LeetCode——1143.最长公共子序列【LCS & 标准代码、空间压缩】

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题解

• 标准的LCS，两套代码，一套标准LCS，一套空间压缩
• 标准代码可以直接通过b数组逆推路径

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AC-Code

• 标准LCS

class Solution {
public:
	int longestCommonSubsequence(string text1, string text2) {
		int len1 = text1.length();
		int len2 = text2.length();
		
		int** dp = new int* [len1 + 1];
		for (int i = 0; i <= len1; ++i) {
			dp[i] = new int[len2 + 1];
			memset(dp[i], 0, sizeof(int) * (len2 + 1));
		}
	/*
		int** b = new int* [len1 + 1];
		for (int i = 0; i <= len1; ++i) {
			b[i] = new int[len2 + 1];
			memset(b[i], 0, sizeof(int) * (len2 + 1));
		}
	*/
		for (int i = 1; i <= len1; ++i) {
			for (int j = 1; j <= len2; ++j) {
				if (text1[i - 1] == text2[j - 1]) {
					dp[i][j] = dp[i - 1][j - 1] + 1;
				//	b[i][j] = 1;    // 左上
				}
				else if (dp[i - 1][j] >= dp[i][j - 1]) {
					dp[i][j] = dp[i - 1][j];
				//	b[i][j] = 3;    // 上
				}
				else {
					dp[i][j] = dp[i][j - 1];
				//	b[i][j] = 2;    // 左
				}

			}
		}

		return dp[len1][len2];
	}
};

• 空间压缩

class Solution {
public:
	int longestCommonSubsequence(string text1, string text2) {
        int len1 = text1.length();
        int len2 = text2.length();
        
		int *dp = new int[len2 + 1];
        memset(dp, 0, sizeof(int) * (len2 + 1));
        
        for(int i = 1; i <= len1; ++i){
            int last = 0;   // dp[i - 1][j - 1]
            for(int j = 1; j <= len2; ++j){
                int temp = dp[j];   // dp[i - 1][j]
                if(text1[i - 1] == text2[j - 1])    dp[j] = last + 1;   // 改完后,dp[j]表示dp[i][j]
                else    dp[j] = max(dp[j - 1], dp[j]);
                last = temp;    // 每次更新last，确保在下一次迭代时，last指向的是那个状态的dp[i - 1][j - 1]
            }
        }
        return dp[len2];
	}
};