Following steps build L [ m + 1 ] [ n + 1 ] in bottom up fashion . Note that L [ i ] [ j ] contains length of LCS of X [ 0. . i - 1 ] and Y [ 0. . j - 1 ]
for ( let i = 0 ; i <= m ; i ++ ) { for ( let j = 0 ; j <= n ; j ++ ) { if ( i == 0 j == 0 ) { L [ i ] [ j ] = 0 ; } else if ( X [ i - 1 ] == Y [ j - 1 ] ) { L [ i ] [ j ] = L [ i - 1 ] [ j - 1 ] + 1 ; } else { L [ i ] [ j ] = Math . max ( L [ i - 1 ] [ j ] , L [ i ] [ j - 1 ] ) ; } } }