710281. Minimum increment/decrement to make array non-Increasing
Minimum increment/decrement to make array non-Increasing
Summary
Given an integer array, we need to find the minimum number of increments or decrements required to make the array non-increasing. This problem is related to arrays and priority queues.
Detailed Explanation
The approach to solve this problem is to use a priority queue to keep track of the elements in the array that are not yet non-decreasing. We start by initializing a priority queue with all elements from the input array, where each element is represented as a pair (value, index). Then we repeatedly extract the maximum element from the priority queue and update the array accordingly.
Here's a step-by-step breakdown of the solution:
- Initialize an empty priority queue.
- Iterate through the input array and add each element to the priority queue along with its index.
- While the priority queue is not empty, do the following:
- Extract the maximum element from the priority queue. Let this element be (value, index).
- If the value of the extracted element is greater than or equal to the value at the previous index in the array, update the array by decrementing the value.
- Add the updated element back to the priority queue.
- The number of increments/decrements required to make the array non-increasing is the total number of elements processed.
Time complexity: O(n log n) due to the sorting operation in each iteration of the while loop, where n is the size of the input array. Space complexity: O(n) for storing the priority queue and the updated array.
Optimized Solutions
Java
import java.util.PriorityQueue;
import java.util.Arrays;
public class Main {
public static int minIncrDecr(int[] arr) {
PriorityQueue<Integer> pq = new PriorityQueue<>();
for (int i : arr) {
pq.offer(i);
}
int count = 0;
while (!pq.isEmpty()) {
int max = pq.poll();
if (!pq.isEmpty() && pq.peek() >= max) {
pq.poll();
count++;
} else {
break;
}
}
return count;
}
public static void main(String[] args) {
int[] arr = {5, 3, 2, 1};
System.out.println(minIncrDecr(arr));
}
}