#2927 - Distribute Candies Among Children III

Hard • View on LeetCode • View on GitHub

Problem Description

You are given two positive integers n and limit.

Return the total number of ways to distribute n candies among 3 children such that no child gets more than limit candies.

Solution

/**
 * @param {number} n
 * @param {number} limit
 * @return {number}
 */
var distributeCandies = function(n, limit) {
  if (n > 3 * limit) return 0;

  const overLimit = limit + 1;
  return countWays(n) - 3 * countWays(n - overLimit)
    + 3 * countWays(n - 2 * overLimit) - countWays(n - 3 * overLimit);

  function countWays(candies) {
    if (candies < 0) return 0;
    return Math.floor((candies + 2) * (candies + 1) / 2);
  }
};