Replace sort.Sort call with heapify algorithm in Init.

Fixed package comment.
Renamed some variables for symmetry, added more internal comments and more tests.
Fixes #304.

R=rsc
https://golang.org/cl/157166

src/pkg/container/heap/heap.go

@@ -10,10 +10,10 @@ package heap
 import "sort"
 
 // Any type that implements heap.Interface may be used as a
-// heap with the following invariants (established after Init
-// has been called):
+// min-heap with the following invariants (established after
+// Init has been called):
 //
-//	h.Less(i, j) for 0 <= i < h.Len() and j = 2*i+1 or 2*i+2 and j < h.Len()
+//	!h.Less(j, i) for 0 <= i < h.Len() and j = 2*i+1 or 2*i+2 and j < h.Len()
 //
 type Interface interface {
 	sort.Interface;
@@ -25,9 +25,15 @@ type Interface interface {
 // A heaper must be initialized before any of the heap operations
 // can be used. Init is idempotent with respect to the heap invariants
 // and may be called whenever the heap invariants may have been invalidated.
-// Its complexity is O(n*log(n)) where n = h.Len().
+// Its complexity is O(n) where n = h.Len().
 //
-func Init(h Interface)	{ sort.Sort(h) }
+func Init(h Interface) {
+	// heapify
+	n := h.Len();
+	for i := n/2 - 1; i >= 0; i-- {
+		down(h, i, n)
+	}
+}
 
 
 // Push pushes the element x onto the heap. The complexity is
@@ -41,6 +47,7 @@ func Push(h Interface, x interface{}) {
 
 // Pop removes the minimum element (according to Less) from the heap
 // and returns it. The complexity is O(log(n)) where n = h.Len().
+// Same as Remove(h, 0).
 //
 func Pop(h Interface) interface{} {
 	n := h.Len() - 1;
@@ -56,7 +63,7 @@ func Pop(h Interface) interface{} {
 func Remove(h Interface, i int) interface{} {
 	n := h.Len() - 1;
 	if n != i {
-		h.Swap(n, i);
+		h.Swap(i, n);
 		down(h, i, n);
 		up(h, i);
 	}
@@ -66,7 +73,7 @@ func Remove(h Interface, i int) interface{} {
 
 func up(h Interface, j int) {
 	for {
-		i := (j - 1) / 2;
+		i := (j - 1) / 2;	// parent
 		if i == j || h.Less(i, j) {
 			break
 		}
@@ -78,12 +85,13 @@ func up(h Interface, j int) {
 
 func down(h Interface, i, n int) {
 	for {
-		j := 2*i + 1;
-		if j >= n {
+		j1 := 2*i + 1;
+		if j1 >= n {
 			break
 		}
-		if j1 := j + 1; j1 < n && !h.Less(j, j1) {
-			j = j1	// = 2*i + 2
+		j := j1;	// left child
+		if j2 := j1 + 1; j2 < n && !h.Less(j1, j2) {
+			j = j2	// = 2*i + 2  // right child
 		}
 		if h.Less(i, j) {
 			break

src/pkg/container/heap/heap_test.go

@@ -11,10 +11,15 @@ import (
 
 
 type myHeap struct {
-	vector.IntVector;
+	// A vector.Vector implements sort.Interface except for Less,
+	// and it implements Push and Pop as required for heap.Interface.
+	vector.Vector;
 }
 
 
+func (h *myHeap) Less(i, j int) bool	{ return h.At(i).(int) < h.At(j).(int) }
+
+
 func (h *myHeap) verify(t *testing.T, i int) {
 	n := h.Len();
 	j1 := 2*i + 1;
@@ -36,16 +41,28 @@ func (h *myHeap) verify(t *testing.T, i int) {
 }
 
 
-func (h *myHeap) Push(x interface{})	{ h.IntVector.Push(x.(int)) }
-
+func TestInit0(t *testing.T) {
+	h := new(myHeap);
+	for i := 20; i > 0; i-- {
+		h.Push(0)	// all elements are the same
+	}
+	Init(h);
+	h.verify(t, 0);
 
-func (h *myHeap) Pop() interface{}	{ return h.IntVector.Pop() }
+	for i := 1; h.Len() > 0; i++ {
+		x := Pop(h).(int);
+		h.verify(t, 0);
+		if x != 0 {
+			t.Errorf("%d.th pop got %d; want %d", i, x, 0)
+		}
+	}
+}
 
 
-func TestInit(t *testing.T) {
+func TestInit1(t *testing.T) {
 	h := new(myHeap);
 	for i := 20; i > 0; i-- {
-		h.Push(i)
+		h.Push(i)	// all elements are different
 	}
 	Init(h);
 	h.verify(t, 0);
@@ -86,3 +103,64 @@ func Test(t *testing.T) {
 		}
 	}
 }
+
+
+func TestRemove0(t *testing.T) {
+	h := new(myHeap);
+	for i := 0; i < 10; i++ {
+		h.Push(i)
+	}
+	h.verify(t, 0);
+
+	for h.Len() > 0 {
+		i := h.Len() - 1;
+		x := Remove(h, i).(int);
+		if x != i {
+			t.Errorf("Remove(%d) got %d; want %d", i, x, i)
+		}
+		h.verify(t, 0);
+	}
+}
+
+
+func TestRemove1(t *testing.T) {
+	h := new(myHeap);
+	for i := 0; i < 10; i++ {
+		h.Push(i)
+	}
+	h.verify(t, 0);
+
+	for i := 0; h.Len() > 0; i++ {
+		x := Remove(h, 0).(int);
+		if x != i {
+			t.Errorf("Remove(0) got %d; want %d", x, i)
+		}
+		h.verify(t, 0);
+	}
+}
+
+
+func TestRemove2(t *testing.T) {
+	N := 10;
+
+	h := new(myHeap);
+	for i := 0; i < N; i++ {
+		h.Push(i)
+	}
+	h.verify(t, 0);
+
+	m := make(map[int]int);
+	for h.Len() > 0 {
+		m[Remove(h, (h.Len()-1)/2).(int)] = 1;
+		h.verify(t, 0);
+	}
+
+	if len(m) != N {
+		t.Errorf("len(m) = %d; want %d", len(m), N)
+	}
+	for i := 0; i < len(m); i++ {
+		if _, exists := m[i]; !exists {
+			t.Errorf("m[%d] doesn't exist", i)
+		}
+	}
+}