二分查找的灵活应用

二分查找
1.找任意一个出现key的下标
   思路：mid位置小于key则low右移，大于key则high左移，等于则直接返回mid
2.找第一个出现key的下标
   思路：mid位置小于key则low右移，大于等于key则high左移，若low不越界且该位置的值等于key，则直接返回low,否则表示该值不存在
3.找最大的小于key的下标
   思路：mid位置小于key则low右移，大于等于key则high左移，若high不越界则直接返回high,否则表示该值不存在
4.找最后一个出现key的下标
   思路：mid位置小于等于key则low右移，大于key则high左移，若high不越界且该位置的值等于key，则直接返回high,否则表示该值不存在
5.找最小的大于key的下标

   思路：mid位置小于等于key则low右移，大于key则high左移，若low不越界则直接返回low,否则表示该值不存在

代码：

#include "stdafx.h"#include <iostream>using namespace std;//二分查找//1.找任意一个出现key的下标//  思路：mid位置小于key则low右移，大于key则high左移，等于则直接返回midint BinarySearchAnyKey(int nArr[], int nLength, int key){    int nLow = 0;int nHigh = nLength - 1;    int nMid = 0;    while (nLow <= nHigh)    {        nMid = nLow + ((nHigh - nLow) >> 1);        if (nArr[nMid] > key)        {nHigh = nMid - 1;        }else if (nArr[nMid] < key){nLow = nMid + 1;}else{return nMid;}    }return -1;}//2.找第一个出现key的下标//  思路：mid位置小于key则low右移，大于等于key则high左移，若low不越界且该位置的值等于key，则直接返回low,否则表示该值不存在int BinarySearchFirstKey(int nArr[], int nLength, int key){int nLow = 0;int nHigh = nLength - 1;int nMid = 0;while (nLow <= nHigh){nMid = nLow + ((nHigh - nLow) >> 1);if (nArr[nMid] >= key)//相等向左移{nHigh = nMid - 1;}else {nLow = nMid + 1;}}if (nLow >= 0 && nLow < nLength && nArr[nLow] == key){return nLow;}else{        return -1;}}//3.找最大的小于key的下标//  思路：mid位置小于key则low右移，大于等于key则high左移，若high不越界则直接返回high,否则表示该值不存在int BinarySearchMaxIndexLessThanKey(int nArr[], int nLength, int key){int nLow = 0;int nHigh = nLength - 1;int nMid = 0;while (nLow <= nHigh){nMid = nLow + ((nHigh - nLow) >> 1);if (nArr[nMid] >= key)//相等向左移{nHigh = nMid - 1;}else {nLow = nMid + 1;}}if (nHigh >= 0 && nHigh < nLength){return nHigh;}else{return -1;}}//4.找最后一个出现key的下标//  思路：mid位置小于等于key则low右移，大于key则high左移，若high不越界且该位置的值等于key，则直接返回high,否则表示该值不存在int BinarySearchLastKey(int nArr[], int nLength, int key){int nLow = 0;int nHigh = nLength - 1;int nMid = 0;while (nLow <= nHigh){nMid = nLow + ((nHigh - nLow) >> 1);if (nArr[nMid] > key){nHigh = nMid - 1;}else //相等向右移{nLow = nMid + 1;}}if (nHigh >= 0 && nHigh < nLength && nArr[nHigh] == key){return nHigh;}else{return -1;}}//5.找最小的大于key的下标//  思路：mid位置小于等于key则low右移，大于key则high左移，若low不越界则直接返回low,否则表示该值不存在int BinarySearchMinIndexMoreThanKey(int nArr[], int nLength, int key){int nLow = 0;int nHigh = nLength - 1;int nMid = 0;while (nLow <= nHigh){nMid = nLow + ((nHigh - nLow) >> 1);if (nArr[nMid] > key){nHigh = nMid - 1;}else//相等向右移{nLow = nMid + 1;}}if (nLow >= 0 && nLow < nLength){return nLow;}else{return -1;}}void Mix(int nArr[], int nLength, int key){cout << "找到任一" << key << "的位置：" << BinarySearchAnyKey(nArr, nLength, key) << endl;cout << "找到第一次出现" << key << "的位置：" << BinarySearchFirstKey(nArr, nLength, key) << endl;cout << "找到最大的小于" << key << "的数的位置：" << BinarySearchMaxIndexLessThanKey(nArr, nLength, key) << endl;cout << "找到最后一次出现" << key << "的位置：" << BinarySearchLastKey(nArr, nLength, key) << endl;cout << "找到最小的大于" << key << "的数的位置：" << BinarySearchMinIndexMoreThanKey(nArr, nLength, key) << endl << endl;}int _tmain(int argc, _TCHAR* argv[]){int nArr[8] = {2,3,3,3,3,5,6,7};    Mix(nArr, 8, 3);    Mix(nArr, 8, 4);system("pause");return 0;}

运行结果：