C语言数据结构---二叉树---堆的应用

1.建堆（向上调整）

1.1大堆

#include<stdio.h>
void swap(int *p1,int *p2)
{int temp = *p1;*p1 = *p2;*p2 = temp;
}
void Ajustup(int *a,int child)//向上调整
{int parent = (child - 1) / 2;while (child > 0){if (a[child] > a[parent]){swap(&a[child], &a[parent]);child= parent;parent = (child - 1) / 2;}else{break;}}
}
int main()
{int a[8] = { 4, 2, 8, 1, 5, 6, 9, 7 };//建堆for (int i = 0;i < sizeof(a)/sizeof(int);i++){Ajustup(a, i);}for (int i = 0;i < sizeof(a) / sizeof(int);i++){printf("%d ", a[i]);}return 0;
}

打印结果为：9，7，8，5，2，4，6，1

1.2小堆

#include<stdio.h>
void swap(int* p1, int* p2)
{int temp = *p1;*p1 = *p2;*p2 = temp;
}
void Ajustup(int* a, int child)//向上调整
{int parent = (child - 1) / 2;while (child > 0){if (a[child] < a[parent]){swap(&a[child], &a[parent]);child = parent;parent = (child - 1) / 2;}else{break;}}
}
int main()
{int a[8] = { 4, 2, 8, 1, 5, 6, 9, 7 };//建堆for (int i = 0; i < sizeof(a) / sizeof(int); i++){Ajustup(a, i);}for (int i = 0; i < sizeof(a) / sizeof(int); i++){printf("%d ", a[i]);}return 0;
}

2.建堆（向下调整）

那我们向下调整建堆的话，应该怎么去建堆才能让整个树变成堆呢？

每次向下调整之前，左右子树必须是⼀个堆，才能调整；
只有从第一个非叶子节点(父亲结点)开始，因为第一个非叶子节点（父亲结点）的左右子树才是堆

 2.1大堆

//从下往上建堆
#include<stdio.h>
void swap(int* p1, int* p2)
{int temp = *p1;*p1 = *p2;*p2 = temp;
}
void AjustDown(int* a, int parent, int n)//向下调整
{int child = 2 * parent + 1;while (child < n){if (child + 1 < n && a[child] < a[child + 1]){child++;}if (a[parent] < a[child]){swap(&a[child], &a[parent]);parent = child;child = 2 * parent + 1;}else{break;}}
}int main(){int a[11] = {4,2,8,1,5,6,9,7,2,7,9};int n = sizeof(a) / sizeof(int);//建堆for (int i =(n-2)/2; i >=0; i--){AjustDown(a, i, n);}for (int i = 0; i <n; i++){printf("%d ", a[i]);}return 0;}

打印结果：9 7 9 4 7 6 8 1 2 2 5

2.2小堆

//从下往上建堆
#include<stdio.h>
void swap(int* p1, int* p2)
{int temp = *p1;*p1 = *p2;*p2 = temp;
}
void AjustDown(int* a, int parent, int n)//向下调整
{int child = 2 * parent + 1;while (child < n){if (child + 1 < n && a[child] > a[child + 1]){child++;}if (a[parent] > a[child]){swap(&a[child], &a[parent]);parent = child;child = 2 * parent + 1;}else{break;}}
}int main(){int a[11] = {4,2,8,1,5,6,9,7,2,7,9};int n = sizeof(a) / sizeof(int);//建堆for (int i =(n-2)/2; i >=0; i--){AjustDown(a, i, n);}for (int i = 0; i <n; i++){printf("%d ", a[i]);}return 0;}

打印结果：1 2 6 2 5 8 9 7 4 7 9

3.排序

3.1降序，建小堆

下面图片是建好小堆后进行排序

#include<stdio.h>
//排降序，建小堆
void swap(int* p1, int* p2)
{int temp = *p1;*p1 = *p2;*p2 = temp;
}
void Ajustup(int* a, int child)//向上调整
{int parent = (child - 1) / 2;while (child > 0){if (a[child] < a[parent]){swap(&a[child], &a[parent]);child = parent;parent = (child - 1) / 2;}else{break;}}
}
void AjustDown(int* a, int parent, int n)//向下调整
{int child = 2 * parent + 1;while (child < n){if (child + 1 < n && a[child] > a[child + 1]){child++;}if (a[parent] >a[child]){swap(&a[child], &a[parent]);parent = child;child = 2 * parent + 1;}else{break;}}
}
int main()
{int a[8] = { 4, 2, 8, 1, 5, 6, 9, 7 };//建小堆for (int i = 0; i < sizeof(a) / sizeof(int); i++){Ajustup(a, i);}// 1 2 6 4 5 8 9 7int end = sizeof(a) / sizeof(int) - 1;while (end > 0){//swap(&a[parent], &a[childswap(&a[0], &a[end]);AjustDown(a, 0, end);end--;}for (int i = 0; i < sizeof(a) / sizeof(int); i++){printf("%d ", a[i]);}return 0;
}

总结：先建堆，在向下调整为降序

3.2升序，建大堆

#include<stdio.h>
//排升序，建大堆
// 交换两个元素
void swap(int* p1, int* p2)
{int temp = *p1;*p1 = *p2;*p2 = temp;
}// 向上调整函数，用于构建大堆
void Ajustup(int* a, int child)
{int parent = (child - 1) / 2;while (child > 0){// 如果子节点大于父节点，交换两者if (a[child] > a[parent]) {swap(&a[child], &a[parent]);child = parent;parent = (child - 1) / 2;}else{break;}}
}// 向下调整函数，用于保持大堆性质
void AjustDown(int* a, int parent, int n)
{int child = 2 * parent + 1; // 左子节点while (child < n){// 如果有右子节点，且右子节点更大，选择右子节点if (child + 1 < n && a[child] < a[child + 1]){child++;}// 如果父节点小于子节点，交换两者if (a[parent] < a[child]){swap(&a[parent], &a[child]);parent = child;child = 2 * parent + 1; // 更新子节点}else{break; // 堆的性质已满足}}
}int main()
{int a[8] = { 4, 2, 8, 1, 5, 6, 9, 7 };// 1. 构建大堆for (int i = 0; i < sizeof(a) / sizeof(int); i++){Ajustup(a, i);}// 2. 堆排序（升序）int end = sizeof(a) / sizeof(int) - 1;while (end > 0){// 将堆顶（最大值）放到数组末尾swap(&a[0], &a[end]);// 调整剩余部分为大堆AjustDown(a, 0, end);end--;}// 3. 打印排序结果for (int i = 0; i < sizeof(a) / sizeof(int); i++){printf("%d ", a[i]);}return 0;
}

3.3降序，建小堆（只用向下调整）

#include<stdio.h>
//排降序，建小堆
void swap(int* p1, int* p2)
{int temp = *p1;*p1 = *p2;*p2 = temp;
}
void AjustDown(int* a, int parent, int n)//向下调整
{int child = 2 * parent + 1;while (child < n){if (child + 1 < n && a[child] > a[child + 1]){child++;}if (a[parent] > a[child]){swap(&a[child], &a[parent]);parent = child;child = 2 * parent + 1;}else{break;}}
}
int main()
{int a[8] = { 4, 2, 8, 1, 5, 6, 9, 7 };int n = sizeof(a) / sizeof(int);//建小堆for (int i =(n-2)/2 ; i >=0; i--){AjustDown(a, i, n);}// 1 2 6 4 5 8 9 7int end = sizeof(a) / sizeof(int) - 1;while (end > 0){swap(&a[0], &a[end]);AjustDown(a, 0, end);end--;}for (int i = 0; i < sizeof(a) / sizeof(int); i++){printf("%d ", a[i]);}return 0;
}

3.4升序，建大堆（只用向下调整）

#include<stdio.h>
//排升序，建大堆
void swap(int* p1, int* p2)
{int temp = *p1;*p1 = *p2;*p2 = temp;
}
void AjustDown(int* a, int parent, int n)//向下调整
{int child = 2 * parent + 1;while (child < n){if (child + 1 < n && a[child] <a[child + 1]){child++;}if (a[parent] < a[child]){swap(&a[child], &a[parent]);parent = child;child = 2 * parent + 1;}else{break;}}
}
int main()
{int a[8] = { 4, 2, 8, 1, 5, 6, 9, 7 };int n = sizeof(a) / sizeof(int);//建大堆for (int i =(n-2)/2 ; i >=0; i--){AjustDown(a, i, n);}// 1 2 6 4 5 8 9 7int end = sizeof(a) / sizeof(int) - 1;while (end > 0){//swap(&a[parent], &a[childswap(&a[0], &a[end]);AjustDown(a, 0, end);end--;}for (int i = 0; i < sizeof(a) / sizeof(int); i++){printf("%d ", a[i]);}return 0;
}

4.TOP-K问题

#include<stdio.h>
#include<time.h>
#include<stdlib.h>
void swap(int* p1, int* p2)
{int temp = *p1;*p1 = *p2;*p2 = temp;
}
void AjustDown(int a[], int parent, int n)//向下调整
{int child = 2 * parent + 1;while (child < n){if (child + 1 < n && a[child] >a[child + 1])//小堆{child++;}if (a[parent] > a[child]){swap(&a[child], &a[parent]);parent = child;child = 2 * parent + 1;}else{break;}}
}
void CreateNDate()
{// 造数据int n = 1000;srand(time(0));char* file = "fuck.txt";FILE* fin = fopen(file, "w");if (fin == NULL){perror("fopen error");return;}for (int i = 0; i < n; ++i){int x = rand();// % 100;fprintf(fin, "%d\n", x);}fclose(fin);
}
void PrintTopK(int k)
{int* a = (int*)malloc(sizeof(int)*k);if (a== NULL){perror("malloc error");return;}FILE* fin = fopen("fuck.txt", "r");if (fin == NULL){perror("fopen error");return;}for (int i = 0; i < k; ++i)//从文件读数据{fscanf(fin, "%d", &a[i]);}for (int i = (k - 2) / 2; i >= 0; i--)//小堆{AjustDown(a, i, k);}/*for (int i = k - 1; i > 0; i--){swap(&a[0], &a[i]);// 将堆顶元素与数组元素交换AjustDown(a, 0, i);//对数组第一个元素调整，向下调整交换后剩下的元素}for (int j = 0; j < k; j++)//直接排序{printf("%d ", a[j]);}printf("\n");*///访问文件下数据int num = 0;while (fscanf(fin, "%d", &num)!=EOF){if (a[0] < num){a[0] = num;AjustDown(a, 0, k);}}for (int i = k - 1; i > 0; i--){swap(&a[0], &a[i]);// 将堆顶元素与数组元素交换AjustDown(a, 0, i);//对数组第一个元素调整，向下调整交换后剩下的元素}for (int j = 0; j < k; j++){printf("%d ", a[j]);}printf("\n");fclose(fin);
}int main() 
{int k = 0;printf("输入K:");scanf("%d", &k);CreateNDate();PrintTopK(k);return 0;
}