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/**
 * Given s1, s2, s3, find whether s3 is formed by the interleaving of s1 and s2.
 * For example,
 * Given:
 * s1 = "aabcc",
 * s2 = "dbbca",
 * When s3 = "aadbbcbcac", return true.
 * When s3 = "aadbbbaccc", return false.
 */
public class Solution {
    public boolean isInterleave(String s1, String s2, String s3) {
        if(s1.length() + s2.length() != s3.length())
            return false;
        boolean[][] matched = new boolean[s1.length() + 1][s2.length() + 1];
        matched[0][0] = true;
        // initialization 
        for(int i1 = 1; i1 <= s1.length(); i1++) {
            if(s3.charAt(i1 - 1) == s1.charAt(i1 - 1))
                matched[i1][0] = true;
            else
                break;
        }
        for(int i2 = 1; i2 <= s2.length(); i2++) {
            if(s3.charAt(i2 - 1) == s2.charAt(i2 - 1))
                matched[0][i2] = true;
            else
                break;
        }
        for(int i1 = 1; i1 <= s1.length(); i1++) {
            char c1 = s1.charAt(i1 - 1);
            for(int i2 = 1; i2 <= s2.length(); i2++) {
                int i3 = i1 + i2;
                char c2 = s2.charAt(i2 - 1);
                char c3 = s3.charAt(i3 - 1);
                if(c1 == c3) 
                    matched[i1][i2] |= matched[i1 - 1][i2];
                if(c2 == c3)
                    matched[i1][i2] |= matched[i1][i2 - 1];
            }
        }
        return matched[s1.length()][s2.length()];
    }
}