new file: trees/heap/maxHeap.go

tests/treeTests/maxHeap_test.go

@@ -0,0 +1,204 @@
+package tests
+
+import (
+	"math/rand"
+	"sort"
+	"testing"
+
+	"datastructures/trees/heap"
+)
+
+// isMaxHeap verifies the max-heap property over the backing array: every
+// parent is >= each of its children.
+func isMaxHeap(a []int) bool {
+	for i := range a {
+		left := 2*i + 1
+		right := 2*i + 2
+		if left < len(a) && a[i] < a[left] {
+			return false
+		}
+		if right < len(a) && a[i] < a[right] {
+			return false
+		}
+	}
+	return true
+}
+
+func TestMaxHeap_PopEmpty(t *testing.T) {
+	h := heap.NewMaxHeap[int]()
+
+	val, ok := h.PopMax()
+	if ok {
+		t.Fatalf("PopMax on empty heap: got ok=true, val=%d; want ok=false", val)
+	}
+	if val != 0 {
+		t.Fatalf("PopMax on empty heap: got val=%d; want zero value 0", val)
+	}
+}
+
+func TestMaxHeap_InsertMaintainsHeapProperty(t *testing.T) {
+	h := heap.NewMaxHeap[int]()
+
+	for _, v := range []int{5, 3, 8, 1, 9, 2, 7, 6, 4, 0} {
+		h.Insert(v)
+		if !isMaxHeap(h.Array) {
+			t.Fatalf("heap property violated after inserting %d: %v", v, h.Array)
+		}
+	}
+}
+
+func TestMaxHeap_PopMaxReturnsDescending(t *testing.T) {
+	h := heap.NewMaxHeap[int]()
+
+	input := []int{5, 3, 8, 1, 9, 2, 7, 6, 4, 0}
+	for _, v := range input {
+		h.Insert(v)
+	}
+
+	var got []int
+	for {
+		val, ok := h.PopMax()
+		if !ok {
+			break
+		}
+		got = append(got, val)
+
+		// heap property must hold after every pop
+		if !isMaxHeap(h.Array) {
+			t.Fatalf("heap property violated after pop: %v", h.Array)
+		}
+	}
+
+	want := make([]int, len(input))
+	copy(want, input)
+	sort.Sort(sort.Reverse(sort.IntSlice(want)))
+
+	if len(got) != len(want) {
+		t.Fatalf("popped %d values; want %d", len(got), len(want))
+	}
+	for i := range want {
+		if got[i] != want[i] {
+			t.Fatalf("pop order = %v; want descending %v", got, want)
+		}
+	}
+}
+
+func TestMaxHeap_Duplicates(t *testing.T) {
+	h := heap.NewMaxHeap[int]()
+
+	for _, v := range []int{4, 4, 4, 2, 2, 7, 7, 7, 7} {
+		h.Insert(v)
+	}
+
+	prev := int(^uint(0) >> 1) // max int, so first pop always <= prev
+	for {
+		val, ok := h.PopMax()
+		if !ok {
+			break
+		}
+		if val > prev {
+			t.Fatalf("pop order not non-increasing: got %d after %d", val, prev)
+		}
+		prev = val
+	}
+}
+
+func TestMaxHeap_Heapify(t *testing.T) {
+	h := heap.NewMaxHeap[int]()
+
+	input := []int{5, 3, 8, 1, 9, 2, 7, 6, 4, 0}
+	if err := h.Heapify(input); err != nil {
+		t.Fatalf("Heapify returned error: %v", err)
+	}
+
+	if !isMaxHeap(h.Array) {
+		t.Fatalf("Heapify did not produce a valid max heap: %v", h.Array)
+	}
+
+	// Heapify must clone: mutating the source must not affect the heap.
+	input[0] = 999
+	if h.Array[0] == 999 {
+		t.Fatalf("Heapify did not clone the input slice")
+	}
+
+	// The root must be the maximum.
+	if h.Array[0] != 9 {
+		t.Fatalf("root after Heapify = %d; want max 9", h.Array[0])
+	}
+}
+
+func TestMaxHeap_HeapifyOnNonEmptyErrors(t *testing.T) {
+	h := heap.NewMaxHeap[int]()
+	h.Insert(1)
+
+	if err := h.Heapify([]int{2, 3}); err == nil {
+		t.Fatal("Heapify on non-empty heap: got nil error; want error")
+	}
+}
+
+func TestMaxHeap_HeapifyThenPopSorts(t *testing.T) {
+	input := []int{42, -7, 0, 15, 15, 3, 99, -100, 8}
+
+	h := heap.NewMaxHeap[int]()
+	if err := h.Heapify(input); err != nil {
+		t.Fatalf("Heapify returned error: %v", err)
+	}
+
+	var got []int
+	for {
+		val, ok := h.PopMax()
+		if !ok {
+			break
+		}
+		got = append(got, val)
+	}
+
+	want := make([]int, len(input))
+	copy(want, input)
+	sort.Sort(sort.Reverse(sort.IntSlice(want)))
+
+	for i := range want {
+		if got[i] != want[i] {
+			t.Fatalf("Heapify+PopMax = %v; want %v", got, want)
+		}
+	}
+}
+
+func TestMaxHeap_Randomized(t *testing.T) {
+	r := rand.New(rand.NewSource(1))
+
+	for trial := 0; trial < 50; trial++ {
+		n := r.Intn(200)
+		input := make([]int, n)
+		for i := range input {
+			input[i] = r.Intn(1000) - 500
+		}
+
+		h := heap.NewMaxHeap[int]()
+		for _, v := range input {
+			h.Insert(v)
+		}
+		if !isMaxHeap(h.Array) {
+			t.Fatalf("trial %d: invalid heap after inserts: %v", trial, h.Array)
+		}
+
+		var got []int
+		for {
+			val, ok := h.PopMax()
+			if !ok {
+				break
+			}
+			got = append(got, val)
+		}
+
+		want := make([]int, len(input))
+		copy(want, input)
+		sort.Sort(sort.Reverse(sort.IntSlice(want)))
+
+		for i := range want {
+			if got[i] != want[i] {
+				t.Fatalf("trial %d: pop order = %v; want %v", trial, got, want)
+			}
+		}
+	}
+}

trees/heap/maxHeap.go

@@ -0,0 +1,115 @@
+package heap
+
+import (
+	"cmp"
+	"errors"
+	"slices"
+)
+
+//  node is stored at index i:
+//  left child is at index 2*i + 1.
+//  right child is at index 2*i + 2.
+//  parent index [(i-1)/2].
+
+// MaxHeap :: binary heap implementation,  Insertion - O(log n).
+// Array[] is managed internally , treat it as read only
+type MaxHeap[T cmp.Ordered] struct {
+	Array []T
+}
+
+// NewMinHeap() :: Creates a new min heap tree.
+func NewMaxHeap[T cmp.Ordered]() *MaxHeap[T] {
+	return &MaxHeap[T]{}
+}
+
+// Insert() -> adds new value to heap.
+// O(logn)
+func (h *MaxHeap[T]) Insert(val T) {
+	h.Array = append(h.Array, val)
+
+	h.siftUp(len(h.Array) - 1)
+}
+
+// siftUp() :: moves the smaller value node up, used when inserting.
+// O(logn)
+func (h *MaxHeap[T]) siftUp(i int) {
+	for i > 0 {
+		parentIndex := (i - 1) / 2
+
+		if h.Array[i] > h.Array[parentIndex] {
+			// swap places
+			h.Array[i], h.Array[parentIndex] = h.Array[parentIndex], h.Array[i]
+			i = parentIndex
+		} else {
+			break
+		}
+	}
+}
+
+// siftDown() :: receives an index to move its value down the tree.
+// O(logn)
+func (h *MaxHeap[T]) siftDown(i int) {
+	n := len(h.Array)
+
+	for {
+
+		smallest := i
+
+		left := 2*i + 1
+		right := 2*i + 2
+
+		if left < n && h.Array[left] > h.Array[smallest] {
+			smallest = left
+		}
+		if right < n && h.Array[right] > h.Array[smallest] {
+			smallest = right
+		}
+
+		if smallest == i {
+			break
+		}
+
+		// sink down
+		h.Array[i], h.Array[smallest] = h.Array[smallest], h.Array[i]
+		i = smallest
+
+	}
+}
+
+// PopMin() -> returns the root
+func (h *MaxHeap[T]) PopMax() (T, bool) {
+	var zero T
+	if len(h.Array) <= 0 {
+		return zero, false
+	}
+
+	last := len(h.Array) - 1
+	root := h.Array[0]
+
+	// move last value to the root
+	h.Array[0] = h.Array[last]
+
+	// GC cleanup
+	h.Array[last] = zero
+
+	h.Array = h.Array[:last]
+
+	h.siftDown(0)
+
+	return root, true
+}
+
+// Heapify() -> makes arbitrary slice a heap from scratch . returns error if
+// the heap is not empty
+func (h *MaxHeap[T]) Heapify(array []T) error {
+	if len(h.Array) != 0 {
+		return errors.New("Can only init Heapify on empty heap")
+	}
+
+	h.Array = slices.Clone(array)
+
+	for i := len(h.Array)/2 - 1; i >= 0; i-- {
+		h.siftDown(i)
+	}
+	return nil
+}

trees/heap/minHeap.go

@@ -39,9 +39,10 @@ func (h *MinHeap[T]) siftUp(i int) {
 		if h.Array[i] < h.Array[parentIndex] {
 			// swap places
 			h.Array[i], h.Array[parentIndex] = h.Array[parentIndex], h.Array[i]
+			i = parentIndex
+		} else {
+			break
 		}
-
-		i = parentIndex
 	}
 }