最长公共子序列

最新推荐文章于 2025-05-24 12:00:00 发布

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本文介绍了一种求解两个字符序列最长公共子序列(LCS)的算法实现过程。通过动态规划方法，构造二维数组来记录中间结果，并利用辅助数组追踪回溯路径，最终返回最长公共子序列。

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class Solution
{
    public int[][] LCSLength(char []a, char []b)
    {
        int lenA = a.length;
        int lenB = b.length;
        int [][]dp = new int[lenA+1][lenB+1];
        int [][]flag = new int[lenA+1][lenB+1];
        for(int i=1; i<=lenA; i++)
        {
            for(int j=1; j<=lenB; j++)
            {
                if(a[i-1] == b[j-1]) 
                {
                    dp[i][j] = dp[i-1][j-1]+1;
                    flag[i][j] = 1;
                }
                else if(dp[i-1][j] >= dp[i][j-1])
                {
                    dp[i][j] = dp[i-1][j];
                    flag[i][j] = 2;
                }
                else 
                {
                    dp[i][j] = dp[i][j-1];
                    flag[i][j] = 3;
                }
            }
        }
        return flag;
    }
    public String LCS(char []a, int i, int j, int [][]flag)
    {
        if(i==0 || j==0) return "";
        if(flag[i][j] == 1) return LCS(a, i-1, j-1, flag) + a[i-1];
        else if(flag[i][j] == 2) return LCS(a, i-1, j, flag);
        else return LCS(a, i, j-1, flag);
    }
}