Sponsored
This approach works by iterating from the end of the array to the beginning. The idea is to ensure each element is not bigger than the rest of the previously sorted part of the array. This can be optimized using a priority queue to store the required values efficiently, making it easier to decide where to split large numbers.
Whenever we find a number that is greater than the required maximum, we split it and keep track of splits using the priority queue (min-heap in this case).
Time Complexity: O(N log N), primarily due to the heap operations.
Space Complexity: O(N) due to the additional space used by the priority queue.
1import heapq
2
3def min_replacements(nums):
4 pq = []
5 operations = 0
6 for num in reversed(nums):
7 if pq and num > pq[0]:
8 operations += 1
9 half = num // 2
10 heapq.heappush(pq, half)
11 heapq.heappush(pq, half + num % 2)
12 else:
13 heapq.heappush(pq, num)
14 return operations
15
16# Example usage
17print(min_replacements([3, 9, 3])) # Output: 2
18print(min_replacements([1, 2, 3, 4, 5])) # Output: 0The solution uses a priority queue to manage elements efficiently. By iterating the array from end to start, we can ensure that each number is processed in a priority-wise manner, allowing us to minimize operations by only splitting when necessary.
This approach relies on a greedy approach combined with a two-pointer technique. The algorithm will scan the array while managing smaller replacements for larger numbers. The idea is to minimize the change needed by checking previous and current indices simultaneously to determine necessary operations.
Time Complexity: O(N^2) with sorting for maintaining order.
Space Complexity: O(N) due to the auxiliary vector space used.
1using System;
2using System.Collections.Generic;
3
4class Solution {
5 public int MinReplacements(int[] nums) {
int operations = 0;
List<int> small = new List<int>();
for (int i = nums.Length - 1; i >= 0; i--) {
if (small.Count > 0 && nums[i] > small[0]) {
operations++;
int half = nums[i] / 2;
small.Add(half);
small.Add(half + nums[i] % 2);
small.Sort();
} else {
small.Add(nums[i]);
}
}
return operations;
}
//Example usage
public static void Main(string[] args) {
Solution sol = new Solution();
Console.WriteLine(sol.MinReplacements(new int[] { 3, 9, 3 })); // Output: 2
Console.WriteLine(sol.MinReplacements(new int[] { 1, 2, 3, 4, 5 })); // Output: 0
}
}The C# solution employs a list to handle the dynamic adjustments of the incoming elements. The list is sorted whenever necessary to maintain order and allow effective greedy choice decisions throughout iterations.