What is the time complexity of Minimum Increment to Make Array Unique?

The optimal solution has a time complexity of O(n log n).

What data structures are used to solve Minimum Increment to Make Array Unique?

This problem uses Array, Greedy, Sorting, Counting. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Minimum Increment to Make Array Unique?

Insight 1: Sorting the array allows us to process elements in ascending order, making it easier to identify and resolve duplicates. Insight 2: Using a 'tracker' variable helps maintain the next available unique value. If the current number is less than the tracker, we need to increment it, otherwise, we update the tracker.

Which companies ask LeetCode 945. Minimum Increment to Make Array Unique in interviews?

This problem is frequently asked at Coursera, PayPal, ZScaler.

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Minimum Increment to Make Array Unique - LeetCode 945 Solution

Q: How to solve Minimum Increment to Make Array Unique?

The solution uses a greedy approach. First, we sort the input array. Then, we iterate through the sorted array, maintaining a 'tracker' variable. If the current element is less than the tracker, we increment it to the tracker's value (requiring tracker - num moves) and increment the tracker. If the current element is greater than or equal to the tracker, it's already unique relative to the previous elements. In this case, we update the tracker to be the current element + 1. This ensures that the next element will be unique if it's equal to the current element.

Minimum Increment to Make Array Unique - Complete Solution Guide

Minimum Increment to Make Array Unique is LeetCode problem 945, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

You are given an integer array nums . In one move, you can pick an index i where 0 <= i < nums.length and increment nums[i] by 1 . Return the minimum number of moves to make every value in nums unique . The test cases are generated so that the answer fits in a 32-bit integer. Example 1: Input: nums = [1,2,2] Output: 1 Explanation: After 1 move, the array could be [1, 2, 3]. Example 2: Input: nums = [3,2,1,2,1,7] Output: 6 Explanation: After 6 moves, the array could be [3, 4, 1, 2, 5, 7]. It can

Detailed Explanation

The problem asks us to find the minimum number of increments needed to make all elements in an integer array unique. We're allowed to increment any element by 1 in each move. The goal is to minimize the total number of moves required to ensure no two elements in the array have the same value.

Solution Approach

The solution uses a greedy approach. First, we sort the input array. Then, we iterate through the sorted array, maintaining a 'tracker' variable. If the current element is less than the tracker, we increment it to the tracker's value (requiring tracker - num moves) and increment the tracker. If the current element is greater than or equal to the tracker, it's already unique relative to the previous elements. In this case, we update the tracker to be the current element + 1. This ensures that the next element will be unique if it's equal to the current element.

Step-by-Step Algorithm

Step 1: Sort the input array 'nums' in ascending order.
Step 2: Initialize a variable 'moves' to 0. This will store the total number of moves.
Step 3: Initialize a variable 'tracker' to 0. This will keep track of the next available unique value.
Step 4: Iterate through the sorted array 'nums'.
Step 5: Inside the loop, check if the current element 'num' is less than 'tracker'.
Step 6: If 'num' is less than 'tracker', it means we need to increment 'num' to make it unique. Add 'tracker - num' to 'moves', and increment 'tracker' by 1.
Step 7: If 'num' is greater than or equal to 'tracker', it means 'num' is already unique (or can be made unique without incrementing current num by more than needed). Update 'tracker' to 'num + 1'.
Step 8: After the loop finishes, return 'moves'.

Key Insights

Insight 1: Sorting the array allows us to process elements in ascending order, making it easier to identify and resolve duplicates.
Insight 2: Using a 'tracker' variable helps maintain the next available unique value. If the current number is less than the tracker, we need to increment it, otherwise, we update the tracker.
Insight 3: The problem guarantees the answer fits in a 32-bit integer, meaning we don't need to worry about integer overflow issues during calculations.

Complexity Analysis

Time Complexity: O(n log n)

Space Complexity: O(1)

Topics

This problem involves: Array, Greedy, Sorting, Counting.

Companies

Asked at: Coursera, PayPal, ZScaler.

Minimum Increment to Make Array Unique | LeetCode 945

Medium

Array Greedy Sorting Counting

Time: O(n log n)Space: O(1)

Solution Code

Available in:

import java.util.Arrays;

class Solution {
    public int minIncrementForUnique(int[] nums) {
        Arrays.sort(nums);
        int moves = 0;
        int tracker = 0;
        for (int num : nums) {
            if (num < tracker) {
                moves += tracker - num;
                tracker += 1;
            } else {
                tracker = num + 1;
            }
        }
        return moves;
    }
}

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Problem Info

Description

Problem 945: Minimum Increment to Make Array Unique - Detailed explanation and solution approaches.

Topics

Array Greedy Sorting Counting

Companies

CourseraPayPalZScaler

Stats

Difficulty:Medium

Languages:4

Companies:3

Problem #:945

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

8 steps

1
Step 1: Sort the input array 'nums' in ascending order.
2
Step 2: Initialize a variable 'moves' to 0. This will store the total number of moves.
3
Step 3: Initialize a variable 'tracker' to 0. This will keep track of the next available unique value.
4
Step 4: Iterate through the sorted array 'nums'.
5
Step 5: Inside the loop, check if the current element 'num' is less than 'tracker'.
6
Step 6: If 'num' is less than 'tracker', it means we need to increment 'num' to make it unique. Add 'tracker - num' to 'moves', and increment 'tracker' by 1.
7
Step 7: If 'num' is greater than or equal to 'tracker', it means 'num' is already unique (or can be made unique without incrementing current num by more than needed). Update 'tracker' to 'num + 1'.
8
Step 8: After the loop finishes, return 'moves'.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n log n)

✨ Log-linear - Great for sorting algorithms!

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The dominant operation is sorting the array, which typically takes O(n log n) time using comparison-based sorting algorithms like merge sort or quicksort. The subsequent iteration through the sorted array takes O(n) time, but it's dominated by the sorting time. The space complexity is O(1) because we're only using a few constant extra variables ('moves', 'tracker') and sorting in-place (depending on the sorting algorithm implementation).

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Counting Approach

Count occurrences of each number. If a number appears more than once, increment one instance until it becomes a value not present in counts, accumulating moves.

Time: O(N + M), where N is the length of nums and M is the range of values in numsSpace: O(M), where M is the range of values in nums

Trade-offs: This approach can be faster if the range of numbers in `nums` is small, as it avoids sorting. However, it requires additional space to store the counts. If M (the range of values in `nums`) is significantly larger than N (the length of `nums`), sorting becomes more efficient and memory friendly.

✨

Key Insights

1Insight 1: Sorting the array allows us to process elements in ascending order, making it easier to identify and resolve duplicates.
2Insight 2: Using a 'tracker' variable helps maintain the next available unique value. If the current number is less than the tracker, we need to increment it, otherwise, we update the tracker.
3Insight 3: The problem guarantees the answer fits in a 32-bit integer, meaning we don't need to worry about integer overflow issues during calculations.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Greedy Algorithm

Making the best choice at each step without looking ahead.

Sorting

Arranging elements in a specific order (ascending/descending).

Edge Cases

Edge case 1: Empty array: If the input array is empty, the algorithm will correctly return 0 moves because the loop won't execute.
Edge case 2: Array with all same elements: The algorithm will correctly increment the necessary elements to make them unique. For example, if nums = [2, 2, 2], the algorithm will increment to [2, 3, 4], requiring 1 + 2 = 3 moves.
Edge case 3: Already sorted and unique array: If the array is already sorted and contains unique values, the algorithm will correctly return 0 moves. The tracker will always be one greater than the current num

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not sorting the array first: Sorting is crucial for the greedy approach to work correctly. Without sorting, the 'tracker' won't be able to accurately determine the next available unique value.

✗Common mistake 2: Forgetting to increment the 'tracker' after incrementing a 'num': If we don't increment the tracker after resolving a duplicate, we might end up creating another duplicate in the next iteration.

✗Common mistake 3: Using incorrect sorting algorithm leading to higher time complexity: Choosing a poor sorting algorithm increases time complexity impacting the runtime.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Assigning unique IDs: When assigning unique IDs to database records or other objects, you might encounter collisions. This algorithm helps minimize the number of ID increments needed to resolve these collisions.

🏦Real-world scenario 2: Scheduling tasks: In task scheduling, you might need to adjust start times to avoid overlaps. This problem is analogous to finding the minimum adjustments to make all start times unique.

🎮Real-world scenario 3: Resource allocation: If you have limited resources and multiple requests for those resources, you might need to adjust the requested quantities to ensure everyone gets a unique allocation. This could be useful when dealing with bandwidth or memory allocation.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Medium problems are the bread and butter of technical interviews. Practice explaining your approach before coding.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

👨‍💻 From Experience

This problem pattern appears frequently in real codebases. I've used similar logic when building production systems.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: July 16, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jul 14

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 7

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJun 30

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

What are common greedy problem patterns?

Activity selection (sort by end time), interval scheduling (sort by start/end), Huffman coding (always combine smallest), fractional knapsack (sort by value/weight ratio), and minimum spanning tree. Look for problems where local decisions don't affect future options.

How much time should I spend on a medium problem in interviews?

In a 45-minute interview, aim for: 5-10 minutes understanding and clarifying, 5-10 minutes discussing approach, 20-25 minutes coding, and 5-10 minutes testing. If stuck after 15 minutes of thinking, verbalize your thought process and ask for hints.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Minimum Increment to Make Array Unique"?

For this medium-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether greedy techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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