let findLength = function (a, b) {
    if (a.length === 0 || b.length === 0) {
        return 0;
    }

    // create our dynamic programming grid, which will cache our subproblem answers
    let cache = [];
    for (let row = 0; row < a.length + 1; row++) { // +1's are for empty string. We need the empty string row/col as a base case
        cache.push(new Array(b.length + 1).fill(0));
    }

    let max = 0;
    for (let row = 0; row < a.length + 1; row++) {
        for (let col = 0; col < b.length + 1; col++) {
            // base case, empty sets being solved against each other.
            if (row === 0 || col === 0) {
                cache[row][col] = 0;
            } else if (b[row - 1] === a[col - 1]) { // Match! The two numbers are equal.
                // the answer for this subset will be 1 + the subproblem answer for this cell is one above, and to the left, of the current cell.
                cache[row][col] = 1 + cache[row - 1][col - 1];
                // we have a new answer, compare it against our current max
                max = Math.max(max, cache[row][col]);
            }
        }
    }

    return max;
};