可删除某些字符的最长回文字符串(2016腾讯在线笔试题)

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输入:amka时,删除字符m可以得到最长回文字符串aka,则输出3

输入:abcddcka,删除b和k时,acddca是最长回文字符串,输出6

思路:用两个指针,一个指向字符串一个字符,一个指向字符串最后一个字符,

如果两个字符串相等,如abcda,时就进行递归看bcd中的最长回文字符串

如果不想等,就找abcd,和bcda中的最长回文字符串

对于递归的公共子问题,用动态规划解决

程序如下:

#include"stdafx.h"#include<iostream>#include<stdlib.h>#include<stdio.h>using namespace std;int Length_record[1000][1000];int max(int a, int b){return a > b ? a : b;}int number_of_reverse(char* str, int start, int end, int crruentLength, int &max_Length){if (Length_record[start][end] != -1){if (crruentLength + Length_record[start][end] > max_Length)max_Length = crruentLength + Length_record[start][end];return Length_record[start][end];}if (Length_record[start][end] == -1){if (start == end){crruentLength++;if (crruentLength > max_Length)max_Length = crruentLength;Length_record[start][end] = 1;}if (end - start == 1){if (str[start] == str[end]){crruentLength += 2;Length_record[start][end] = 2;}else{crruentLength++;Length_record[start][end] = 1;}if (crruentLength > max_Length)max_Length = crruentLength;}if (end - start > 1){if (str[end] == str[start])Length_record[start][end]=2+number_of_reverse(str, start + 1, end - 1, crruentLength + 2, max_Length);else{Length_record[start][end] =max( number_of_reverse(str, start, end - 1, crruentLength, max_Length), number_of_reverse(str, start + 1, end, crruentLength, max_Length));}}}return Length_record[start][end];}int number_of_delete(char *str){if (str == NULL)cout << "0" << endl;int nLength = strlen(str);int max_Length = 0;number_of_reverse(str, 0, nLength - 1, 0, max_Length);return max_Length;}int main(){memset(Length_record, -1, sizeof(Length_record));char str[1000];cin >> str;int a = number_of_delete(str);cout << a << endl;}