#1388 - Pizza With 3n Slices

Problem Description

There is a pizza with 3n slices of varying size, you and your friends will take slices of pizza as follows:

You will pick any pizza slice.
Your friend Alice will pick the next slice in the anti-clockwise direction of your pick.
Your friend Bob will pick the next slice in the clockwise direction of your pick.
Repeat until there are no more slices of pizzas.

Given an integer array slices that represent the sizes of the pizza slices in a clockwise direction, return the maximum possible sum of slice sizes that you can pick.

Solution

/**
 * @param {number[]} slices
 * @return {number}
 */
var maxSizeSlices = function(slices) {
  const n = slices.length;
  const count = n / 3;
  const case1 = selectMaxSum(slices, count - 1, 2, n - 2);
  const case2 = selectMaxSum(slices, count, 1, n - 1);

  return Math.max(slices[0] + case1, case2);

  function selectMaxSum(arr, count, start, end, memo = new Map()) {
    const key = `${count},${start},${end}`;
    if (count === 0 || start > end) return 0;
    if (memo.has(key)) return memo.get(key);

    const includeFirst = arr[start] + selectMaxSum(arr, count - 1, start + 2, end, memo);
    const excludeFirst = selectMaxSum(arr, count, start + 1, end, memo);
    const result = Math.max(includeFirst, excludeFirst);

    memo.set(key, result);
    return result;
  }
};