DP-LCS

最长公共子串LCS的使用

 

public class DP_LCS {
    public static void main(String[] args) {
        char[] A = {'s','a','d','s','t','o','r','y'};
        char[] B = {'a','d','m','i','n','s','t','o','r','y'};

        int dp[][] = new int[A.length+1][B.length+1];
        for(int i = 0;i<dp.length;i++){
            dp[i][0] = 0;
        }
        for (int j = 0;j<dp[0].length;j++){
            dp[0][j] = 0;
        }
        //dp[4][6]表示asds admins的LCS长度
        //假如A[4] == B[6]  dp[4][6] = dp[3][5]+1
        //否则dp[4][6] = max(dp[3][6],dp[4][5])
        //dp[3][6]为asd和admins
        //dp[4][5]为asds和admin
        for (int i = 1;i<A.length;i++){
            for (int j = 1;j<B.length;j++){
                if(A[i] == B[j]){
                    dp[i][j] = dp[i-1][j-1]+1;
                }else{
                    //这是为什么不是直接赋值以上的
                    //dp[i][j] = dp[i-1][j-1];
                    dp[i][j] = Integer.max(dp[i-1][j],dp[i][j-1]);
                }
                //System.out.println("i:"+i+" j: "+j+" dp: "+dp[i][j]);
            }
        }
        System.out.println(dp[A.length-1][B.length-1]);
    }
}