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This approach iteratively distributes candies to people in a sequence, considering one cycle at a time until all candies are allocated.
Time Complexity: O(sqrt(2 * candies)). This is because the linear sum of the sequence continues until all candies are exhausted, which resembles the behavior of an arithmetic series.
Space Complexity: O(num_people), since we maintain an array to store the number of candies for each person.
1using System;
2
3class Program {
4 public static int[] DistributeCandies(int candies, int numPeople) {
5 int[] result = new int[numPeople];
6 int i = 0;
7 int amount = 1;
8 while (candies > 0) {
9 result[i % numPeople] += Math.Min(candies, amount);
10 candies -= amount;
11 amount++;
12 i++;
13 }
14 return result;
15 }
16
17 static void Main() {
18 int candies = 10;
19 int numPeople = 3;
20 int[] result = DistributeCandies(candies, numPeople);
21 foreach (int num in result) {
22 Console.Write(num + " ");
23 }
24 }
25}In this C# implementation, the allocation is managed with an array, distributing candies in sequence using a loop. Arithmetic and basic operations, such as Min, facilitate this distribution task efficiently.
Using a mathematical approach, calculate full rounds of distribution first to optimize the solution as opposed to simulating step-by-step distribution.
Time Complexity: O(sqrt(2 * candies)) due to converging arithmetic series.
Space Complexity: O(num_people).
1def
This Python solution effectively reduces the operational complexity by calculating in larger blocks, then using an arithmetic method to fill any remaining candies. It allows for quicker transition between distribution cycles.