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_MIN

struct 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 6

int 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);
}