LeetCode 462 | Minimum Moves to Equal Array Elements II | Java | Medium | Math | CodeByTushu
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In today’s video, we solve LeetCode 462 — Minimum Moves to Equal Array Elements II using Math and Sorting in Java.
We are given an integer array nums of size n, and in each move, we can increment or decrement any single element by 1. Our objective is to determine the minimum total number of moves required to make all elements equal. Unlike the previous problem where moves were restricted to increments, allowing both increments and decrements transforms this challenge into finding a central point that minimizes total absolute deviation across a one-dimensional coordinate line.
By applying the median minimization theorem, the sum of absolute distances to all points is mathematically minimized when the target value is chosen as the median of the array. We sort the array in ascending order to directly access the median element in constant time, then execute a linear pass to accumulate the absolute differences using a 64-bit integer accumulator to safely guard against intermediate overflow, achieving an optimal O(N log N) time complexity with O(1) auxiliary space.
🔥 Problem Highlights
✅ Median Minimization Theorem: L1 norm / absolute deviation is minimized at the median
✅ Dual-pivot quicksort aligns elements for constant-time median extraction
✅ Pairwise distance invariant proves optimality across symmetric index intervals
✅ 64-bit long accumulator safely prevents 32-bit arithmetic overflow during summation
✅ Single-pass linear distance aggregation guarantees cache-friendly memory access
✅ Optimal O(N log N) overall runtime with strictly O(1) auxiliary space
⏱️ TIMESTAMPS
00:00 Intro & 100 Days Century Milestone Celebration
00:40 Problem Understanding & Constraints Analysis
01:53 Key Breakthrough: The Median Minimization Theorem
02:48 Optimal Sort & Accumulate Pipeline
03:29 Clean Java 17 Solution Walkthrough Line by Line
04:13 Test Cases Walkthrough & 100 Days Century Streak Celebration
04:50 Time Complexity Analysis (O(N log N) Sorting)
05:22 Space Complexity Analysis (O(1) Auxiliary Space)
05:53 Outro & Celebration of 100 Consecutive Days!
📂 Problem Folder & Detailed Documentation:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/tree/main/solutions/November/02-November/462-Minimum-Moves-to-Equal-Array-Elements-II
☕ Java Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/November/02-November/462-Minimum-Moves-to-Equal-Array-Elements-II/Solution.java
🐍 Python Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/November/02-November/462-Minimum-Moves-to-Equal-Array-Elements-II/solution.py
⚡ C++ Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/November/02-November/462-Minimum-Moves-to-Equal-Array-Elements-II/solution.cpp
🌐 JavaScript Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/November/02-November/462-Minimum-Moves-to-Equal-Array-Elements-II/solution.js
🔗 LeetCode Source Code
📌 https://codebytushu.com/leetcode/problem/minimum-moves-to-equal-array-elements-ii
🌐 All LeetCode Solutions
📌 https://codebytushu.com/Leetcode/
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🔥 Perfect For
LeetCode Medium Problems
Java DSA Preparation
Median Minimization Theorem
Array & Sorting Patterns
L1 Norm Distance Optimization
Time Complexity Optimization
Coding Interview Preparation
Problem Solving
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💬 Question of the Day
Why does the median of an array minimize the sum of absolute deviations rather than the mean?
1️⃣ The derivative of |x - k| produces step functions whose balance point is zero at the median
2️⃣ The mean is only valid for quadratic penalty functions and fails for all discrete arrays
3️⃣ The median always divides the total sum of elements into two equal integer halves
4️⃣ The mean requires higher sorting overhead than the median on randomized inputs
#LeetCode462 #LeetCode #MinimumMovesToEqualArrayElementsII #Java #JavaDSA #Array #Sorting #Math #DSA #CodingInterview #ProblemSolving #LeetCodeMedium #DailyLeetCode #JavaProgramming #CodeByTushu
👇 Comment the answer below! 🔥 Close description
In today’s video, we solve LeetCode 462 — Minimum Moves to Equal Array Elements II using Math and Sorting in Java.
We are given an integer array nums of size n, and in each move, we can increment or decrement any single element by 1. Our objective is to determine the minimum total number of moves required to make all elements equal. Unlike the previous problem where moves were restricted to increments, allowing both increments and decrements transforms this challenge into finding a central point that minimizes total absolute deviation across a one-dimensional coordinate line.
By applying the median minimization theorem, the sum of absolute distances to all points is mathematically minimized when the target value is chosen as the median of the array. We sort the array in ascending order to directly access the median element in constant time, then execute a linear pass to accumulate the absolute differences using a 64-bit integer accumulator to safely guard against intermediate overflow, achieving an optimal O(N log N) time complexity with O(1) auxiliary space.
🔥 Problem Highlights
✅ Median Minimization Theorem: L1 norm / absolute deviation is minimized at the median
✅ Dual-pivot quicksort aligns elements for constant-time median extraction
✅ Pairwise distance invariant proves optimality across symmetric index intervals
✅ 64-bit long accumulator safely prevents 32-bit arithmetic overflow during summation
✅ Single-pass linear distance aggregation guarantees cache-friendly memory access
✅ Optimal O(N log N) overall runtime with strictly O(1) auxiliary space
⏱️ TIMESTAMPS
00:00 Intro & 100 Days Century Milestone Celebration
00:40 Problem Understanding & Constraints Analysis
01:53 Key Breakthrough: The Median Minimization Theorem
02:48 Optimal Sort & Accumulate Pipeline
03:29 Clean Java 17 Solution Walkthrough Line by Line
04:13 Test Cases Walkthrough & 100 Days Century Streak Celebration
04:50 Time Complexity Analysis (O(N log N) Sorting)
05:22 Space Complexity Analysis (O(1) Auxiliary Space)
05:53 Outro & Celebration of 100 Consecutive Days!
📂 Problem Folder & Detailed Documentation:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/tree/main/solutions/November/02-November/462-Minimum-Moves-to-Equal-Array-Elements-II
☕ Java Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/November/02-November/462-Minimum-Moves-to-Equal-Array-Elements-II/Solution.java
🐍 Python Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/November/02-November/462-Minimum-Moves-to-Equal-Array-Elements-II/solution.py
⚡ C++ Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/November/02-November/462-Minimum-Moves-to-Equal-Array-Elements-II/solution.cpp
🌐 JavaScript Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/November/02-November/462-Minimum-Moves-to-Equal-Array-Elements-II/solution.js
🔗 LeetCode Source Code
📌 https://codebytushu.com/leetcode/problem/minimum-moves-to-equal-array-elements-ii
🌐 All LeetCode Solutions
📌 https://codebytushu.com/Leetcode/
📱 Join CodeByTushu on WhatsApp
Get coding updates, LeetCode solutions, daily questions and more.
https://whatsapp.com/channel/0029Vb8k5mCDeON2Xwlkxe40
❤️ Donate
📌 https://codebytushu.com/Leetcode/donate.php
🔥 Perfect For
LeetCode Medium Problems
Java DSA Preparation
Median Minimization Theorem
Array & Sorting Patterns
L1 Norm Distance Optimization
Time Complexity Optimization
Coding Interview Preparation
Problem Solving
🌐 Follow CodeByTushu
▶️ YouTube: https://www.youtube.com/@codebytushu
📸 Instagram: https://instagram.com/codebytushu/
💼 LinkedIn: https://www.linkedin.com/company/codebytushu/
🌍 Website: https://codebytushu.com
🐙 GitHub: https://github.com/CodeByTushu
❤️ Don’t Forget To
👍 Like | 💬 Comment | 🔔 Subscribe
💬 Question of the Day
Why does the median of an array minimize the sum of absolute deviations rather than the mean?
1️⃣ The derivative of |x - k| produces step functions whose balance point is zero at the median
2️⃣ The mean is only valid for quadratic penalty functions and fails for all discrete arrays
3️⃣ The median always divides the total sum of elements into two equal integer halves
4️⃣ The mean requires higher sorting overhead than the median on randomized inputs
#LeetCode462 #LeetCode #MinimumMovesToEqualArrayElementsII #Java #JavaDSA #Array #Sorting #Math #DSA #CodingInterview #ProblemSolving #LeetCodeMedium #DailyLeetCode #JavaProgramming #CodeByTushu
👇 Comment the answer below! 🔥 Close description