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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.
1function distributeCandies(candies, num_people) {
2 const result = new Array(num_people).fill(0);
3 let i = 0;
4 let amount = 1;
5 while (candies > 0) {
6 result[i % num_people] += Math.min(candies, amount);
7 candies -= amount;
8 amount++;
9 i++;
10 }
11 return result;
12}
13
14// Example usage:
15let candies = 7;
16let num_people = 4;
17console.log(distributeCandies(candies, num_people));This JavaScript solution uses a fill operation on an array to handle candy distribution among people. Looping with a counter controls the sequence of distribution while Math.min prevents overallocation.
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.