动态规划练习 8

题目：Palindrome (POJ 1159)

链接：http://acm.pku.edu.cn/JudgeOnline/problem?id=1159

#include <iostream>
#include <string>
#include <memory.h>
#include <algorithm>

using namespace std;

short min_fix[5001][5001];

int min_fix_char_recursion(const char *input, int i, int j)
{
    if (i < j)
    {
        if (input[i] != input[j])
        {
            return min(
                min_fix_char_recursion(input, i + 1, j),
                min_fix_char_recursion(input, i, j - 1)) + 1;
        }
        else
        {
            return min_fix_char_recursion(input, i + 1, j - 1);
        }
    }

    return 0;
}

int main(int argc, char **argv)
{
    int n;
    string input;

    cin >> n;
    cin >> input;

    memset(min_fix, 0, sizeof(min_fix));

    if (input.size() >= 3 && input.size() <= 5000)
    {
        // recursion version.
        // cout << min_fix_char_recursion(input.c_str(), 0, input.size() - 1) << endl;
        // recursion ends at any positions in input string.
        // so, dp begins at any positions in input string.
        for (int i = (int)input.size() - 1; i >= 0; --i)
        {
            for (int j = i + 1; j < (int)input.size(); ++j)
            {
                if (input[i] == input[j])
                {
                    min_fix[i][j] = min_fix[i + 1][j - 1];
                }
                else
                {
                    min_fix[i][j] = min(min_fix[i + 1][j], min_fix[i][j - 1]) + 1;
                }
            }
        }

        cout << min_fix[0][input.size() - 1] << endl;
    }

    return 0;
}