This problem asks whether it's possible to partition a grid of positive integers into two connected sections with equal sums. You are required to find if such a partition is feasible with either a horizontal or vertical cut. The key approach involves array scanning and hash lookup techniques to efficiently solve the problem.
Problem Statement
You are given an m x n matrix grid of positive integers. Your task is to determine if it's possible to make either one horizontal or one vertical cut on the grid such that the sum of the values in the resulting sections are equal.
The cut must divide the grid into two connected sections where every cell in a section is reachable from any other cell in that section. If such a partition exists, return true; otherwise, return false.
Examples
Example 1
Input: grid = [[1,4],[2,3]]
Output: true
Example 2
Input: grid = [[1,2],[3,4]]
Output: true
Example 3
Input: grid = [[1,2,4],[2,3,5]]
Output: false
Constraints
- 1 <= m == grid.length <= 105
- 1 <= n == grid[i].length <= 105
- 2 <= m * n <= 105
- 1 <= grid[i][j] <= 105
Solution Approach
Prefix Sum Calculation
Calculate the prefix sum of the entire grid to quickly compute the sum of any subgrid. This step ensures that you can efficiently check possible cuts by comparing the sums of sections that would result from both vertical and horizontal cuts.
Array Scanning with Hash Lookup
Use array scanning along with hash lookups to identify potential cuts. You can iterate over the grid rows or columns and check if any possible partition results in equal sums using the precomputed prefix sum values.
Connected Component Validation
Once potential cuts are found, ensure that the resulting sections are connected. Check for disconnected components within any of the sections, which would invalidate the partition.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
The time complexity depends on how the prefix sum is computed and how efficiently you can check possible cuts using array scanning and hash lookups. The space complexity is determined by the storage required for the prefix sum and the hash maps used during the scanning process.
What Interviewers Usually Probe
- Tests ability to manage large grids and perform efficient lookups.
- Evaluates understanding of array manipulation, hash tables, and matrix partitioning.
- Checks for efficient computation of subgrid sums and partition validation.
Common Pitfalls or Variants
Common pitfalls
- Failing to handle large grids efficiently, leading to time limit exceeded errors.
- Incorrectly assuming that a section is always connected after a cut, without checking for disconnection.
- Not properly calculating prefix sums for quick access to subgrid sums, leading to unnecessary recomputation.
Follow-up variants
- What if you are only allowed to make a horizontal cut?
- Can the solution be optimized further for even larger grids?
- How would the solution change if the grid contained negative numbers?
How GhostInterview Helps
- GhostInterview helps by guiding you through the necessary array scanning and hash lookup techniques to solve the problem efficiently.
- The platform provides step-by-step assistance in calculating prefix sums and managing grid partitions, ensuring you're on track with optimal solutions.
- GhostInterview offers hints to tackle common pitfalls like ensuring connected sections and avoiding recomputation during the cut validation.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What is the key technique for solving the Equal Sum Grid Partition II problem?
The problem is best approached using array scanning combined with hash lookups, particularly leveraging prefix sums to calculate subgrid sums efficiently.
How do I handle large grid sizes in this problem?
You should optimize your solution using prefix sums and hash maps to avoid recalculating sums repeatedly, which could lead to time limit exceeded errors.
What happens if a section becomes disconnected after a cut?
A disconnected section invalidates the partition, so you must ensure that the resulting sections after the cut remain connected.
Can I use dynamic programming to solve this problem?
Dynamic programming isn't necessary for this problem. Using prefix sums and hash lookups provides a more efficient solution with less overhead.
How can GhostInterview assist with tackling this problem?
GhostInterview offers hints on array scanning and hash lookup methods and provides guidance on handling grid partitions and common pitfalls effectively.
Need direct help with Equal Sum Grid Partition II instead of spending more time grinding it?
Download GhostInterview when you want a LeetCode solver, not another long practice loop. Capture Equal Sum Grid Partition II from a screenshot, get the answer path and complexity, and use supported stealth workflows that stay outside captured layers.
Capture the prompt fast instead of rewriting the problem by hand.
Get the solution path, trade-offs, and complexity summary in one pass.
Stay outside captured layers on supported screen-share workflows.
Stay in the same pattern family
Determine if an m x n matrix grid can be split into two non-empty sections with equal sums by making a single horizontal or vertical cut.
Open problem page#3434 Maximum Frequency After Subarray OperationDetermine the maximum frequency of a target value k after applying one subarray addition operation efficiently using array scanning and hash maps.
Open problem page#3044 Most Frequent PrimeFind the most frequent prime over 10 from numbers generated by scanning a 2D matrix in all straight directions efficiently.
Open problem page