algorithm-class/MCA算法突击课/第01期/mca_test/Code01_PalindromeSubsequence.java

package 第01期.mca_test;

// 测试链接：https://leetcode.com/problems/longest-palindromic-subsequence/
public class Code01_PalindromeSubsequence {

	public static int lpsl1(String s) {
		if (s == null || s.length() == 0) {
			return 0;
		}
		char[] str = s.toCharArray();
		return f(str, 0, str.length - 1);
	}

	// str[L..R]最长回文子序列长度返回
	public static int f(char[] str, int L, int R) {
		if (L == R) {
			return 1;
		}
		if (L == R - 1) {
			return str[L] == str[R] ? 2 : 1;
		}
		int p1 = f(str, L + 1, R - 1);
		int p2 = f(str, L, R - 1);
		int p3 = f(str, L + 1, R);
		int p4 = str[L] != str[R] ? 0 : (2 + f(str, L + 1, R - 1));
		return Math.max(Math.max(p1, p2), Math.max(p3, p4));
	}

	public static int lpsl2(String s) {
		if (s == null || s.length() == 0) {
			return 0;
		}
		char[] str = s.toCharArray();
		int N = str.length;
		int[][] dp = new int[N][N];
		dp[N - 1][N - 1] = 1;
		for (int i = 0; i < N - 1; i++) {
			dp[i][i] = 1;
			dp[i][i + 1] = str[i] == str[i + 1] ? 2 : 1;
		}
		for (int L = N - 3; L >= 0; L--) {
			for (int R = L + 2; R < N; R++) {
				dp[L][R] = Math.max(dp[L][R - 1], dp[L + 1][R]);
				if (str[L] == str[R]) {
					dp[L][R] = Math.max(dp[L][R], 2 + dp[L + 1][R - 1]);
				}
			}
		}
		return dp[0][N - 1];
	}

	public static int longestPalindromeSubseq1(String s) {
		if (s == null || s.length() == 0) {
			return 0;
		}
		if (s.length() == 1) {
			return 1;
		}
		char[] str = s.toCharArray();
		char[] reverse = reverse(str);
		return longestCommonSubsequence(str, reverse);
	}

	public static char[] reverse(char[] str) {
		int N = str.length;
		char[] reverse = new char[str.length];
		for (int i = 0; i < str.length; i++) {
			reverse[--N] = str[i];
		}
		return reverse;
	}

	public static int longestCommonSubsequence(char[] str1, char[] str2) {
		int N = str1.length;
		int M = str2.length;
		int[][] dp = new int[N][M];
		dp[0][0] = str1[0] == str2[0] ? 1 : 0;
		for (int i = 1; i < N; i++) {
			dp[i][0] = str1[i] == str2[0] ? 1 : dp[i - 1][0];
		}
		for (int j = 1; j < M; j++) {
			dp[0][j] = str1[0] == str2[j] ? 1 : dp[0][j - 1];
		}
		for (int i = 1; i < N; i++) {
			for (int j = 1; j < M; j++) {
				dp[i][j] = Math.max(dp[i - 1][j], dp[i][j - 1]);
				if (str1[i] == str2[j]) {
					dp[i][j] = Math.max(dp[i][j], dp[i - 1][j - 1] + 1);
				}
			}
		}
		return dp[N - 1][M - 1];
	}

	public static int longestPalindromeSubseq2(String s) {
		if (s == null || s.length() == 0) {
			return 0;
		}
		if (s.length() == 1) {
			return 1;
		}
		char[] str = s.toCharArray();
		int N = str.length;
		int[][] dp = new int[N][N];
		dp[N - 1][N - 1] = 1;
		for (int i = 0; i < N - 1; i++) {
			dp[i][i] = 1;
			dp[i][i + 1] = str[i] == str[i + 1] ? 2 : 1;
		}
		for (int i = N - 3; i >= 0; i--) {
			for (int j = i + 2; j < N; j++) {
				dp[i][j] = Math.max(dp[i][j - 1], dp[i + 1][j]);
				if (str[i] == str[j]) {
					dp[i][j] = Math.max(dp[i][j], dp[i + 1][j - 1] + 2);
				}
			}
		}
		return dp[0][N - 1];
	}

}