有关回文数的一个问题

[问题表述]

给定了一个字符串s 和一个最大修改次数max
只能修改s中的字符，最多修改max次

定义回文分数：
如果s不是回文，则为0
否则：
若s长度是奇数，分数为1
若s长度是偶数，分数为s的一半字串的回文分数+1
 
求能得到的最大回文分数 

 

[思想]：见代码，通过循环(当然递归的方式也可以解决，总体是改进的折半的思想)，已经解决，64－79行代码很重要

/* 2. * main.cpp 3. * 4. * Created on: 2009-6-22 5. * Author: NeeSky 6. */#include <iostream> #include <string> using namespace std;//Marco Definitioon #define MaxSize 100 //Global change times bool MarkChanged[MaxSize]; bool NowMarkArray[MaxSize];/*** * Reset the Gloabl Array to false */void ResetMarkArray(bool *p){for(int i=0;i<MaxSize;++i){p[i]=false;}return;}/*** * Store the result to MarkArray（mainly from NowMarkArray） */void StoreNowPolicy(bool *p, int N) {for (int i = 0; i < N; ++i) {MarkChanged[i] = p[i];}return;}/*** * Statistic the change times from bool array(mainly from NowMarkArray) */int getTimes_fromBoolArray(bool *p, int N) {int sum = 0;for (int i = 0; i < N; ++i) {if (p[i]==true)++sum;}return sum;}/*** * Probe the Palindromic Numbers ,process the pStr Array */int ProbePalindromic(string strProblem,int MaxChangedTimes) {char *pStr=&strProblem[0];int N=strProblem.length();int Score=0;int head = 0;int tail = N - 1;ResetMarkArray(NowMarkArray);ResetMarkArray(MarkChanged);bool firstwhile = true;while (head <= tail) {int start = head;int end = tail;while (start < end) {if (pStr[start] != pStr[end]) //Need change {if ((head+tail)%2==1) {if (pStr[start]==pStr[((head+tail)/2-start)]) {pStr[end]=pStr[start]; //change itNowMarkArray[end] = true;if (!firstwhile)NowMarkArray[N - end - 1] = true;} else {pStr[start]=pStr[end]; //change itNowMarkArray[start] = true;if (!firstwhile)NowMarkArray[N - start - 1] = true;}} else {pStr[start]=pStr[end]; //change itNowMarkArray[start] = true;}}++start;--end;}if (getTimes_fromBoolArray(NowMarkArray, N) <= MaxChangedTimes) {StoreNowPolicy(NowMarkArray, N); //store the result ++Score;if ((head+tail)%2==0)break;elsetail = (head + tail) / 2; // continue half probe } elsebreak;firstwhile = false;}return Score;}int main(void) {string strA = "coder";cout<<strA<<"< MaxChange 2>:"<<" Score－"<<ProbePalindromic(strA, 2)<<endl;strA = "abcbxabcba";cout<<strA<<"< MaxChange 1>:"<<" Score－"<<ProbePalindromic(strA, 1)<<endl;strA = "ssssssssssssssss";cout<<strA<<"< MaxChange 15>:"<<" Score－"<<ProbePalindromic(strA, 15)<<endl;strA = "vyyvvzzvvxxvvxxv";cout<<strA<<"< MaxChange 4>:"<<" Score－"<<ProbePalindromic(strA, 4)<<endl;strA = "a";cout<<strA<<"< MaxChange 0>:"<<" Score－"<<ProbePalindromic(strA, 0)<<endl;strA="abcdaagcda";cout<<strA<<"< MaxChange 2>:"<<" Score－"<<ProbePalindromic(strA, 2)<<endl;return 0;}

 

 

[输出]：

coder    < MaxChange 2>:     Score－1
abcbxabcba    < MaxChange 1>:     Score－2
ssssssssssssssss    < MaxChange 15>:     Score－5
vyyvvzzvvxxvvxxv    < MaxChange 4>:     Score－3
a    < MaxChange 0>:     Score－1
abcdaagcda    < MaxChange 2>:     Score－2

 

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之前的abcdaagcda    < MaxChange 2>:     Score－1    //此处明显应该为2－－－该问题已经解决