714007. Minimum Steps Required
Minimum Steps Required
Summary
The problem "Minimum Steps Required" is a classic example of a greedy algorithm. Given a sequence of integers, we need to find the minimum number of steps required to reduce the sum of all elements in the sequence to zero.
Detailed Explanation
To solve this problem, we'll use a greedy approach. The idea is to always subtract the maximum element from the sequence until its sum becomes zero or negative. This is because reducing the maximum element first will give us the highest reduction in the sum and also ensure that the remaining elements are minimized.
Here's a step-by-step breakdown of the solution:
- First, sort the sequence in descending order to find the maximum element.
- While the sum of the sequence is positive:
- Subtract the maximum element from the sequence.
- Update the maximum element by finding the new maximum in the remaining sequence.
- The minimum number of steps required will be the total number of subtractions performed.
The time complexity of this algorithm is O(n log n) due to the sorting step, where n is the size of the input sequence. The space complexity is O(1), as we only need a constant amount of space to store the maximum element and the sum of the sequence.
Optimized Solutions
Java
public int minSteps(int[] arr) {
Arrays.sort(arr);
int steps = 0;
int sum = 0;
for (int num : arr) {
if (sum + num <= 0) break;
sum += -num;
steps++;
}
return steps;
}