11. Make Array Elements Unique

The problem can be found at the following link: Problem Link

Problem Description

Given an array arr[], the goal is to make all elements unique with the minimum number of increment operations. In each operation, any element in the array can be incremented by 1.

Examples:

Input:

arr[] = [1, 2, 2]

Output:

1

Explanation: Increasing arr[2] by 1 results in [1, 2, 3], which makes all elements unique. The minimum number of operations required is 1.

Input:

arr[] = [1, 1, 2, 3]

Output:

3

Explanation: To make all elements unique, increase arr[0] by 3. Thus, the resulting array [4, 1, 2, 3] has all unique values. Hence, the answer is 3.

Input:

arr[] = [5, 4, 3, 2, 1]

Output:

0

Explanation: All elements are already unique, so no operations are needed.

Constraints:

• 1 ≤ arr.size() ≤ 10^6

• 0 ≤ arr[i] ≤ 10^6

My Approach

1. Sorting and Increment Calculation

   • First, sort the array to group identical elements together and handle them in order.

   • Traverse the sorted array from the second element onwards. If an element is not greater than the previous one, increment it to be previous + 1 to maintain uniqueness.

2. Increment Count

   • For every adjustment made, keep a running count of the increments needed.

3. Edge Cases

   • If the array already has unique elements, no operations are needed.

   • If the array has all elements the same, each must be incremented to achieve uniqueness.

Time and Auxiliary Space Complexity

• Expected Time Complexity: O(n log n), due to sorting the array initially.

• Expected Auxiliary Space Complexity: O(1), as we perform the operations in place and use only a constant amount of additional space for the counters.

Code (C++)

class Solution {
public:
    int minIncrements(vector<int>& arr) {
        if (arr.empty()) return 0;

        int ans = 0;
        sort(arr.begin(), arr.end());
        for (int i = 1; i < arr.size(); i++) {
            if (arr[i] <= arr[i - 1]) {
                ans += arr[i - 1] - arr[i] + 1;
                arr[i] = arr[i - 1] + 1;
            }
        }
        return ans;
    }
};

Code (Java)

class Solution {
    public int minIncrements(int[] arr) {
        if (arr.length == 0) return 0;

        int ans = 0;
        Arrays.sort(arr);
        for (int i = 1; i < arr.length; i++) {
            if (arr[i] <= arr[i - 1]) {
                ans += arr[i - 1] - arr[i] + 1;
                arr[i] = arr[i - 1] + 1;
            }
        }
        return ans;
    }
}

Code (Python)

class Solution:
    def minIncrements(self, arr):
        if not arr:
            return 0

        arr.sort()
        ans = 0

        for i in range(1, len(arr)):
            if arr[i] <= arr[i - 1]:
                ans += arr[i - 1] - arr[i] + 1
                arr[i] = arr[i - 1] + 1

        return ans

Contribution and Support

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