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Leetcode 1827. Minimum Operations to Make the Array Increasing

Problem Statement

You are given an integer array nums (0-indexed). In one operation, you can choose an element of the array and increment it by 1.

Return the minimum number of operations needed to make nums strictly increasing.

An array nums is strictly increasing if nums[i] < nums[i+1] for all 0 <= i < nums.length - 1. An array of length 1 is trivially strictly increasing.

Clarifying Questions

  1. Input Constraints:
    • What is the range of values for the elements in nums?
    • What is the length range of the array nums?
  2. Edge Cases:
    • What should be returned for an array of length 1?
    • How to deal with already strictly increasing arrays?

Strategy

To make the array strictly increasing:

  1. Traverse through the array from the second element.
  2. For each element, check if it’s less than or equal to the previous element.
  3. If it is, increment it to one more than the previous element.
  4. Count the number of increments (operations) performed.

Code

Here is the Java code to solve this problem:

public class Solution {
    public int minOperations(int[] nums) {
        int operations = 0;
        
        // Traverse the array from the second element
        for (int i = 1; i < nums.length; i++) {
            // If the current element is not greater than the previous one
            if (nums[i] <= nums[i - 1]) {
                // Calculate the increments needed to make nums[i] > nums[i - 1]
                int incrementNeeded = nums[i - 1] - nums[i] + 1;
                // Apply the increments
                nums[i] += incrementNeeded;
                // Add the increments to the operations counter
                operations += incrementNeeded;
            }
        }
        
        return operations;
    }
}

Time Complexity

The time complexity of this solution is (O(n)), where (n) is the length of the array nums. This is because we are performing a single pass through the array to make the necessary adjustments.

Space Complexity

The space complexity is (O(1)) since we are not using any additional space that scales with the input size.

Example

  1. Input: nums = [1, 1, 1]
    • Output: 3
    • Explanation:
      • Increment nums[1] to 2, nums becomes [1, 2, 1] (1 operation).
      • Increment nums[2] to 3, nums becomes [1, 2, 3] (2 operations).
      • Total operations = 1 + 2 = 3.

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