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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).
1using System;
class Program {
public static int[] DistributeCandies(int candies, int numPeople) {
int[] result = new int[numPeople];
int i = 0;
while (candies > 0) {
int give = i + 1;
if (candies < give) give = candies;
result[i % numPeople] += give;
candies -= give;
i++;
}
return result;
}
static void Main() {
int candies = 10;
int numPeople = 3;
int[] result = DistributeCandies(candies, numPeople);
foreach (int num in result) {
Console.Write(num + " ");
}
}
}The C# code leverages reflective calculation of sequential candy distributions to cover full rounds as fast as possible with minimal additional computations upon iteration.