g2301_2400.s2305_fair_distribution_of_cookies.Solution Maven / Gradle / Ivy

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Java-based LeetCode algorithm problem solutions, regularly updated

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package g2301_2400.s2305_fair_distribution_of_cookies;

// #Medium #Array #Dynamic_Programming #Bit_Manipulation #Backtracking #Bitmask
// #2022_06_16_Time_14_ms_(84.35%)_Space_39.6_MB_(92.46%)

/**
 * 2305 - Fair Distribution of Cookies\.
 *
 * Medium
 *
 * You are given an integer array `cookies`, where `cookies[i]` denotes the number of cookies in the i^th bag. You are also given an integer `k` that denotes the number of children to distribute **all** the bags of cookies to. All the cookies in the same bag must go to the same child and cannot be split up.
 *
 * The **unfairness** of a distribution is defined as the **maximum** **total** cookies obtained by a single child in the distribution.
 *
 * Return _the **minimum** unfairness of all distributions_.
 *
 * **Example 1:**
 *
 * **Input:** cookies = [8,15,10,20,8], k = 2
 *
 * **Output:** 31
 *
 * **Explanation:** One optimal distribution is [8,15,8] and [10,20]
 *
 * - The 1^st child receives [8,15,8] which has a total of 8 + 15 + 8 = 31 cookies.
 *
 * - The 2^nd child receives [10,20] which has a total of 10 + 20 = 30 cookies.
 *
 * The unfairness of the distribution is max(31,30) = 31.
 *
 * It can be shown that there is no distribution with an unfairness less than 31. 
 *
 * **Example 2:**
 *
 * **Input:** cookies = [6,1,3,2,2,4,1,2], k = 3
 *
 * **Output:** 7
 *
 * **Explanation:** One optimal distribution is [6,1], [3,2,2], and [4,1,2]
 *
 * - The 1^st child receives [6,1] which has a total of 6 + 1 = 7 cookies.
 *
 * - The 2^nd child receives [3,2,2] which has a total of 3 + 2 + 2 = 7 cookies.
 *
 * - The 3^rd child receives [4,1,2] which has a total of 4 + 1 + 2 = 7 cookies.
 *
 * The unfairness of the distribution is max(7,7,7) = 7.
 *
 * It can be shown that there is no distribution with an unfairness less than 7. 
 *
 * **Constraints:**
 *
 * *   `2 <= cookies.length <= 8`
 * *   1 <= cookies[i] <= 10⁵
 * *   `2 <= k <= cookies.length`
**/
public class Solution {
    private int res = Integer.MAX_VALUE;

    public int distributeCookies(int[] c, int k) {
        int[] nums = new int[k];
        dfs(c, nums, 0);
        return res;
    }

    private void dfs(int[] c, int[] nums, int cur) {
        if (cur == c.length) {
            int r = 0;
            for (int num : nums) {
                r = Math.max(r, num);
            }
            res = Math.min(res, r);
            return;
        }
        for (int i = 0; i < nums.length; i++) {
            if (nums[i] + c[cur] > res) {
                continue;
            }
            nums[i] += c[cur];
            dfs(c, nums, cur + 1);
            nums[i] -= c[cur];
        }
    }
}