算法-排序-k排序

算法导论第三版第八章思考题8-5
时间复杂度Θ(nlg(n/k))。
利用最小堆完成，把元素分成k个堆，每个堆大小⌈n/k⌉。
利用堆作为子排序稳定，也可以采用其他排序作为子排序，子排序的算法时间复杂度保证在Θ(klgk)就行。

#include "k_sort_heap.h"
int left_k_sort(int parent)
{return (parent << 1) + 1;
}
int right_k_sort(int parent)
{return (parent << 1) + 2;
}
void heapify_k_sort(int *array,int heap_size,int parent_index)
{int smallest = parent_index;int left = left_k_sort(parent_index);int right = right_k_sort(parent_index);if(left < heap_size && array[left]< array[smallest]){smallest = left;}if(right < heap_size && array[right] < array[smallest]){smallest = right;}if(smallest != parent_index){int temp = array[parent_index];array[parent_index] = array[smallest];array[smallest] = temp;heapify_k_sort(array,heap_size,smallest);}
}
void build_k_sort_heap(int *array,int length)
{for (int i = length/2 - 1; i >=0; --i) {heapify_k_sort(array,length,i);}
}
int extra_minimum(int *array,int & heap_size)
{int minimum = array[0];array[0] = array[heap_size-1];heap_size--;heapify_k_sort(array,heap_size,0);return minimum;
}
void k_sort(int *array,int length,int k)
{int initial_heap_size = length/k + (length % k == 0 ? 0 : 1);int *heap = new int [initial_heap_size];int current_heap_size = 0;for (int i = 0; i < k; ++i) {for (int j = 0; j < initial_heap_size; ++j){if(i + (j * k) < length){heap[j] = array[i + (j * k)];current_heap_size++;}}build_k_sort_heap(heap,current_heap_size);int j = 0;while (current_heap_size>0){array[i + (j * k)] = extra_minimum(heap,current_heap_size);j++;}}delete[] heap;
}