import java.util.Arrays;

/**
 * Given s1, s2, s3, find whether s3 is formed by the interleaving of s1 and s2.
 *
 * Example 1:
 * Input: s1 = "aabcc", s2 = "dbbca", s3 = "aadbbcbcac"
 * Output: true
 *
 * Example 2:
 * Input: s1 = "aabcc", s2 = "dbbca", s3 = "aadbbbaccc"
 * Output: false
 *
 * Approach: Dynamic programming O(n^2) time and memory.
 */
public class InterleavingString {
    public boolean isInterleave(String s1, String s2, String s3) {
        if (s3.length() != s1.length() + s2.length()) {
            return false;
        }
        boolean dp[][] = new boolean[s1.length() + 1][s2.length() + 1];
        for (int i = 0; i <= s1.length(); i++) {
            for (int j = 0; j <= s2.length(); j++) {
                if (i == 0 && j == 0) {
                    dp[i][j] = true;
                } else if (i == 0) {
                    dp[i][j] = dp[i][j - 1] && s2.charAt(j - 1) == s3.charAt(i + j - 1);
                } else if (j == 0) {
                    dp[i][j] = dp[i - 1][j] && s1.charAt(i - 1) == s3.charAt(i + j - 1);
                } else {
                    dp[i][j] = (dp[i - 1][j] && s1.charAt(i - 1) == s3.charAt(i + j - 1)) || (dp[i][j - 1] && s2.charAt(j - 1) == s3.charAt(i + j - 1));
                }
            }
        }
        return dp[s1.length()][s2.length()];
    }

}
