Longest Common Subsequence (Java)

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The longest common subsequence (LCS) problem is the problem of finding the longest subsequence common to all sequences in a set of sequences (often just two sequences).

Analysis

Let dp[i+1][j+1] be the length of the longest common subsequence of string a & b, when a[i] and b[j] are compared to each other. (0<=i<=a.length-1, 0<=j<=b.length-1) longest-common-subsequence-java

Java Solution

public static int getLongestCommonSubsequence(String a, String b){
	int m = a.length();
	int n = b.length();
	int[][] dp = new int[m+1][n+1];
 
	for(int i=0; i<=m; i++){
		for(int j=0; j<=n; j++){
			if(i==0 || j==0){
				dp[i][j]=0;
			}else if(a.charAt(i-1)==b.charAt(j-1)){
				dp[i][j] = 1 + dp[i-1][j-1];
			}else{
				dp[i][j] = Math.max(dp[i-1][j], dp[i][j-1]);
			}
		}
	}
 
	return dp[m][n];
}

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