Leetcode #1183: Maximum Number of Ones
In this guide, we solve Leetcode #1183 Maximum Number of Ones 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
Consider a matrix M with dimensions width * height, such that every cell has value 0 or 1, and any square sub-matrix of M of size sideLength * sideLength has at most maxOnes ones. Return the maximum possible number of ones that the matrix M can have.
Quick Facts
- Difficulty: Hard
- Premium: Yes
- Tags: Greedy, Math, Sorting, Heap (Priority Queue)
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: width = 3, height = 3, sideLength = 2, maxOnes = 1
Output: 4
Explanation:
In a 3*3 matrix, no 2*2 sub-matrix can have more than 1 one.
The best solution that has 4 ones is:
[1,0,1]
[0,0,0]
[1,0,1]
Python Solution
class Solution:
def maximumNumberOfOnes(
self, width: int, height: int, sideLength: int, maxOnes: int
) -> int:
x = sideLength
cnt = [0] * (x * x)
for i in range(width):
for j in range(height):
k = (i % x) * x + (j % x)
cnt[k] += 1
cnt.sort(reverse=True)
return sum(cnt[:maxOnes])
Complexity
The time complexity is , where and are the number of rows and columns of the matrix, respectively. The space complexity is O(1) to O(n).
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.