6.2-1 直接上MAX-HEAPIFY的go語言實現:
package main
import (
"fmt"
)
type heapify interface {
LEFT(i int) int
RIGHT(i int) int
MaxHeapify(i int)
}
type maxHeap []int
func (A maxHeap) LEFT(i int) int {
return i << 1
}
func (A maxHeap) RIGHT(i int) int {
return (i<<1 + 1)
}
func (A maxHeap) MaxHeapify(i int) {
largest := i
l := A.LEFT(i)
r := A.RIGHT(i)
if l <= len(A) && A[l-1] > A[i-1] {
largest = l
}
if r <= len(A) && A[r-1] > A[largest-1] {
largest = r
}
if largest != i {
A[largest-1], A[i-1] = A[i-1], A[largest-1]
A.MaxHeapify(largest)
}
}
func main() {
a := maxHeap{27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0}
var h heapify = a
h.MaxHeapify(3)
fmt.Println(h)
}
6.2-2 :參考MAX-HEAPIFY,寫出能夠維護相應最小堆的MIN-HEAPIFY(A,i)的偽代碼,并比較MIN-HEAPIFY與MAX-HEAPIFY的運行時間
答:與上題同理,運行時間相同,時間復雜度都為O(h),h為該堆的高度。
6.2-3 :當元素A[i]比其他孩子的值都大時,調用MAX-HEAPIFY(A,i)會有什么結果?
答:不執行遞歸,原數組不變。
6.2-4:當i>A.heap-size/2時,調用MAX-HEAPIFY會有什么結果?
答:原數組不變。因為此時為葉結點。
6.2-5:試用循環控制結構取代遞歸,重寫MAX-HEAPIFY的代碼
golang實現:
package main
import (
"fmt"
)
type heapify interface {
LEFT(i int) int
RIGHT(i int) int
MaxHeapify(i int)
}
type maxHeap []int
func (A maxHeap) LEFT(i int) int {
return i << 1
}
func (A maxHeap) RIGHT(i int) int {
return (i<<1 + 1)
}
func (A maxHeap) MaxHeapify(i int) {
for i <= len(A) {
largest := i
l := A.LEFT(i)
r := A.RIGHT(i)
if l <= len(A) && A[l-1] > A[i-1] {
largest = l
}
if r <= len(A) && A[r-1] > A[largest-1] {
largest = r
}
if largest != i {
A[largest-1], A[i-1] = A[i-1], A[largest-1]
i = largest
} else {
return
}
}
}
func main() {
a := maxHeap{27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0}
var h heapify = a
h.MaxHeapify(3)
fmt.Println(h)
}
6.2-6 證明:對一個大小為n的堆,MAX-HEAPIFY的最壞情況運行時間為O(lgn)。
答:書p86已經給出了答案,不再贅述。