Sponsored
Sponsored
This approach leverages backtracking to explore all possible ways of distributing the bags of cookies among the children. We utilize a recursive function to attempt to give each bag of cookies to any of the available children. At each step, we update the total cookies received by the child to whom the current bag is assigned. The goal is to minimize the maximum number of cookies any child receives, known as unfairness.
Time Complexity: O(k^n), where n is the number of cookie bags and k is the number of children. The solution explores every distribution possibility.
Space Complexity: O(k + n), due to the recursion stack and the distribution array.
1using System;
2
3public class Solution {
4 public int DistributeCookies(int[] cookies, int k) {
5 int[] distribution = new int[k];
6 int minUnfairness = int.MaxValue;
7 Distribute(cookies, distribution, 0, ref minUnfairness);
8 return minUnfairness;
9 }
10
11 private void Distribute(int[] cookies, int[] distribution, int index, ref int minUnfairness) {
12 if (index == cookies.Length) {
13 int currentMax = Int32.MinValue;
14 foreach (int d in distribution) {
15 currentMax = Math.Max(currentMax, d);
16 }
17 minUnfairness = Math.Min(minUnfairness, currentMax);
18 return;
19 }
20
21 for (int i = 0; i < distribution.Length; i++) {
22 distribution[i] += cookies[index];
23 Distribute(cookies, distribution, index + 1, ref minUnfairness);
24 distribution[i] -= cookies[index];
25 }
26 }
27}This C# solution recursively attempts to allocate each cookies bag to children, recording the suboptimal scenario progression. Backtracking resets conditions explored previously, ensuring the minimum unfairness restricts the output from each exhaustive search.
This approach uses bitmasking in conjunction with dynamic programming to keep track of all combinations of cookie distributions among k children. We aim to optimize processing by encoding choices using bitmasks to represent different subsets of cookies. This method alleviates computational overhead by avoiding permutation/combination evaluation via iterative states and sub-state record tracking. We leverage a DP technique where dp[mask][children] represents the minimum unfairness achievable assigning the selected cookie combination (mask) across given children.
Time Complexity: O(n * 2^n * k), dealing with both subset and child assignment constraints.
Space Complexity: O(2^n * k), necessary for complete subset and branch caching.
The Java solution operationalizes dynamic progression using bitmasks that allow covert manipulation of data subsets to gauge state possibilities efficiently. Entire setups for distributions are availed through recursive substate calculations, tracking maximums per subset iteratively. Versatility remains uncontrolled by primitive optimization, bypassing multilateral brute forcing.