Leetcode #1536: Minimum Swaps to Arrange a Binary Grid
In this guide, we solve Leetcode #1536 Minimum Swaps to Arrange a Binary Grid 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 an n x n binary grid, in one step you can choose two adjacent rows of the grid and swap them. A grid is said to be valid if all the cells above the main diagonal are zeros.
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: grid = [[0,0,1],[1,1,0],[1,0,0]]
Output: 3
Python Solution
class Solution:
def minSwaps(self, grid: List[List[int]]) -> int:
n = len(grid)
pos = [-1] * n
for i in range(n):
for j in range(n - 1, -1, -1):
if grid[i][j] == 1:
pos[i] = j
break
ans = 0
for i in range(n):
k = -1
for j in range(i, n):
if pos[j] <= i:
ans += j - i
k = j
break
if k == -1:
return -1
while k > i:
pos[k], pos[k - 1] = pos[k - 1], pos[k]
k -= 1
return ans
Complexity
The time complexity is , and the space complexity is . 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.