945 Minimum Increment to Make Array Unique

This is a problem that requires simulation. But one thing needs to be carefully taken care off, that is we can’t use a dictionary to keep frequencies.

I made a mistake of using a dictionary and whenever the current frequency is not 1 (which means it’s not unique), I updated the next key with freq[current] - 1 and updated the current frequency.

You might have noticed the flaw in this - if I have consecutive numbers this would have worked. But since I don’t I mustn’t update the next key, rather the next number must be added with freq[current] - 1.

This way, we are making sure that we are accurately counting the number of steps to make array unique - and most importantly - not counting the steps multiple times.

Code:

Java

class Solution {
    public int minIncrementForUnique(int[] arr) {
        if (arr == null || arr.length == 0)
            return 0;
 
        int maxVal = 0;
        for (int x : arr) {
            maxVal = Math.max(maxVal, x);
        }
 
        int moves = 0;
        int[] freq = new int[arr.length + maxVal];
        for (int num : arr)
            freq[num]++;
 
        for (int i = 0; i < freq.length - 1; i++) {
            if (freq[i] <= 1) //no need to move anything!
                continue;
 
            moves += freq[i] - 1;
            freq[i + 1] += freq[i] - 1;
        }
 
        return moves;
    }
}

Big O Analysis

• Runtime

  The runtime complexity here is $O(N)$ since we are visiting all elements in the array only once.

• Memory The memory usage is $O(len(arr)+maxVal)$ since we use array to store frequencies.

— A

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