diff --git a/graph/dijkstra.go b/graph/dijkstra.go
new file mode 100644
index 000000000..26b2becbc
--- /dev/null
+++ b/graph/dijkstra.go
@@ -0,0 +1,62 @@
+package graph
+
+import "github.com/TheAlgorithms/Go/sort"
+
+type Item struct {
+	node int
+	dist int
+}
+
+func (a Item) More(b interface{}) bool {
+	// reverse direction for minheap
+	return a.dist < b.(Item).dist
+}
+func (a Item) Idx() int {
+	return a.node
+}
+
+func (g *Graph) Dijkstra(start, end int) (int, bool) {
+	visited := make(map[int]bool)
+	nodes := make(map[int]*Item)
+
+	nodes[start] = &Item{
+		dist: 0,
+		node: start,
+	}
+	pq := sort.MaxHeap{}
+	pq.Init(nil)
+	pq.Push(*nodes[start])
+
+	visit := func(curr Item) {
+		visited[curr.node] = true
+		for n, d := range g.edges[curr.node] {
+			if visited[n] {
+				continue
+			}
+
+			item := nodes[n]
+			dist2 := curr.dist + d
+			if item == nil {
+				nodes[n] = &Item{node: n, dist: dist2}
+				pq.Push(*nodes[n])
+			} else if item.dist > dist2 {
+				item.dist = dist2
+				pq.Update(*item)
+			}
+		}
+	}
+
+	for pq.Size() > 0 {
+		curr := pq.Pop().(Item)
+		if curr.node == end {
+			break
+		}
+		visit(curr)
+	}
+
+	item := nodes[end]
+	if item == nil {
+		return -1, false
+	}
+	return item.dist, true
+}
diff --git a/graph/dijkstra_test.go b/graph/dijkstra_test.go
new file mode 100644
index 000000000..168c7da69
--- /dev/null
+++ b/graph/dijkstra_test.go
@@ -0,0 +1,51 @@
+package graph
+
+import (
+	"testing"
+)
+
+var tc_dijkstra = []struct {
+	name     string
+	edges    [][]int
+	node0    int
+	node1    int
+	expected int
+}{
+	{
+		"straight line graph",
+		[][]int{{0, 1, 5}, {1, 2, 2}},
+		0, 2, 7,
+	},
+	{
+		"unconnected node",
+		[][]int{{0, 1, 5}},
+		0, 2, -1,
+	},
+	{
+		"double paths",
+		[][]int{{0, 1, 5}, {1, 3, 5}, {0, 2, 5}, {2, 3, 4}},
+		0, 3, 9,
+	},
+	{
+		"double paths extended",
+		[][]int{{0, 1, 5}, {1, 3, 5}, {0, 2, 5}, {2, 3, 4}, {3, 4, 1}},
+		0, 4, 10,
+	},
+}
+
+func TestDijkstra(t *testing.T) {
+	for _, tc := range tc_dijkstra {
+		t.Run(tc.name, func(t *testing.T) {
+			var graph Graph
+			for _, edge := range tc.edges {
+				graph.AddWeightedEdge(edge[0], edge[1], edge[2])
+			}
+
+			actual, _ := graph.Dijkstra(tc.node0, tc.node1)
+			if actual != tc.expected {
+				t.Errorf("expected %d, got %d, from node %d to %d, with %v",
+					tc.expected, actual, tc.node0, tc.node1, tc.edges)
+			}
+		})
+	}
+}
diff --git a/sort/heapsort.go b/sort/heapsort.go
index 698c7610f..0c44eb515 100644
--- a/sort/heapsort.go
+++ b/sort/heapsort.go
@@ -1,50 +1,134 @@
 package sort
 
-type maxHeap struct {
-	slice    []int
+type MaxHeap struct {
+	slice    []Comparable
 	heapSize int
+	indices  map[int]int
 }
 
-func buildMaxHeap(slice []int) maxHeap {
-	h := maxHeap{slice: slice, heapSize: len(slice)}
-	for i := len(slice) / 2; i >= 0; i-- {
-		h.MaxHeapify(i)
+func buildMaxHeap(slice0 []int) MaxHeap {
+	var slice []Comparable
+	for _, i := range slice0 {
+		slice = append(slice, Int(i))
 	}
+	h := MaxHeap{}
+	h.Init(slice)
 	return h
 }
 
-func (h maxHeap) MaxHeapify(i int) {
+func (h *MaxHeap) Init(slice []Comparable) {
+	if slice == nil {
+		slice = make([]Comparable, 0)
+	}
+
+	h.slice = slice
+	h.heapSize = len(slice)
+	h.indices = make(map[int]int)
+	h.Heapify()
+}
+
+func (h MaxHeap) Heapify() {
+	for i, v := range h.slice {
+		h.indices[v.Idx()] = i
+	}
+	for i := h.heapSize / 2; i >= 0; i-- {
+		h.heapifyDown(i)
+	}
+}
+
+func (h *MaxHeap) Pop() Comparable {
+	if h.heapSize == 0 {
+		return nil
+	}
+
+	i := h.slice[0]
+	h.heapSize--
+
+	h.slice[0] = h.slice[h.heapSize]
+	h.updateidx(0)
+	h.heapifyDown(0)
+
+	h.slice = h.slice[0:h.heapSize]
+	return i
+}
+
+func (h *MaxHeap) Push(i Comparable) {
+	h.slice = append(h.slice, i)
+	h.updateidx(h.heapSize)
+	h.heapifyUp(h.heapSize)
+	h.heapSize++
+}
+
+func (h MaxHeap) Size() int {
+	return h.heapSize
+}
+
+func (h MaxHeap) Update(i Comparable) {
+	h.slice[h.indices[i.Idx()]] = i
+	h.heapifyUp(h.indices[i.Idx()])
+	h.heapifyDown(h.indices[i.Idx()])
+}
+
+func (h MaxHeap) updateidx(i int) {
+	h.indices[h.slice[i].Idx()] = i
+}
+
+func (h MaxHeap) heapifyUp(i int) {
+	if i == 0 {
+		return
+	}
+	p := i / 2
+
+	if h.slice[i].More(h.slice[p]) {
+		h.slice[i], h.slice[p] = h.slice[p], h.slice[i]
+		h.updateidx(i)
+		h.updateidx(p)
+		h.heapifyUp(p)
+	}
+}
+
+func (h MaxHeap) heapifyDown(i int) {
 	l, r := 2*i+1, 2*i+2
 	max := i
 
-	if l < h.size() && h.slice[l] > h.slice[max] {
+	if l < h.heapSize && h.slice[l].More(h.slice[max]) {
 		max = l
 	}
-	if r < h.size() && h.slice[r] > h.slice[max] {
+	if r < h.heapSize && h.slice[r].More(h.slice[max]) {
 		max = r
 	}
-	//log.Printf("MaxHeapify(%v): l,r=%v,%v; max=%v\t%v\n", i, l, r, max, h.slice)
 	if max != i {
 		h.slice[i], h.slice[max] = h.slice[max], h.slice[i]
-		h.MaxHeapify(max)
+		h.updateidx(i)
+		h.updateidx(max)
+		h.heapifyDown(max)
 	}
 }
 
-func (h maxHeap) size() int { return h.heapSize } // ???
+type Comparable interface {
+	Idx() int
+	More(interface{}) bool
+}
+type Int int
+
+func (a Int) More(b interface{}) bool {
+	return a > b.(Int)
+}
+func (a Int) Idx() int {
+	return int(a)
+}
 
 func HeapSort(slice []int) []int {
 	h := buildMaxHeap(slice)
-	//log.Println(slice)
 	for i := len(h.slice) - 1; i >= 1; i-- {
 		h.slice[0], h.slice[i] = h.slice[i], h.slice[0]
 		h.heapSize--
-		h.MaxHeapify(0)
-		/*if i == len(h.slice)-1 || i == len(h.slice)-3 || i == len(h.slice)-5 {
-			element := (i - len(h.slice)) * -1
-			fmt.Println("Heap after removing ", element, " elements")
-			fmt.Println(h.slice)
+		h.heapifyDown(0)
+	}
 
-		}*/
+	res := []int{}
+	for _, i := range h.slice {
+		res = append(res, int(i.(Int)))
 	}
-	return h.slice
+	return res
 }