Palindrome subsequence

最新推荐文章于 2021-04-20 23:30:50 发布

原创最新推荐文章于 2021-04-20 23:30:50 发布 · 433 阅读

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本文介绍了一种计算字符串中回文子序列数量的算法。通过动态规划方法，该算法能够有效地找出任意长度的回文子序列，并适用于多种编程竞赛场景。

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Palindrome subsequence

Problem Description

In mathematics, a subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements. For example, the sequence

#include<iostream>
#include<iomanip>
#include<cstring>
#include<string>
#include<cstdio>
#include<algorithm>
using namespace std;
#define mod 10007
char str[1005];
int dp[1005][1005];
int main()
{
    int t, i, j, k, len;
    int cnt = 1;
    scanf("%d", &t);
    //getchar();
    while (t--)
    {
        scanf("%s", str);
        len = strlen(str);
        for (int i = 0; i < len; i++)
        {
            dp[i][i] = 1;
        }

        for (i = 1; i < len; i++)
        {
            for (j = i - 1; j >= 0; j--)
            {

                    dp[j][i] = (dp[j + 1][i] + dp[j][i - 1] - dp[j + 1][i - 1] + mod) % mod;

                if (str[i] == str[j])
                {
                    dp[j][i] = (dp[j][i] + dp[j + 1][i - 1] + 1 + mod) % mod;
                }
            }
        }
        printf("Case %d: %d\n", cnt++, dp[0][len - 1]);
    }
    return 0;

 }