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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).
1#include <iostream>
#include <vector>
#include <cmath>
using namespace std;
vector<int> distributeCandies(int candies, int num_people) {
vector<int> result(num_people, 0);
int i;
for (i = 0; candies > 0; i++) {
int give = i + 1;
if (candies < give) {
give = candies;
}
result[i % num_people] += give;
candies -= give;
}
return result;
}
int main() {
int candies = 10, num_people = 3;
vector<int> result = distributeCandies(candies, num_people);
for (int num : result) {
cout << num << " ";
}
return 0;
}A mathematical implementation optimizing the allocation process by calculating it over complete rounds first, ensuring full advancements before using iterative computations.