import java.util.Arrays;

public class StringDistances {

	// https://en.wikipedia.org/wiki/Longest_common_subsequence_problem
	public static int[] getLCS(int[] x, int[] y) {
		int m = x.length;
		int n = y.length;
		int[][] lcs = new int[m + 1][n + 1];
		for (int i = 0; i < m; i++) {
			for (int j = 0; j < n; j++) {
				if (x[i] == y[j]) {
					lcs[i + 1][j + 1] = lcs[i][j] + 1;
				} else {
					lcs[i + 1][j + 1] = Math.max(lcs[i + 1][j], lcs[i][j + 1]);
				}
			}
		}
		int cnt = lcs[m][n];
		int[] res = new int[cnt];
		for (int i = m - 1, j = n - 1; i >= 0 && j >= 0; ) {
			if (x[i] == y[j]) {
				res[--cnt] = x[i];
				--i;
				--j;
			} else if (lcs[i + 1][j] > lcs[i][j + 1]) {
				--j;
			} else {
				--i;
			}
		}
		return res;
	}

	// https://en.wikipedia.org/wiki/Levenshtein_distance
	public static int getLevensteinDistance(String a, String b) {
		int m = a.length();
		int n = b.length();
		int[][] len = new int[m + 1][n + 1];
		for (int i = 0; i <= m; i++) {
			len[i][0] = i;
		}
		for (int j = 0; j <= n; j++) {
			len[0][j] = j;
		}
		for (int i = 0; i < m; i++) {
			for (int j = 0; j < n; j++) {
				if (a.charAt(i) == b.charAt(j)) {
					len[i + 1][j + 1] = len[i][j];
				} else {
					len[i + 1][j + 1] = 1 + Math.min(len[i][j], Math.min(len[i + 1][j], len[i][j + 1]));
				}
			}
		}
		return len[m][n];
	}

	// Usage example
	public static void main(String[] args) {
		int[] x = {1, 5, 4, 2, 3, 7, 6};
		int[] y = {2, 7, 1, 3, 5, 4, 6};
		int[] lcs = getLCS(x, y);
		System.out.println(Arrays.toString(lcs));

		String a = "abc";
		String b = "ac";
		System.out.println(getLevensteinDistance(a, b));
	}
}