Leetcode #2125: Number of Laser Beams in a Bank
In this guide, we solve Leetcode #2125 Number of Laser Beams in a Bank in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Anti-theft security devices are activated inside a bank. You are given a 0-indexed binary string array bank representing the floor plan of the bank, which is an m x n 2D matrix.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, Math, String, Matrix
Intuition
There is a mathematical invariant or formula that directly leads to the result.
Using math avoids unnecessary loops and reduces complexity.
Approach
Derive the formula or update rule, then compute the answer directly.
Handle edge cases like overflow or zero carefully.
Steps:
- Identify the math relationship.
- Compute the result with a loop or formula.
- Handle edge cases.
Example
Input: bank = ["011001","000000","010100","001000"]
Output: 8
Explanation: Between each of the following device pairs, there is one beam. In total, there are 8 beams:
* bank[0][1] -- bank[2][1]
* bank[0][1] -- bank[2][3]
* bank[0][2] -- bank[2][1]
* bank[0][2] -- bank[2][3]
* bank[0][5] -- bank[2][1]
* bank[0][5] -- bank[2][3]
* bank[2][1] -- bank[3][2]
* bank[2][3] -- bank[3][2]
Note that there is no beam between any device on the 0th row with any on the 3rd row.
This is because the 2nd row contains security devices, which breaks the second condition.
Python Solution
class Solution:
def numberOfBeams(self, bank: List[str]) -> int:
ans = pre = 0
for row in bank:
if (cur := row.count("1")) > 0:
ans += pre * cur
pre = cur
return ans
Complexity
The time complexity is , where and are the number of rows and columns, respectively. The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.