标签：const top while fir use each ram and return
The longest common subsequence (LCS) problem is the problem of finding the longest subsequence common to all sequences in a set of sequences (often just two sequences). It differs from the longest common substring problem: unlike substrings, subsequences are not required to occupy consecutive positions within the original sequences.
ABCDGH and AEDFHR is ADH of length 3.AGGTAB and GXTXAYB is GTAB of length 4以s1={1,3,4,5,6,7,7,8},s2={3,5,7,4,8,6,7,8,2}为例。
1.构建二维矩阵A[n+1][n+1] s1为列，s2为行
（1）A[0][any]=0,A[any][0]=0
（2）if(s1[columnIndex-1]==s2[rowIndex-1])则A[rowIndex][columnIndex]=A[rowIndex-1][columnIndex-1]+1;
else A[rowIndex][columnIndex]=max(A[rowIndex][columnIndex-1],A[rowIndex-1][columnIndex])
（3）由A[8][9]可知最大子序列长度。
图如下：
2.针对构建的二维矩阵求最长子序列
（1）当columnIndex>0或者rowIndex>0时。
（2）如果s1[columnIndex-1]==s2[rowIndex-1]则longestSequence.unshift(s1[columnIndex-1]).rowIndex--;columnIndex--.
（3）如果不等，
则1.如果A[rowIndex][columnIndex]==A[rowIndex][columnIndex-1];columnIndex--;//向左
2.否则 rowIndex--;
代码如下：
/** * @param {string[]} set1 * @param {string[]} set2 * @return {string[]} */ export default function longestCommonSubsequence(set1, set2) { // Init LCS matrix. const lcsMatrix = Array(set2.length + 1).fill(null).map(() => Array(set1.length + 1).fill(null)); // Fill first row with zeros. for (let columnIndex = 0; columnIndex <= set1.length; columnIndex += 1) { lcsMatrix[0][columnIndex] = 0; } // Fill first column with zeros. for (let rowIndex = 0; rowIndex <= set2.length; rowIndex += 1) { lcsMatrix[rowIndex][0] = 0; } // Fill rest of the column that correspond to each of two strings. for (let rowIndex = 1; rowIndex <= set2.length; rowIndex += 1) { for (let columnIndex = 1; columnIndex <= set1.length; columnIndex += 1) { if (set1[columnIndex - 1] === set2[rowIndex - 1]) { lcsMatrix[rowIndex][columnIndex] = lcsMatrix[rowIndex - 1][columnIndex - 1] + 1; } else { lcsMatrix[rowIndex][columnIndex] = Math.max( lcsMatrix[rowIndex - 1][columnIndex], lcsMatrix[rowIndex][columnIndex - 1], ); } } } // Calculate LCS based on LCS matrix. if (!lcsMatrix[set2.length][set1.length]) { // If the length of largest common string is zero then return empty string. return [‘‘]; } const longestSequence = []; let columnIndex = set1.length; let rowIndex = set2.length; while (columnIndex > 0 || rowIndex > 0) { if (set1[columnIndex - 1] === set2[rowIndex - 1]) { // Move by diagonal left-top. longestSequence.unshift(set1[columnIndex - 1]); columnIndex -= 1; rowIndex -= 1; } else if (lcsMatrix[rowIndex][columnIndex] === lcsMatrix[rowIndex][columnIndex - 1]) { // Move left. columnIndex -= 1; } else { // Move up. rowIndex -= 1; } } return longestSequence; }
标签：const top while fir use each ram and return
原文地址：https://www.cnblogs.com/Archer-Fang/p/10551181.html
