Simulate Bomb Explosions and Falling Boxes solution and explanation
The problem
The problem statement is not available yet.
Approach overview
Problem Overview: You get a grid of boxes and a list of bomb strikes. Each bomb clears the boxes in its blast zone, then the boxes above each cleared cell fall down under gravity. You need the final state of the grid after every bomb has gone off.
Approach 1: Direct Simulation (O(B * R * C) time, O(1) extra space)
For each bomb, mark every cell in its blast area as empty. Then, for each column, scan from the bottom up and shift the remaining boxes down to fill the gaps. This is the straightforward model of the problem. Each bomb costs a full pass over the affected columns, so it is correct but slow when there are many bombs. Use it to confirm your understanding of the rules before optimizing.
Approach 2: Column-wise Compaction with Two Pointers (O(B * R + R * C) time, O(R) space)
Gravity acts independently on each column, so you can treat every column as its own stack. Keep a write pointer per column that marks the next free slot from the bottom. When you process a column, copy surviving boxes into their compacted positions in one pass. Blast effects are applied as marks first, then each column is compacted once. This removes the repeated shifting work and reduces the cost of each bomb to the cells it actually touches.
Approach 3: Lazy Removal with Per-Column Counters (O(B + R * C) time, O(R * C) space)
Instead of moving boxes after each bomb, record removals as counts or flags and resolve them only when the final state is needed. Each column tracks how many cells below a given row have been removed, so a box's final height is its original row minus the removals beneath it. Prefix-style counters let you answer each box's fate in constant time. This gives the best asymptotic behavior when the number of bombs is large, at the cost of extra bookkeeping.
Recommended for interviews: Interviewers expect you to start with the direct simulation to show you understand the gravity and blast rules. The brute force proves correctness, but the column-wise compaction or lazy removal shows you can separate the independent columns and avoid repeated work. Explain the tradeoff between per-bomb updates and deferred resolution before you code.
Review related patterns in simulation, array, and matrix problems on FleetCode to build the same habits.
The written solution for this problem is still being prepared. Try it yourself in the meantime.
Try solving it yourselfComplexity analysis
| Approach | Time | Space | When to Use |
|---|---|---|---|
| Direct Simulation | O(B * R * C) | O(1) | Small grids or few bombs, to verify rules |
| Column-wise Compaction | O(B * R + R * C) | O(R) | General case, clean and easy to reason about |
| Lazy Removal with Counters | O(B + R * C) | O(R * C) | Many bombs and memory is not a constraint |
Frequently asked questions
Is Simulate Bomb Explosions and Falling Boxes easy or hard?
It is rated Medium with a 56.7% acceptance rate. The rules are simple, but the difficulty comes from handling the falling step efficiently and avoiding off-by-one errors in the blast range. Getting a correct brute force is usually quick, and the optimization takes most of the effort.
Simulate Bomb Explosions and Falling Boxes Python/Java solution
Python and Java solutions follow the same structure. Apply the blast marks to the grid, then loop over each column from bottom to top and copy surviving boxes to a write index. In Python, use list indexing for the grid. In Java, use a 2D int array and track the write row with an integer variable.
How to solve Simulate Bomb Explosions and Falling Boxes in O(n)?
Process the bombs by recording which cells are removed, without moving boxes after each one. Then compact each column a single time from bottom to top using a write pointer. Every cell is visited a constant number of times, so the total work is linear in the grid size plus the number of bombs.
What is the best approach for Simulate Bomb Explosions and Falling Boxes?
The best approach treats each column as an independent stack and compacts it once after applying the blast marks. This avoids shifting boxes after every bomb. Deferred removal with per-column counters is even more efficient when the number of bombs is large.
Is Simulate Bomb Explosions and Falling Boxes asked at Google/Amazon/Meta?
This problem is tagged General on FleetCode and is not confirmed in a specific company list here. It is a simulation problem, so the skills it tests show up often in interviews at large tech companies. Check recent interview reports on your target company before assuming it appears.
What data structure is used in Simulate Bomb Explosions and Falling Boxes?
The main structure is the 2D grid itself, usually stored as a matrix of integers or booleans. Optimized solutions add per-column arrays or stacks to track write positions and removal counts. No heavy data structures like heaps or tries are required.
What is the time complexity of Simulate Bomb Explosions and Falling Boxes?
The direct simulation runs in O(B * R * C) time, where B is the number of bombs and R by C is the grid size. Column-wise compaction reduces this to O(B * R + R * C). The lazy counter approach reaches O(B + R * C).