算法导论学习3

2.3    算法设计

分治法：将复杂问题分解为与原问题相似的简单的问题，递归解决这些子问题！

合并排序的思想就是将n问题分解为n/2子问题，直到分解的子问题为1时递归结束。然后将需要将分解后的排好顺序的子数组合并。

 

/************************************************************** * Copyright (C), 2011-2020,Inspur communications Tech. Co., Ltd. * FileName: merge_sort.cpp * Description: * Version: * Function List: 1. MergeArray,MergeSort 2. main * History: 1. 2. * Author: MaXiaobo Version : 1.0 Date: 2011-5-11 ****************************************************************/#include <stdio.h>#include <stdlib.h>#include <math.h>#include <assert.h>#define NUM 9 //the number of the sort array#define MAX 1000 //the max of the sort arrayvoid MergeArray(int *sort_array, int a, int b, int c);void MergeSort(int *sort_array, int a, int b);int main(int argc, char *argv[]){int i;int temp_array[NUM] = {1,6,2,9,12,34,5,7,8};printf("the initial array is:");for (i = 0; i < NUM; i++){printf("%d ", temp_array[i]);}printf("/n");MergeSort(temp_array, 0, NUM - 1);printf("the sorted array is: ");for (i = 0; i < NUM; i++){printf("%d ", temp_array[i]);}printf("/n");return 0;}/************************************************************* * Function: MergeArray * Description: 对两个已经排序过的数组进行合并 * Calls: * Called By: MergeArray * Input: 1. sort_array 合并数组 2. a,b,c分别为数组的索引下标 * Output: * Return: * Others: * History: 1. 2. * Author: MaXiaobo Version : 1.0 Date: 2011-5-11 **************************************************************/void MergeArray(int *sort_array, int a, int b, int c){assert(NULL != sort_array);int i, j, k;int len_a,len_b;len_a = b + 1 -a;len_b = c - b;int *array_one, *array_two;array_one = new int[len_a + 1];array_two = new int[len_b + 1];array_one[len_a] = MAX; //在数组最后设置一个哨兵，判断当前数组是否遍历完毕array_two[len_b] = MAX; //非常重要for (i = 0; i < len_a; i++){array_one[i] = sort_array[a + i];}for (j = 0; j < len_b; j++){array_two[j] = sort_array[b + 1 + j];}i = j = 0;for (k = a; k < c + 1; k++){if (array_one[i] <= array_two[j])//在数组最后一定要设置一个哨兵元素{sort_array[k] = array_one[i];i++;}else{sort_array[k] = array_two[j];j++;}}delete array_one;delete array_two;}/************************************************************* * Function: MergeSort * Description: 对数组进行合并排序 * Calls: * Called By: main * Input: 1. sort_array 合并数组 2. a,b,分别为数组的起始和结束索引下标 * Output: * Return: * Others: * History: 1. 2. * Author: MaXiaobo Version : 1.0 Date: 2011-5-11 **************************************************************/void MergeSort(int *sort_array, int a, int b){assert(NULL != sort_array);int p, q;p = a;q = b;if (p < q){int mid = floor(float(p + q)/(float)2);MergeSort(sort_array, p, mid);MergeSort(sort_array, mid + 1, q);MergeArray(sort_array, p, mid, q);}}

 

其中在合并数组中，新建的两个动态数组中，哨兵元素的设置非常重要，如果没有哨兵元素，遍历数组可能会出问题~！

 

运行结果如下：