Add Dynamic Programming Algorithms (#776)

* Add dynamic programming problem implementations and their tests

* Fix bugs and improve test cases for dynamic programming algorithms

* Fix linters

* Modify Dice Throw Test Function Name

dynamic/burstballoons.go

@@ -0,0 +1,31 @@
+package dynamic
+
+import "github.com/TheAlgorithms/Go/math/max"
+
+// MaxCoins returns the maximum coins we can collect by bursting the balloons
+func MaxCoins(nums []int) int {
+	n := len(nums)
+	if n == 0 {
+		return 0
+	}
+
+	nums = append([]int{1}, nums...)
+	nums = append(nums, 1)
+
+	dp := make([][]int, n+2)
+	for i := range dp {
+		dp[i] = make([]int, n+2)
+	}
+
+	for length := 1; length <= n; length++ {
+		for left := 1; left+length-1 <= n; left++ {
+			right := left + length - 1
+			for k := left; k <= right; k++ {
+				coins := nums[left-1] * nums[k] * nums[right+1]
+				dp[left][right] = max.Int(dp[left][right], dp[left][k-1]+dp[k+1][right]+coins)
+			}
+		}
+	}
+
+	return dp[1][n]
+}

dynamic/burstballoons_test.go

@@ -0,0 +1,33 @@
+package dynamic_test
+
+import (
+	"testing"
+
+	"github.com/TheAlgorithms/Go/dynamic"
+)
+
+type testCaseBurstBalloons struct {
+	nums     []int
+	expected int
+}
+
+func getBurstBalloonsTestCases() []testCaseBurstBalloons {
+	return []testCaseBurstBalloons{
+		{[]int{3, 1, 5, 8}, 167}, // Maximum coins from [3,1,5,8]
+		{[]int{1, 5}, 10},        // Maximum coins from [1,5]
+		{[]int{1}, 1},            // Single balloon
+		{[]int{}, 0},             // No balloons
+	}
+
+}
+
+func TestMaxCoins(t *testing.T) {
+	t.Run("Burst Balloons test cases", func(t *testing.T) {
+		for _, tc := range getBurstBalloonsTestCases() {
+			actual := dynamic.MaxCoins(tc.nums)
+			if actual != tc.expected {
+				t.Errorf("MaxCoins(%v) = %d; expected %d", tc.nums, actual, tc.expected)
+			}
+		}
+	})
+}

dynamic/dicethrow.go

@@ -0,0 +1,33 @@
+// dicethrow.go
+// description: Solves the Dice Throw Problem using dynamic programming
+// reference: https://www.geeksforgeeks.org/dice-throw-problem/
+// time complexity: O(m * n)
+// space complexity: O(m * n)
+
+package dynamic
+
+// DiceThrow returns the number of ways to get sum `sum` using `m` dice with `n` faces
+func DiceThrow(m, n, sum int) int {
+	dp := make([][]int, m+1)
+	for i := range dp {
+		dp[i] = make([]int, sum+1)
+	}
+
+	for i := 1; i <= n; i++ {
+		if i <= sum {
+			dp[1][i] = 1
+		}
+	}
+
+	for i := 2; i <= m; i++ {
+		for j := 1; j <= sum; j++ {
+			for k := 1; k <= n; k++ {
+				if j-k >= 0 {
+					dp[i][j] += dp[i-1][j-k]
+				}
+			}
+		}
+	}
+
+	return dp[m][sum]
+}

dynamic/dicethrow_test.go

@@ -0,0 +1,42 @@
+package dynamic_test
+
+import (
+	"testing"
+
+	"github.com/TheAlgorithms/Go/dynamic"
+)
+
+type testCaseDiceThrow struct {
+	numDice   int
+	numFaces  int
+	targetSum int
+	expected  int
+}
+
+// getDiceThrowTestCases provides the test cases for DiceThrow
+func getDiceThrowTestCases() []testCaseDiceThrow {
+	return []testCaseDiceThrow{
+		{2, 6, 7, 6},  // Two dice, six faces each, sum = 7
+		{1, 6, 3, 1},  // One die, six faces, sum = 3
+		{3, 4, 5, 6},  // Three dice, four faces each, sum = 5
+		{1, 6, 1, 1},  // One die, six faces, sum = 1
+		{2, 6, 12, 1}, // Two dice, six faces each, sum = 12
+		{3, 6, 18, 1}, // Three dice, six faces each, sum = 18
+		{2, 6, 20, 0}, // Two dice, six faces each, sum = 20 (impossible)
+		{1, 1, 1, 1},  // One die, one face, sum = 1
+		{1, 1, 2, 0},  // One die, one face, sum = 2 (impossible)
+		{2, 1, 2, 1},  // Two dice, one face each, sum = 2
+	}
+}
+
+// TestDiceThrow tests the DiceThrow function with basic test cases
+func TestDiceThrow(t *testing.T) {
+	t.Run("Basic test cases", func(t *testing.T) {
+		for _, tc := range getDiceThrowTestCases() {
+			actual := dynamic.DiceThrow(tc.numDice, tc.numFaces, tc.targetSum)
+			if actual != tc.expected {
+				t.Errorf("DiceThrow(%d, %d, %d) = %d; expected %d", tc.numDice, tc.numFaces, tc.targetSum, actual, tc.expected)
+			}
+		}
+	})
+}

dynamic/eggdropping.go

@@ -0,0 +1,47 @@
+package dynamic
+
+import (
+	"github.com/TheAlgorithms/Go/math/max"
+	"github.com/TheAlgorithms/Go/math/min"
+)
+
+// EggDropping finds the minimum number of attempts needed to find the critical floor
+// with `eggs` number of eggs and `floors` number of floors
+func EggDropping(eggs, floors int) int {
+	// Edge case: If there are no floors, no attempts needed
+	if floors == 0 {
+		return 0
+	}
+	// Edge case: If there is one floor, one attempt needed
+	if floors == 1 {
+		return 1
+	}
+	// Edge case: If there is one egg, need to test all floors one by one
+	if eggs == 1 {
+		return floors
+	}
+
+	// Initialize DP table
+	dp := make([][]int, eggs+1)
+	for i := range dp {
+		dp[i] = make([]int, floors+1)
+	}
+
+	// Fill the DP table for 1 egg
+	for j := 1; j <= floors; j++ {
+		dp[1][j] = j
+	}
+
+	// Fill the DP table for more than 1 egg
+	for i := 2; i <= eggs; i++ {
+		for j := 2; j <= floors; j++ {
+			dp[i][j] = int(^uint(0) >> 1) // initialize with a large number
+			for x := 1; x <= j; x++ {
+				// Recurrence relation to fill the DP table
+				res := max.Int(dp[i-1][x-1], dp[i][j-x]) + 1
+				dp[i][j] = min.Int(dp[i][j], res)
+			}
+		}
+	}
+	return dp[eggs][floors]
+}

dynamic/eggdropping_test.go

@@ -0,0 +1,35 @@
+package dynamic_test
+
+import (
+	"testing"
+
+	"github.com/TheAlgorithms/Go/dynamic"
+)
+
+type testCaseEggDropping struct {
+	eggs     int
+	floors   int
+	expected int
+}
+
+func getEggDroppingTestCases() []testCaseEggDropping {
+	return []testCaseEggDropping{
+		{1, 10, 10}, // One egg, need to test all floors
+		{2, 10, 4},  // Two eggs and ten floors
+		{3, 14, 4},  // Three eggs and fourteen floors
+		{2, 36, 8},  // Two eggs and thirty-six floors
+		{2, 0, 0},   // Two eggs, zero floors
+	}
+
+}
+
+func TestEggDropping(t *testing.T) {
+	t.Run("Egg Dropping test cases", func(t *testing.T) {
+		for _, tc := range getEggDroppingTestCases() {
+			actual := dynamic.EggDropping(tc.eggs, tc.floors)
+			if actual != tc.expected {
+				t.Errorf("EggDropping(%d, %d) = %d; expected %d", tc.eggs, tc.floors, actual, tc.expected)
+			}
+		}
+	})
+}

dynamic/interleavingstrings.go

@@ -0,0 +1,36 @@
+// interleavingstrings.go
+// description: Solves the Interleaving Strings problem using dynamic programming
+// reference: https://en.wikipedia.org/wiki/Interleaving_strings
+// time complexity: O(m*n)
+// space complexity: O(m*n)
+
+package dynamic
+
+// IsInterleave checks if string `s1` and `s2` can be interleaved to form string `s3`
+func IsInterleave(s1, s2, s3 string) bool {
+	if len(s1)+len(s2) != len(s3) {
+		return false
+	}
+
+	dp := make([][]bool, len(s1)+1)
+	for i := range dp {
+		dp[i] = make([]bool, len(s2)+1)
+	}
+
+	dp[0][0] = true
+	for i := 1; i <= len(s1); i++ {
+		dp[i][0] = dp[i-1][0] && s1[i-1] == s3[i-1]
+	}
+
+	for j := 1; j <= len(s2); j++ {
+		dp[0][j] = dp[0][j-1] && s2[j-1] == s3[j-1]
+	}
+
+	for i := 1; i <= len(s1); i++ {
+		for j := 1; j <= len(s2); j++ {
+			dp[i][j] = (dp[i-1][j] && s1[i-1] == s3[i+j-1]) || (dp[i][j-1] && s2[j-1] == s3[i+j-1])
+		}
+	}
+
+	return dp[len(s1)][len(s2)]
+}

dynamic/interleavingstrings_test.go

@@ -0,0 +1,38 @@
+package dynamic_test
+
+import (
+	"testing"
+
+	"github.com/TheAlgorithms/Go/dynamic"
+)
+
+type testCaseInterleaving struct {
+	s1, s2, s3 string
+	expected   bool
+}
+
+func getInterleavingTestCases() []testCaseInterleaving {
+	return []testCaseInterleaving{
+		{"aab", "axy", "aaxaby", true},   // Valid interleaving
+		{"aab", "axy", "abaaxy", false},  // Invalid interleaving
+		{"", "", "", true},               // All empty strings
+		{"abc", "", "abc", true},         // Only s1 matches s3
+		{"", "xyz", "xyz", true},         // Only s2 matches s3
+		{"abc", "xyz", "abxcyz", true},   // Valid interleaving
+		{"aaa", "aaa", "aaaaaa", true},   // Identical strings
+		{"aaa", "aaa", "aaaaaaa", false}, // Extra character
+		{"abc", "def", "abcdef", true},   // Concatenation order
+		{"abc", "def", "adbcef", true},   // Valid mixed interleaving
+	}
+}
+
+func TestIsInterleave(t *testing.T) {
+	t.Run("Interleaving Strings test cases", func(t *testing.T) {
+		for _, tc := range getInterleavingTestCases() {
+			actual := dynamic.IsInterleave(tc.s1, tc.s2, tc.s3)
+			if actual != tc.expected {
+				t.Errorf("IsInterleave(%q, %q, %q) = %v; expected %v", tc.s1, tc.s2, tc.s3, actual, tc.expected)
+			}
+		}
+	})
+}

dynamic/longestarithmeticsubsequence.go

@@ -0,0 +1,34 @@
+// longestarithmeticsubsequence.go
+// description: Implementation of the Longest Arithmetic Subsequence problem
+// reference: https://en.wikipedia.org/wiki/Longest_arithmetic_progression
+// time complexity: O(n^2)
+// space complexity: O(n^2)
+
+package dynamic
+
+// LongestArithmeticSubsequence returns the length of the longest arithmetic subsequence
+func LongestArithmeticSubsequence(nums []int) int {
+	n := len(nums)
+	if n <= 1 {
+		return n
+	}
+
+	dp := make([]map[int]int, n)
+	for i := range dp {
+		dp[i] = make(map[int]int)
+	}
+
+	maxLength := 1
+
+	for i := 1; i < n; i++ {
+		for j := 0; j < i; j++ {
+			diff := nums[i] - nums[j]
+			dp[i][diff] = dp[j][diff] + 1
+			if dp[i][diff]+1 > maxLength {
+				maxLength = dp[i][diff] + 1
+			}
+		}
+	}
+
+	return maxLength
+}

dynamic/longestarithmeticsubsequence_test.go

@@ -0,0 +1,38 @@
+package dynamic_test
+
+import (
+	"testing"
+
+	"github.com/TheAlgorithms/Go/dynamic"
+)
+
+type testCaseLongestArithmeticSubsequence struct {
+	nums     []int
+	expected int
+}
+
+func getLongestArithmeticSubsequenceTestCases() []testCaseLongestArithmeticSubsequence {
+	return []testCaseLongestArithmeticSubsequence{
+		{[]int{3, 6, 9, 12}, 4},                  // Arithmetic sequence of length 4
+		{[]int{9, 4, 7, 2, 10}, 3},               // Arithmetic sequence of length 3
+		{[]int{20, 1, 15, 3, 10, 5, 8}, 4},       // Arithmetic sequence of length 4
+		{[]int{1, 2, 3, 4, 5}, 5},                // Arithmetic sequence of length 5
+		{[]int{10, 7, 4, 1}, 4},                  // Arithmetic sequence of length 4
+		{[]int{1, 5, 7, 8, 5, 3, 4, 3, 1, 2}, 4}, // Arithmetic sequence of length 4
+		{[]int{1, 3, 5, 7, 9}, 5},                // Arithmetic sequence of length 5
+		{[]int{5, 10, 15, 20}, 4},                // Arithmetic sequence of length 4
+		{[]int{1}, 1},                            // Single element, length is 1
+		{[]int{}, 0},                             // Empty array, length is 0
+	}
+}
+
+func TestLongestArithmeticSubsequence(t *testing.T) {
+	t.Run("Longest Arithmetic Subsequence test cases", func(t *testing.T) {
+		for _, tc := range getLongestArithmeticSubsequenceTestCases() {
+			actual := dynamic.LongestArithmeticSubsequence(tc.nums)
+			if actual != tc.expected {
+				t.Errorf("LongestArithmeticSubsequence(%v) = %v; expected %v", tc.nums, actual, tc.expected)
+			}
+		}
+	})
+}