【算法导论】之堆排序

堆的简介

    一般说堆，说的是二叉堆。堆数据结构是一种数组对象，它可以被看作为一棵完全二叉树。树中的每个节点与数组中存放该节点值的那个元素对应。

    堆有两个属性:堆能容纳的元素个数，堆中存放的元素个数。二叉堆有两种：大根堆和小跟堆，它们应该满足的性质：A[parent[i]]>=A[i]或A[parent[i]]<=A[i]。以下就是一个大根堆。

堆的操作

保持堆的性质

Heap * init_heap(){    Heap *p = (Heap *)malloc(sizeof(Heap));    p->array_addr = NULL;    p->capacity = 0;    p->size = 0;    return p;}

/**调整heap中的第i个节点子树为大根堆**/int heap_adjust(Heap * const heap,const int i){    if(heap == NULL || heap != NULL && heap->array_addr == NULL) return 0;    int left = i * 2 +1 ;    int right = i * 2 + 2;    int largest = i;    int swap = 0;    if(left < heap -> size && *(heap->array_addr + left) > *(heap->array_addr + largest))        largest = left;    if(right < heap -> size && *(heap->array_addr + right) > *(heap->array_addr + largest))        largest = right;    if(largest != i){        swap =  *(heap->array_addr + i);        *(heap->array_addr + i) = *(heap->array_addr + largest);        *(heap->array_addr + largest) = swap;        return heap_adjust(heap,largest);    }    return 1;}

/**构建大根堆   从下向上构建大根堆**/int build_heap(Heap * const heap){    if(heap == NULL || heap != NULL && (heap->array_addr == NULL || heap->capacity <= 0)){        return 0;    }    int i = (heap->capacity-1) / 2;    for(;i >= 0;i--){        heap_adjust(heap,i);    }    return 1;}

堆排序

/**将堆顶元素与尾部元素对换   调整堆**/int heap_sort(Heap * const heap){    if(heap == NULL) return 0;    if(build_heap(heap)){        int i = heap -> capacity -1;        int swap = 0;        for(;i > 0 ;i--){            swap = *(heap -> array_addr + i);            *(heap -> array_addr + i) = *(heap -> array_addr + 0);            *(heap -> array_addr + 0) = swap;            heap -> size = heap -> size -1;            heap_adjust(heap,0);        }        return 1;    }else return 0;}

优先队列

    优先级队列支持如下操作：

    1)取出最大元素，但不移除。

    2)抽取最大元素

    3)在指定位置，用key取代A[i]的值，但key必须比A[i]要大

    4)在队列中增加元素

/**返回优先队列最大元素*/int heap_max(Heap * const heap){   if(heap == NULL || heap -> size <1){        return -1;   }   return *(heap -> array_addr + 0);}

/**A[0]与末位元素对调    从上至下调整队列**/int extract_max(Heap * const heap){   if(heap == NULL || heap -> size < 1 || heap -> array_addr == NULL) return -1;   int max = *(heap -> array_addr + 0);   *(heap -> array_addr + 0) = *(heap -> array_addr + heap -> size -1);   heap -> size -= 1;   heap_adjust(heap,0);   return max;}

int increase_key(Heap * const heap,int i,int key){   if(heap == NULL || heap -> size < 1 || heap -> array_addr == NULL) return -1;   if(key < *(heap -> array_addr + i)) return -1;   *(heap -> array_addr + i) = key;   int index = i;   int swap = 0;   while(index > 0 && *(heap -> array_addr + index) > *(heap -> array_addr + index / 2)){      swap = *(heap -> array_addr + index);      *(heap -> array_addr + index) = *(heap -> array_addr + index / 2);      *(heap -> array_addr + index / 2) = swap;      index /= 2;   }}int heap_insert(Heap * const heap,int key){   if(heap == NULL || heap -> size < 1 || heap -> array_addr == NULL) return -1;   heap -> size += 1;   *(heap -> array_addr + index) = INT_MIN;   increase_key(heap,heap -> size - 1,key);   return 1;}