Detailed explanation of the longest common subsequence algorithm in PHP

Detailed explanation of the longest common subsequence algorithm in PHP

The longest common subsequence (LCS) is a common string matching algorithm, which is mainly used to compare two strings similarity. In PHP, the LCS algorithm can be implemented through the idea of ​​dynamic programming. The principle and code implementation of the algorithm will be introduced in detail below.

1. Algorithm principle
   The core idea of ​​the longest common subsequence algorithm is that for any two strings X and Y, find the longest common subsequence L such that L is the sum of A subsequence of Y, and there is no common subsequence longer than L. Under the idea of ​​dynamic programming, we can use a two-dimensional array dpi to represent the length of the longest common subsequence of the first i characters of string X and the first j characters of string Y.

Specifically, we can follow the following steps to solve for the longest common subsequence:
1) Initialize a dp array, where dpi represents the first i characters of the string The length of the longest common subsequence of the first j characters of Y.
2) Traverse each character of strings X and Y. If X[i] is equal to Y[j], then the value of dpi can be obtained by dpi-1 1; otherwise, the value of dpi is dpi-1 and The larger value in dpi.
3) Finally, dpm is the length of the longest common subsequence of strings X and Y, where m and n are the lengths of strings X and Y.

2. Code implementation
   The following is a code example that uses the PHP language to implement the longest common subsequence algorithm:

function LCS($str1, $str2)
{
    $m = strlen($str1);
    $n = strlen($str2);

    $dp = array();
    for ($i = 0; $i <= $m; $i++) {
        $dp[$i][0] = 0;
    }
    for ($j = 0; $j <= $n; $j++) {
        $dp[0][$j] = 0;
    }

    for ($i = 1; $i <= $m; $i++) {
        for ($j = 1; $j <= $n; $j++) {
            if ($str1[$i - 1] == $str2[$j - 1]) {
                $dp[$i][$j] = $dp[$i - 1][$j - 1] + 1;
            } else {
                $dp[$i][$j] = max($dp[$i - 1][$j], $dp[$i][$j - 1]);
            }
        }
    }

    $lcs = '';
    $i = $m;
    $j = $n;
    while ($i > 0 && $j > 0) {
        if ($str1[$i - 1] == $str2[$j - 1]) {
            $lcs = $str1[$i - 1] . $lcs;
            $i--;
            $j--;
        } elseif ($dp[$i - 1][$j] > $dp[$i][$j - 1]) {
            $i--;
        } else {
            $j--;
        }
    }

    return $lcs;
}

$str1 = "abcdefg";
$str2 = "bcedgh";

$lcs = LCS($str1, $str2);
echo "最长公共子序列: " . $lcs;

In the above code, we first initialize a binary Dimensional array dp, and set the elements in the first row and first column to 0. We then use two nested for loops to calculate each element in the dp array. Finally, we find the longest common subsequence through backtracking and return it.

3. Conclusion
   The longest common subsequence algorithm is an efficient string matching algorithm, suitable for solving string similarity problems. Through the idea of ​​dynamic programming, we can solve the longest common subsequence with a time complexity of O(m*n). In PHP, we can use the above code example to implement this algorithm and get the longest common subsequence of two strings.

The above is the detailed content of Detailed explanation of the longest common subsequence algorithm in PHP. For more information, please follow other related articles on the PHP Chinese website!