edgeCap) + current = prev + } + return pathFlow + } + queue.push(v) + } + } + } + return 0 + } + + let maxFlow = 0 + const parent = Array(n).fill(null) + + while (true) { + const pathFlow = findAugmentingPath(parent) + if (pathFlow === 0) break // No augmenting path found + + // Update the capacities and reverse capacities in the residual graph + let v = sink + while (parent[v] !== null) { + const u = parent[v]! + // Update capacity of the forward edge + const forwardEdge = residualGraph[u].find(([node]) => node === v)! + forwardEdge[1] -= pathFlow + // Update capacity of the reverse edge + const reverseEdge = residualGraph[v].find(([node]) => node === u)! + reverseEdge[1] += pathFlow + + v = u + } + + maxFlow += pathFlow + } + + return maxFlow +} From 76dd41225dfaf34334bbbfb4c3c686be7dd18164 Mon Sep 17 00:00:00 2001 From: mapcrafter2048 Date: Fri, 11 Oct 2024 22:37:51 +0530 Subject: [PATCH 09/11] Implement the optimal stack queue implementation in the edmond karp algorithm --- graph/edmonds_karp.ts | 75 +- package-lock.json | 3233 ++++++++++++++++++++++------------------- package.json | 6 +- 3 files changed, 1813 insertions(+), 1501 deletions(-) diff --git a/graph/edmonds_karp.ts b/graph/edmonds_karp.ts index 75fa163a..c8e9a54f 100644 --- a/graph/edmonds_karp.ts +++ b/graph/edmonds_karp.ts @@ -1,3 +1,5 @@ +import { StackQueue } from "../data_structures/queue/stack_queue"; + /** * @function edmondsKarp * @description Compute the maximum flow from a source node to a sink node using the Edmonds-Karp algorithm. @@ -10,87 +12,86 @@ * @return {number} - The maximum flow from the source node to the sink node. * @see https://en.wikipedia.org/wiki/Edmonds%E2%80%93Karp_algorithm */ - export default function edmondsKarp( graph: [number, number][][], source: number, sink: number ): number { - const n = graph.length + const n = graph.length; // Initialize residual graph const residualGraph: [number, number][][] = Array.from( { length: n }, () => [] - ) + ); // Build residual graph from the original graph for (let u = 0; u < n; u++) { for (const [v, cap] of graph[u]) { if (cap > 0) { - residualGraph[u].push([v, cap]) // Forward edge - residualGraph[v].push([u, 0]) // Reverse edge with 0 capacity + residualGraph[u].push([v, cap]); // Forward edge + residualGraph[v].push([u, 0]); // Reverse edge with 0 capacity } } } const findAugmentingPath = (parent: (number | null)[]): number => { - const visited = Array(n).fill(false) - const queue: number[] = [] - queue.push(source) - visited[source] = true - parent[source] = null + const visited = Array(n).fill(false); + const queue = new StackQueue(); + queue.enqueue(source); + visited[source] = true; + parent[source] = null; - while (queue.length > 0) { - const u = queue.shift()! + while (queue.length() > 0) { + const u = queue.dequeue(); for (const [v, cap] of residualGraph[u]) { if (!visited[v] && cap > 0) { - parent[v] = u - visited[v] = true + parent[v] = u; + visited[v] = true; if (v === sink) { // Return the bottleneck capacity along the path - let pathFlow = Infinity - let current = v + let pathFlow = Infinity; + let current = v; while (parent[current] !== null) { - const prev = parent[current]! + const prev = parent[current]!; const edgeCap = residualGraph[prev].find( ([node]) => node === current - )![1] - pathFlow = Math.min(pathFlow, edgeCap) - current = prev + )![1]; + pathFlow = Math.min(pathFlow, edgeCap); + current = prev; } - return pathFlow + return pathFlow; } - queue.push(v) + queue.enqueue(v); } } } - return 0 - } + return 0; + }; - let maxFlow = 0 - const parent = Array(n).fill(null) + let maxFlow = 0; + const parent = Array(n).fill(null); while (true) { - const pathFlow = findAugmentingPath(parent) - if (pathFlow === 0) break // No augmenting path found + const pathFlow = findAugmentingPath(parent); + if (pathFlow === 0) break; // No augmenting path found // Update the capacities and reverse capacities in the residual graph - let v = sink + let v = sink; while (parent[v] !== null) { - const u = parent[v]! + const u = parent[v]!; // Update capacity of the forward edge - const forwardEdge = residualGraph[u].find(([node]) => node === v)! - forwardEdge[1] -= pathFlow + const forwardEdge = residualGraph[u].find(([node]) => node === v)!; + forwardEdge[1] -= pathFlow; // Update capacity of the reverse edge - const reverseEdge = residualGraph[v].find(([node]) => node === u)! - reverseEdge[1] += pathFlow + const reverseEdge = residualGraph[v].find(([node]) => node === u)!; + reverseEdge[1] += pathFlow; - v = u + v = u; } - maxFlow += pathFlow + maxFlow += pathFlow; } - return maxFlow + return maxFlow; } diff --git a/package-lock.json b/package-lock.json index ad263744..78de154d 100644 --- a/package-lock.json +++ b/package-lock.json @@ -9,11 +9,11 @@ "version": "1.0.0", "license": "MIT", "devDependencies": { - 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"jest": "^29.0.3", + "jest": "^29.7.0", "prettier": "^3.2.5", - "ts-jest": "^29.0.2", + "ts-jest": "^29.2.5", "ts-node": "^10.9.1" }, "scripts": { From f97e200e5911f175d0c81c39a78d3d3e5edc0b92 Mon Sep 17 00:00:00 2001 From: mapcrafter2048 Date: Fri, 11 Oct 2024 22:46:25 +0530 Subject: [PATCH 10/11] removed the bisection_method.ts, decimal_convert.ts, euler_method.ts --- maths/bisection_method.ts | 27 --------------------------- maths/decimal_convert.ts | 20 -------------------- maths/euler_method.ts | 25 ------------------------- 3 files changed, 72 deletions(-) delete mode 100644 maths/bisection_method.ts delete mode 100644 maths/decimal_convert.ts delete mode 100644 maths/euler_method.ts diff --git a/maths/bisection_method.ts b/maths/bisection_method.ts deleted file mode 100644 index ec3e7235..00000000 --- a/maths/bisection_method.ts +++ /dev/null @@ -1,27 +0,0 @@ -/** - * @function bisectionMethod - * @description Bisection method is a root-finding method that applies to any continuous function for which one knows two values with opposite signs. - * @param {number} a - The first value - * @param {number} b - The second value - * @param {number} e - The error value - * @param {Function} f - The function - * @return {number} - The root of the function - * @see [BisectionMethod](https://en.wikipedia.org/wiki/Bisection_method) - * @example bisectionMethod(1, 2, 0.01, (x) => x**2 - 2) = 1.4140625 - * @example bisectionMethod(1, 2, 0.01, (x) => x**2 - 3) = 1.732421875 - */ - -export const bisectionMethod = (a: number, b: number, e: number, f: Function): number => { - let c = a - while ((b - a) >= e) { - c = (a + b) / 2 - if (f(c) === 0.0) { - break - } else if (f(c) * f(a) < 0) { - b = c - } else { - a = c - } - } - return c -} \ No newline at end of file diff --git a/maths/decimal_convert.ts b/maths/decimal_convert.ts deleted file mode 100644 index 2413378e..00000000 --- a/maths/decimal_convert.ts +++ /dev/null @@ -1,20 +0,0 @@ -/** - * @function decimalConvert - * @description Convert the binary to decimal. - * @param {string} binary - The input binary - * @return {number} - Decimal of binary. - * @see [DecimalConvert](https://www.programiz.com/javascript/examples/binary-decimal) - * @example decimalConvert(1100) = 12 - * @example decimalConvert(1110) = 14 - */ - -export const decimalConvert = (binary: string): number => { - let decimal = 0 - let binaryArr = binary.split('').reverse() - - for (let i = 0; i < binaryArr.length; i++) { - decimal += parseInt(binaryArr[i]) * Math.pow(2, i) - } - - return decimal -} diff --git a/maths/euler_method.ts b/maths/euler_method.ts deleted file mode 100644 index bc4c4b7c..00000000 --- a/maths/euler_method.ts +++ /dev/null @@ -1,25 +0,0 @@ -/** - * @function eulerMethod - * @description Euler's method is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. - * @param {number} x0 - The initial value of x - * @param {number} y0 - The initial value of y - * @param {number} h - The step size - * @param {number} n - The number of iterations - * @param {Function} f - The function - * @return {number} - The value of y at x - * @see [EulerMethod](https://en.wikipedia.org/wiki/Euler_method) - * @example eulerMethod(0, 1, 0.1, 10, (x, y) => x + y) = 2.5937424601 - * @example eulerMethod(0, 1, 0.1, 10, (x, y) => x * y) = 1.7715614317 - */ - -export const eulerMethod = (x0: number, y0: number, h: number, n: number, f: Function): number => { - let x = x0 - let y = y0 - - for (let i = 1; i <= n; i++) { - y = y + h * f(x, y) - x = x + h - } - - return y -} \ No newline at end of file From 97adbc898544b528c1bfc70196a84c60a8f6e739 Mon Sep 17 00:00:00 2001 From: mapcrafter2048 Date: Fri, 11 Oct 2024 23:00:46 +0530 Subject: [PATCH 11/11] Revert changes to package.json and package-lock.json --- package-lock.json | 3233 ++++++++++++++++++++------------------------- package.json | 6 +- 2 files changed, 1464 insertions(+), 1775 deletions(-) diff --git a/package-lock.json b/package-lock.json index 78de154d..ad263744 100644 --- a/package-lock.json +++ b/package-lock.json @@ -9,11 +9,11 @@ "version": "1.0.0", "license": "MIT", "devDependencies": { - 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