LCS algorithm & largest common substring & longest common subsequence PHP implementation longest common increasing subsequence longest common subsequence c language longest common increasing subsequence

Find the largest common substring & longest common subsequence of two strings

<code>输入：
abcbdab
bdcaba</code>

<code>4</code>

That is, the maximum common substring length of bdcaba and abcbdab is 4

Conventional ideas

enumeration method, calculate All subsequences of the two strings are then compared separately to select the largest substring

Disadvantages: For a string of length n, the number of substrings is 2 to the nth power, and then in sequence Comparing substrings of two strings is too inefficient

Dynamic programming LCS algorithm

Using the idea of ​​dynamic programming to solve this problem, we use a two-digit array$dp[][] to store each string I won’t elaborate on the specific meaning of the corresponding status. Just search it on Baidu and you will know. It is mainly implemented using PHP
The code is as follows:

<code><span><span>function</span><span>lcs</span><span>(<span>$str1</span>, <span>$str2</span>)</span>
{</span><span>// 存储生成的二维矩阵</span><span>$dp</span> = <span>array</span>();
    <span>// 最大子串长度</span><span>$max</span> = <span>0</span>;

    <span>for</span> (<span>$i</span> = <span>0</span>; <span>$i</span> < strlen(<span>$str1</span>); <span>$i</span>++) { 
        <span>for</span> (<span>$j</span> = <span>0</span>; <span>$j</span> < strlen(<span>$str2</span>); <span>$j</span>++) { 
            <span>if</span> (<span>$str1</span>[<span>$i</span>] == <span>$str2</span>[<span>$j</span>]) {
                <span>$dp</span>[<span>$i</span>][<span>$j</span>] = <span>isset</span>(<span>$dp</span>[<span>$i</span>-<span>1</span>][<span>$j</span>-<span>1</span>]) ? <span>$dp</span>[<span>$i</span>-<span>1</span>][<span>$j</span>-<span>1</span>] + <span>1</span> : <span>1</span>;
            } <span>else</span> {
                <span>$dp</span>[<span>$i</span>-<span>1</span>][<span>$j</span>] = <span>isset</span>(<span>$dp</span>[<span>$i</span>-<span>1</span>][<span>$j</span>]) ? <span>$dp</span>[<span>$i</span>-<span>1</span>][<span>$j</span>] : <span>0</span>;
                <span>$dp</span>[<span>$i</span>][<span>$j</span>-<span>1</span>] = <span>isset</span>(<span>$dp</span>[<span>$i</span>][<span>$j</span>-<span>1</span>]) ? <span>$dp</span>[<span>$i</span>][<span>$j</span>-<span>1</span>] : <span>0</span>;

                <span>$dp</span>[<span>$i</span>][<span>$j</span>] = <span>$dp</span>[<span>$i</span>-<span>1</span>][<span>$j</span>] > <span>$dp</span>[<span>$i</span>][<span>$j</span>-<span>1</span>] ? <span>$dp</span>[<span>$i</span>-<span>1</span>][<span>$j</span>] : <span>$dp</span>[<span>$i</span>][<span>$j</span>-<span>1</span>];
            }

            <span>$max</span> = <span>$dp</span>[<span>$i</span>][<span>$j</span>] > <span>$max</span> ? <span>$dp</span>[<span>$i</span>][<span>$j</span>] : <span>$max</span>;
        }
    }

    <span>for</span> (<span>$i</span> = <span>0</span>; <span>$i</span> < strlen(<span>$str1</span>); <span>$i</span>++) { 
        <span>for</span> (<span>$j</span> = <span>0</span>; <span>$j</span> < strlen(<span>$str2</span>); <span>$j</span>++) { 
            <span>echo</span><span>$dp</span>[<span>$i</span>][<span>$j</span>] . <span>" "</span>;
        }
        <span>echo</span><span>"<br />";
    }

    var_dump(<span>$max</span>);
}

lcs(<span>"abcbdab"</span>, <span>"bdcaba"</span>);</code>

Corresponding output:

<code><span>0</span><span>0</span><span>0</span><span>1</span><span>1</span><span>1</span><span>1</span><span>1</span><span>1</span><span>1</span><span>2</span><span>2</span><span>1</span><span>1</span><span>2</span><span>2</span><span>2</span><span>2</span><span>1</span><span>1</span><span>2</span><span>2</span><span>3</span><span>3</span><span>1</span><span>2</span><span>2</span><span>2</span><span>3</span><span>3</span><span>1</span><span>2</span><span>2</span><span>3</span><span>3</span><span>4</span><span>1</span><span>2</span><span>2</span><span>3</span><span>4</span><span>4</span><span>int</span><span>4</span></code>

Conclusion: Through dynamic programming, we reduce the time complexity to O(nm), but there is still a waste of space. The storage of some data is unnecessary and can be further Optimize

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The above introduces the PHP implementation of the LCS algorithm & largest common substring & longest common subsequence, including the longest common subsequence and PHP content. I hope it will be helpful to friends who are interested in PHP tutorials.