Largest Plus Sign — LeetCode 764 Python Solution

MediumArrayDynamic Programming
Problem
#764
Reading time
3 min

The problem

You are given an integer n. You have an n x n binary grid grid with all values initially 1's except for some indices given in the array mines.

Example

Input
n = 5, mines = [[4,2]]
Output
2
Explanation
In the above grid, the largest plus sign can only be of order 2. One of them is shown.

Python solution

Python
class Solution:
    def orderOfLargestPlusSign(self, n: int, mines: List[List[int]]) -> int:
        dp = [[n] * n for _ in range(n)]
        for x, y in mines:
            dp[x][y] = 0
        for i in range(n):
            left = right = up = down = 0
            for j, k in zip(range(n), reversed(range(n))):
                left = left + 1 if dp[i][j] else 0
                right = right + 1 if dp[i][k] else 0
                up = up + 1 if dp[j][i] else 0
                down = down + 1 if dp[k][i] else 0
                dp[i][j] = min(dp[i][j], left)
                dp[i][k] = min(dp[i][k], right)
                dp[j][i] = min(dp[j][i], up)
                dp[k][i] = min(dp[k][i], down)
        return max(max(v) for v in dp)

Complexity

MeasureComplexity
TimeO(n·m) (typical)
SpaceO(n·m) or optimized auxiliary

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 764. Largest Plus Sign is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

Related problems

Frequently asked questions

How hard is LeetCode 764. Largest Plus Sign?
LeetCode 764. Largest Plus Sign is rated Medium on LeetCode.
What topics does LeetCode 764. Largest Plus Sign cover?
LeetCode 764. Largest Plus Sign is tagged Array and Dynamic Programming on LeetCode.

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