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1143. Longest Common Subsequence

Description

Given two strings text1 and text2, return the length of their longest common subsequence. If there is no common subsequence, return 0.

A subsequence of a string is a new string generated from the original string with some characters (can be none) deleted without changing the relative order of the remaining characters.

  • For example, "ace" is a subsequence of "abcde".

A common subsequence of two strings is a subsequence that is common to both strings.

 

Example 1:

Input: text1 = "abcde", text2 = "ace" 
Output: 3  
Explanation: The longest common subsequence is "ace" and its length is 3.

Example 2:

Input: text1 = "abc", text2 = "abc"
Output: 3
Explanation: The longest common subsequence is "abc" and its length is 3.

Example 3:

Input: text1 = "abc", text2 = "def"
Output: 0
Explanation: There is no such common subsequence, so the result is 0.

 

Constraints:

  • 1 <= text1.length, text2.length <= 1000
  • text1 and text2 consist of only lowercase English characters.

Solutions

Solution 1: Dynamic Programming

We define \(f[i][j]\) as the length of the longest common subsequence of the first \(i\) characters of \(text1\) and the first \(j\) characters of \(text2\). Therefore, the answer is \(f[m][n]\), where \(m\) and \(n\) are the lengths of \(text1\) and \(text2\), respectively.

If the \(i\)th character of \(text1\) and the \(j\)th character of \(text2\) are the same, then \(f[i][j] = f[i - 1][j - 1] + 1\); if the \(i\)th character of \(text1\) and the \(j\)th character of \(text2\) are different, then \(f[i][j] = max(f[i - 1][j], f[i][j - 1])\). The state transition equation is:

\[ f[i][j] = \begin{cases} f[i - 1][j - 1] + 1, & \textit{if } text1[i - 1] = text2[j - 1] \\ \max(f[i - 1][j], f[i][j - 1]), & \textit{if } text1[i - 1] \neq text2[j - 1] \end{cases} \]

The time complexity is \(O(m \times n)\), and the space complexity is \(O(m \times n)\). Here, \(m\) and \(n\) are the lengths of \(text1\) and \(text2\), respectively.

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class Solution:
    def longestCommonSubsequence(self, text1: str, text2: str) -> int:
        m, n = len(text1), len(text2)
        f = [[0] * (n + 1) for _ in range(m + 1)]
        for i in range(1, m + 1):
            for j in range(1, n + 1):
                if text1[i - 1] == text2[j - 1]:
                    f[i][j] = f[i - 1][j - 1] + 1
                else:
                    f[i][j] = max(f[i - 1][j], f[i][j - 1])
        return f[m][n]

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class Solution {
    public int longestCommonSubsequence(String text1, String text2) {
        int m = text1.length(), n = text2.length();
        int[][] f = new int[m + 1][n + 1];
        for (int i = 1; i <= m; ++i) {
            for (int j = 1; j <= n; ++j) {
                if (text1.charAt(i - 1) == text2.charAt(j - 1)) {
                    f[i][j] = f[i - 1][j - 1] + 1;
                } else {
                    f[i][j] = Math.max(f[i - 1][j], f[i][j - 1]);
                }
            }
        }
        return f[m][n];
    }
}

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class Solution {
public:
    int longestCommonSubsequence(string text1, string text2) {
        int m = text1.size(), n = text2.size();
        int f[m + 1][n + 1];
        memset(f, 0, sizeof f);
        for (int i = 1; i <= m; ++i) {
            for (int j = 1; j <= n; ++j) {
                if (text1[i - 1] == text2[j - 1]) {
                    f[i][j] = f[i - 1][j - 1] + 1;
                } else {
                    f[i][j] = max(f[i - 1][j], f[i][j - 1]);
                }
            }
        }
        return f[m][n];
    }
};

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func longestCommonSubsequence(text1 string, text2 string) int {
    m, n := len(text1), len(text2)
    f := make([][]int, m+1)
    for i := range f {
        f[i] = make([]int, n+1)
    }
    for i := 1; i <= m; i++ {
        for j := 1; j <= n; j++ {
            if text1[i-1] == text2[j-1] {
                f[i][j] = f[i-1][j-1] + 1
            } else {
                f[i][j] = max(f[i-1][j], f[i][j-1])
            }
        }
    }
    return f[m][n]
}

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function longestCommonSubsequence(text1: string, text2: string): number {
    const m = text1.length;
    const n = text2.length;
    const f = Array.from({ length: m + 1 }, () => Array(n + 1).fill(0));
    for (let i = 1; i <= m; i++) {
        for (let j = 1; j <= n; j++) {
            if (text1[i - 1] === text2[j - 1]) {
                f[i][j] = f[i - 1][j - 1] + 1;
            } else {
                f[i][j] = Math.max(f[i - 1][j], f[i][j - 1]);
            }
        }
    }
    return f[m][n];
}

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impl Solution {
    pub fn longest_common_subsequence(text1: String, text2: String) -> i32 {
        let (m, n) = (text1.len(), text2.len());
        let (text1, text2) = (text1.as_bytes(), text2.as_bytes());
        let mut f = vec![vec![0; n + 1]; m + 1];
        for i in 1..=m {
            for j in 1..=n {
                f[i][j] = if text1[i - 1] == text2[j - 1] {
                    f[i - 1][j - 1] + 1
                } else {
                    f[i - 1][j].max(f[i][j - 1])
                };
            }
        }
        f[m][n]
    }
}

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/**
 * @param {string} text1
 * @param {string} text2
 * @return {number}
 */
var longestCommonSubsequence = function (text1, text2) {
    const m = text1.length;
    const n = text2.length;
    const f = Array.from({ length: m + 1 }, () => Array(n + 1).fill(0));
    for (let i = 1; i <= m; ++i) {
        for (let j = 1; j <= n; ++j) {
            if (text1[i - 1] == text2[j - 1]) {
                f[i][j] = f[i - 1][j - 1] + 1;
            } else {
                f[i][j] = Math.max(f[i - 1][j], f[i][j - 1]);
            }
        }
    }
    return f[m][n];
};

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public class Solution {
    public int LongestCommonSubsequence(string text1, string text2) {
        int m = text1.Length, n = text2.Length;
        int[,] f = new int[m + 1, n + 1];
        for (int i = 1; i <= m; ++i) {
            for (int j = 1; j <= n; ++j) {
                if (text1[i - 1] == text2[j - 1]) {
                    f[i, j] = f[i - 1, j - 1] + 1;
                } else {
                    f[i, j] = Math.Max(f[i - 1, j], f[i, j - 1]);
                }
            }
        }
        return f[m, n];
    }
}

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class Solution {
    fun longestCommonSubsequence(text1: String, text2: String): Int {
        val m = text1.length
        val n = text2.length
        val f = Array(m + 1) { IntArray(n + 1) }
        for (i in 1..m) {
            for (j in 1..n) {
                if (text1[i - 1] == text2[j - 1]) {
                    f[i][j] = f[i - 1][j - 1] + 1
                } else {
                    f[i][j] = Math.max(f[i - 1][j], f[i][j - 1])
                }
            }
        }
        return f[m][n]
    }
}

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