Leetcode #1253: Reconstruct a 2-Row Binary Matrix
In this guide, we solve Leetcode #1253 Reconstruct a 2-Row Binary Matrix 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
Given the following details of a matrix with n columns and 2 rows : The matrix is a binary matrix, which means each element in the matrix can be 0 or 1. The sum of elements of the 0-th(upper) row is given as upper.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Greedy, Array, Matrix
Intuition
A locally optimal choice leads to a globally optimal result for this structure.
That means we can commit to decisions as we scan without backtracking.
Approach
Sort or preprocess if needed, then repeatedly take the best available local choice.
Maintain the minimal state necessary to validate the greedy decision.
Steps:
- Sort or preprocess as needed.
- Iterate and pick the best local option.
- Track the current solution.
Example
Input: upper = 2, lower = 1, colsum = [1,1,1]
Output: [[1,1,0],[0,0,1]]
Explanation: [[1,0,1],[0,1,0]], and [[0,1,1],[1,0,0]] are also correct answers.
Python Solution
class Solution:
def reconstructMatrix(
self, upper: int, lower: int, colsum: List[int]
) -> List[List[int]]:
n = len(colsum)
ans = [[0] * n for _ in range(2)]
for j, v in enumerate(colsum):
if v == 2:
ans[0][j] = ans[1][j] = 1
upper, lower = upper - 1, lower - 1
if v == 1:
if upper > lower:
upper -= 1
ans[0][j] = 1
else:
lower -= 1
ans[1][j] = 1
if upper < 0 or lower < 0:
return []
return ans if lower == upper == 0 else []
Complexity
The time complexity is , where is the length of the array . 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.