d-堆

《数据结构与算法分析——c语言描述》 第六章

代码和二叉堆差不多，有意思的是父亲，儿子编号的推导。

第i行，第j行节点（均从1开始）的编号推导：
前面i-1行的节点加起来：

1+d1+d2+d3+……+di−2=1−di−11−d

然后加上剩下的，就是

1−di−11−d+j

第一个儿子就是

1−di1−d+(j−1)∗d+1

父亲和儿子的关系就是(这个就是强行凑，参考了 让阳光照进心里)

(father−1)∗D+2

binheap.h

#ifndef _BinHeap_H#define D 4 //d堆的设置typedef int ElementType;struct HeapStruct;typedef struct HeapStruct *PriorityQueue;PriorityQueue initialize(int maxElements);PriorityQueue buildHeap(ElementType *arr, int n);void destroy(PriorityQueue h);void makeEmpty(PriorityQueue h);void insert(ElementType X, PriorityQueue h);ElementType deleteMin(PriorityQueue h);int isEmpty(PriorityQueue h);int isFull(PriorityQueue h);void decreaseKey(int pos, ElementType delta, PriorityQueue h);void increaseKey(int pos, ElementType delta, PriorityQueue h);void Delete(int pos, PriorityQueue h);#endif // !_BinHeap_H

binheap.c

#include"binheap.h"#include"fatal.h"#define MinPQSize 4#define MinData INT_MINstruct HeapStruct {    int capacity;    int size;    ElementType* elements;};static int firstSonCursor(int pos) {    return  (pos - 1) * D + 2;//见日志说明}static int faterCursor(int pos) {    if (pos == 1)//这个是必须的，否则pos为1的时候还是返回1，那么就不能调用mindata        return 0;    return (pos - 2) / D + 1;}PriorityQueue initialize(int maxElements) {    PriorityQueue h;    if (maxElements < MinPQSize)        Error("Priority queue size is too small");    h = malloc(sizeof(struct HeapStruct));    if (h == NULL)        Error("OUT OF MEMORY");    h->elements = malloc(sizeof(ElementType)*(maxElements + 1));//多出来的一个用于存放最小的元素，其用来和堆顶比较    if (h->elements == NULL)        Error("OUT OF MEMORY");    h->capacity = maxElements;    h->size = 0;    h->elements[0] = MinData;    return h;}static void percolateDown(int pos, PriorityQueue h) {    ElementType elem = h->elements[pos];    int i, minChild;    for (i = pos; i < h->size; i = minChild) {        int firstChild = firstSonCursor(i);//        minChild = firstChild;        if (firstChild > h->size)            break;        for (int i = 1; (firstChild + i) <= h->size && i < D; i++) {//直接从第二个儿子开始比较            if (h->elements[minChild] > h->elements[firstChild + i])                minChild = firstChild + i;        }        if (elem > h->elements[minChild])            h->elements[i] = h->elements[minChild];        else            break;    }    h->elements[i] = elem;}static void percolateUp(int pos, PriorityQueue h) {    int i;    ElementType elem = h->elements[pos];    for (i = pos; h->elements[faterCursor(i)] > elem; i = faterCursor(i)) {        h->elements[i] = h->elements[faterCursor(i)];    }    h->elements[i] = elem;}PriorityQueue buildHeap(ElementType *arr, int n) {    PriorityQueue h = initialize(n);    h->size = n;    for (int i = 0; i < n; i++) {        h->elements[i + 1] = arr[i];    }    for (int i = faterCursor(n); i > 0; i--) {        percolateDown(i, h);     }    return h;}void destroy(PriorityQueue h) {    free(h->elements);    free(h);}void makeEmpty(PriorityQueue h) {    h->size = 0;}void insert(ElementType X, PriorityQueue h) {    if (isFull(h))        Error("priority queue is full");    h->elements[++h->size] = X;    percolateUp(h->size, h);}ElementType deleteMin(PriorityQueue h) {//    ElementType minElement;    if (isEmpty(h))        Error("priority queue is empty");    minElement = h->elements[1];    h->elements[1] = h->elements[h->size--];//删除右下的元素    percolateDown(1, h);    return minElement;}int isEmpty(PriorityQueue h) {    return h->size == 0;}int isFull(PriorityQueue h) {    return h->size == h->capacity;}void decreaseKey(int pos, ElementType delta, PriorityQueue h) {    if (pos<1 || pos>h->size)        Error("Positon Error");    h->elements[pos] -= delta;    percolateUp(pos, h);}void increaseKey(int pos, ElementType delta, PriorityQueue h) {    if (pos<1 || pos>h->size)        Error("Positon Error");    h->elements[pos] += delta;    percolateDown(pos, h);}void Delete(int pos, PriorityQueue h) {    if (pos<1 || pos>h->size)        Error("Positon Error");    for (int i = pos; i > 1; i= faterCursor(i)) {        h->elements[i] = h->elements[faterCursor(i)];    }    deleteMin(h);}

main.c

#include"binheap.h"#include<stdlib.h>#include<stdio.h>#include"fatal.h"#define N 6int RandInt(int i, int j) {    int temp;    temp = (int)(i + (1.0*rand() / RAND_MAX)*(j - i));    return temp;}void getRandomInt(int *A, int n) {    for (int i = 0; i < n; i++) {        A[i] = i + 1;    }    for (int i = 1; i < n; i++) {        //std::swap(A[i], A[RandInt(0, i)]);          int randAdrr = RandInt(0, i);        int t = A[i];        A[i] = A[randAdrr];        A[randAdrr] = t;    }}struct HeapStruct {    int capacity;    int size;    ElementType* elements;};int main() {    PriorityQueue h = initialize(N);    int a[N];    getRandomInt(a, N);    for (int i = 0; i < N; i++) {        insert(a[i], h);    }    for (int i = 0; i < N; i++) {        printf("%d ", deleteMin(h));    }    destroy(h);    printf("\n");    h = buildHeap(a, N);    for (int i = 0; i < N; i++) {        printf("%d ", deleteMin(h));    }    destroy(h);}