hdu 1159/poj1458 Common Subsequence 最长公共子串

最新推荐文章于 2020-02-07 11:05:28 发布

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本文探讨了最大公共子序列问题的解决方法，通过动态规划（DP）算法求解并提供了一个实例代码。重点阐述了算法背后的逻辑、核心步骤及应用实例。

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Common Subsequence

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 28707 Accepted Submission(s): 12830

Problem Description

A subsequence of a given sequence is the given sequence with some elements (possible none) left out. Given a sequence X = <x1, x2, ..., xm> another sequence Z = <z1, z2, ..., zk> is a subsequence of X if there exists a strictly increasing sequence <i1, i2, ..., ik> of indices of X such that for all j = 1,2,...,k, xij = zj. For example, Z = <a, b, f, c> is a subsequence of X = <a, b, c, f, b, c> with index sequence <1, 2, 4, 6>. Given two sequences X and Y the problem is to find the length of the maximum-length common subsequence of X and Y.
The program input is from a text file. Each data set in the file contains two strings representing the given sequences. The sequences are separated by any number of white spaces. The input data are correct. For each set of data the program prints on the standard output the length of the maximum-length common subsequence from the beginning of a separate line.

Sample Input

abcfbc abfcab
programming contest 
abcd mnp

Sample Output

4
2
0

经典题。

dp方程如下：

for (int i=0; i<len1; i++) {
            for (int j=0; j<len2; j++) {
                if(s1[i]==s2[j]) lcs[i+1][j+1]=lcs[i][j]+1;
                else lcs[i+1][j+1]=max(lcs[i+1][j],lcs[i][j+1]);
            }
        }

#include <algorithm>
#include <iostream>
#include <sstream>
#include <cstring>
#include <cstdlib>
#include <string>
#include <vector>
#include <cstdio>
#include <cmath>
#include <queue>
#include <stack>
#include <map>
#include <set>
using namespace std;
#define Max 200005

string s1,s2;
int lcs[1000][1000];

int main(){
    int len1,len2;
    while (cin>>s1>>s2) {
        len1=s1.length();
        len2=s2.length();
        memset(lcs,0, sizeof(lcs));
        for (int i=0; i<len1; i++) {
            for (int j=0; j<len2; j++) {
                if(s1[i]==s2[j]) lcs[i+1][j+1]=lcs[i][j]+1;
                else lcs[i+1][j+1]=max(lcs[i+1][j],lcs[i][j+1]);
            }
        }
        cout<<lcs[len1][len2]<<endl;
    }
    
    return 0;
}