Finding a Longest Common Subsequence of two strings in javascript

longestCommonSubsequence.js

function forwardTrace(lcsMatrix, set1, set2) {
    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],
            );
          }
        }
    }
}

function backTrace(lcsMatrix, set1, set2) {
    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;
}

function LCS(set1, set2) {

    string1 = set1.trim();
    string2 = set2.trim();

    const len1 = string1.length;
    const len2 = string2.length;

    // create two dimensional array (len1+1)*(len2+1)
    let arr = Array(len2 + 1).fill(null).map(() => Array(len1 + 1).fill(null)); 

    // filling first horizontal and verical line with zeroes
    arr[0].fill(0);
    for (let i = 0; i <= string1.length; i++) {
        arr[i][0] = 0;
    }

    forwardTrace(arr, string1, string2);
    const string = backTrace(arr, string1, string2);

    return string;
}