LeetCode 3418 | Maximum Amount of Money Robot Can Earn | Java | Medium | 3D D P Grid | CodeByTushu
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In today’s video, we solve LeetCode 3418 — Maximum Amount of Money Robot Can Earn using Dynamic Programming in Java.
We are given an m by n grid where each cell either awards coins or subtracts coins when encountering a robber. Starting at the top-left corner and moving only down or right to reach the bottom-right corner, our robot has a special ability to neutralize robbers in at most two cells along its path. Our goal is to determine the maximum possible profit the robot can gain on its route.
We model this decision process using three-dimensional Dynamic Programming where dp[i][j][k] stores the maximum profit achievable at cell (i, j) having utilized k neutralizations so far, with k ranging from zero to two. Arriving at cell (i, j) from either the top or left neighbor, the robot evaluates two choices: absorbing the cell value directly into its balance, or spending one neutralization power to set a negative robber cost to zero. By memoizing the optimal value across all reachable configurations, we handle negative paths seamlessly and guarantee an optimal solution with O(m * n) time complexity and O(m * n) auxiliary space.
🔥 Problem Highlights
✅ Multi-state 3D dynamic programming tracking cell coordinates and neutralization count
✅ Optimal substructure aggregating transitions from top and left neighbors
✅ Selective branch pruning avoiding neutralization on non-negative coin cells
✅ Negative infinity sentinel initialization preventing invalid path transitions
✅ Full support for all-negative coin paths and edge cases
✅ Optimal O(m * n) time complexity and O(m * n) auxiliary space
⏱️ TIMESTAMPS
00:00 Intro & Daily Challenge Kickoff (Streak 98 Days)
01:43 Problem Understanding: Grid Walk & Robber Neutralization
03:30 Key Insights: Why Greedy Fails & 3D State Dimensions
05:11 Dynamic Programming Recurrence & Base Cases
07:11 Clean Java Solution Walkthrough Line by Line
08:38 Test Cases Dry Run & Benchmark Verification (15 ms, Beats 98.5%)
10:29 Time Complexity Analysis (O(M*N) Time)
11:29 Space Complexity Analysis (O(M*N) Auxiliary Space)
12:17 Day 2 Wrap-up & Channel Resources
📂 Problem Folder & Detailed Documentation:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/tree/main/solutions/April/02-April/3418-Maximum-Amount-of-Money-Robot-Can-Earn
☕ Java Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/April/02-April/3418-Maximum-Amount-of-Money-Robot-Can-Earn/Solution.java
🐍 Python Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/April/02-April/3418-Maximum-Amount-of-Money-Robot-Can-Earn/solution.py
⚡ C++ Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/April/02-April/3418-Maximum-Amount-of-Money-Robot-Can-Earn/solution.cpp
🌐 JavaScript Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/April/02-April/3418-Maximum-Amount-of-Money-Robot-Can-Earn/solution.js
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💬 Question of the Day
Why is it never optimal for the robot to use one of its two neutralization abilities on a cell with positive or zero coins?
1️⃣ Because neutralizing a cell sets its value to zero, which would throw away positive coin gains
2️⃣ Because positive cells automatically replenish neutralization charges
3️⃣ Because neutralizations can only be applied at even-numbered grid coordinates
4️⃣ Because moving rightward resets the neutralization counter
#LeetCode3418 #LeetCode #MaximumAmountOfMoneyRobotCanEarn #Java #JavaDSA #DynamicProgramming #Matrix #GridDP #DSA #CodingInterview #ProblemSolving #LeetCodeMedium #DailyLeetCode #JavaProgramming #CodeByTushu
👇 Comment the answer below! 🔥 Close description
In today’s video, we solve LeetCode 3418 — Maximum Amount of Money Robot Can Earn using Dynamic Programming in Java.
We are given an m by n grid where each cell either awards coins or subtracts coins when encountering a robber. Starting at the top-left corner and moving only down or right to reach the bottom-right corner, our robot has a special ability to neutralize robbers in at most two cells along its path. Our goal is to determine the maximum possible profit the robot can gain on its route.
We model this decision process using three-dimensional Dynamic Programming where dp[i][j][k] stores the maximum profit achievable at cell (i, j) having utilized k neutralizations so far, with k ranging from zero to two. Arriving at cell (i, j) from either the top or left neighbor, the robot evaluates two choices: absorbing the cell value directly into its balance, or spending one neutralization power to set a negative robber cost to zero. By memoizing the optimal value across all reachable configurations, we handle negative paths seamlessly and guarantee an optimal solution with O(m * n) time complexity and O(m * n) auxiliary space.
🔥 Problem Highlights
✅ Multi-state 3D dynamic programming tracking cell coordinates and neutralization count
✅ Optimal substructure aggregating transitions from top and left neighbors
✅ Selective branch pruning avoiding neutralization on non-negative coin cells
✅ Negative infinity sentinel initialization preventing invalid path transitions
✅ Full support for all-negative coin paths and edge cases
✅ Optimal O(m * n) time complexity and O(m * n) auxiliary space
⏱️ TIMESTAMPS
00:00 Intro & Daily Challenge Kickoff (Streak 98 Days)
01:43 Problem Understanding: Grid Walk & Robber Neutralization
03:30 Key Insights: Why Greedy Fails & 3D State Dimensions
05:11 Dynamic Programming Recurrence & Base Cases
07:11 Clean Java Solution Walkthrough Line by Line
08:38 Test Cases Dry Run & Benchmark Verification (15 ms, Beats 98.5%)
10:29 Time Complexity Analysis (O(M*N) Time)
11:29 Space Complexity Analysis (O(M*N) Auxiliary Space)
12:17 Day 2 Wrap-up & Channel Resources
📂 Problem Folder & Detailed Documentation:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/tree/main/solutions/April/02-April/3418-Maximum-Amount-of-Money-Robot-Can-Earn
☕ Java Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/April/02-April/3418-Maximum-Amount-of-Money-Robot-Can-Earn/Solution.java
🐍 Python Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/April/02-April/3418-Maximum-Amount-of-Money-Robot-Can-Earn/solution.py
⚡ C++ Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/April/02-April/3418-Maximum-Amount-of-Money-Robot-Can-Earn/solution.cpp
🌐 JavaScript Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/April/02-April/3418-Maximum-Amount-of-Money-Robot-Can-Earn/solution.js
🔗 LeetCode Source Code
📌 Admin type the link
🌐 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
Dynamic Programming
Grid Path Optimization
State Machine DP
Time Complexity Optimization
Coding Interview Preparation
Problem Solving
🌐 Follow CodeByTushu
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📸 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 is it never optimal for the robot to use one of its two neutralization abilities on a cell with positive or zero coins?
1️⃣ Because neutralizing a cell sets its value to zero, which would throw away positive coin gains
2️⃣ Because positive cells automatically replenish neutralization charges
3️⃣ Because neutralizations can only be applied at even-numbered grid coordinates
4️⃣ Because moving rightward resets the neutralization counter
#LeetCode3418 #LeetCode #MaximumAmountOfMoneyRobotCanEarn #Java #JavaDSA #DynamicProgramming #Matrix #GridDP #DSA #CodingInterview #ProblemSolving #LeetCodeMedium #DailyLeetCode #JavaProgramming #CodeByTushu
👇 Comment the answer below! 🔥 Close description