最长公共子序列

思路：把两个序列的最后一位数进行比较 相等就令公共子序列长度+1，然后再令序列长度减少1再继续比较，如果不相等就分别令其中一个序列长度-1再继续比较，先看递归方式会很好理解

static int[][] memo = new int[1000][1000];
	static int[][] dp = new int[1000][1000];
	//暴力递归
	static int longest(char[] x, char[] y, int lenX, int lenY) {
		if(lenX == -1 || lenY == -1)
			return 0;
		if(x[lenX] == y[lenY]) {
			return longest(x, y, lenX-1,lenY-1)+1;
		}
		return Math.max(longest(x,y,lenX-1, lenY), longest(x,y,lenX,lenY-1));
	}
	//记忆化搜索
	static int longestMemo(char[] x, char[] y, int lenX, int lenY) {
		if(lenX == -1 || lenY == -1)
			return 0;
		else if(x[lenX] == y[lenY]) 
			memo[lenX][lenY] = longestMemo(x, y, lenX-1,lenY-1)+1;
		else
			memo[lenX][lenY] = Math.max(longestMemo(x,y,lenX-1, lenY), longestMemo(x,y,lenX,lenY-1));
		return memo[lenX][lenY];
	}
	//dp
	static void longestDp(char[] x, char[] y, int lenX, int lenY){
		for(int i = 0; i <= lenX; i++) {
			for(int j = 0; j <= lenY;j++) {
				if(x[i] == y[j])
					dp[i+1][j+1] = dp[i][j] + 1;
				else
					dp[i+1][j+1] = Math.max(dp[i][j+1], dp[i+1][j]);
			}
		}
		System.out.println(dp[lenX+1][lenY+1]);
	}
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		String X = sc.nextLine();
		String Y = sc.nextLine();
		System.out.println(longest(X.toCharArray(), Y.toCharArray(), X.length()-1, Y.length()-1));
		System.out.println(longestMemo(X.toCharArray(), Y.toCharArray(), X.length()-1, Y.length()-1));;
		longestDp(X.toCharArray(), Y.toCharArray(), X.length()-1, Y.length()-1);		
		//ABCBDAB
		//BDCABA
	}

我本人做dp的题目 习惯性:暴力递归->记忆化搜索->dp

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