How do you solve Largest Plus Sign on LeetCode?

Largest Plus Sign (LeetCode #764) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n²) time complexity and O(n²) space complexity. Key insight: The center of the plus sign must be a 1, and the arms must extend in all four directions without hitting a 0.

What is the brute force solution for Largest Plus Sign?

The brute force approach for Largest Plus Sign is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach checks every possible center point in the grid to see how large a plus sign can be formed. This is straightforward but inefficient, as it involves checking multiple directions for each center. The optimal Optimal Solution approach improves this to O(n²).

What algorithm or data structure is used to solve Largest Plus Sign?

Largest Plus Sign uses the following concepts: Array, Dynamic Programming. The recommended patterns to study are: Dynamic Programming, Grid Traversal.

What are the interview tips for Largest Plus Sign?

Explain your thought process clearly and ask clarifying questions about the problem. Discuss the trade-offs of different approaches, even if you choose to implement one. Practice dry-running your solution with examples to ensure correctness.

What are common mistakes when solving Largest Plus Sign?

Not considering edge cases where the grid is small or fully blocked. Failing to correctly update the maximum order found.

#764

Largest Plus Sign

Medium

ArrayDynamic ProgrammingDynamic ProgrammingGrid Traversal

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n²)
Space	O(1)	O(n²)

💡

Intuition

Time O(n²)Space O(n²)

Instead of checking each cell multiple times, we can preprocess the grid to count how many consecutive 1's are in each direction for every cell. This allows us to compute the maximum order of the plus sign in constant time for each cell.

⚙️

Algorithm

4 steps

1Step 1: Create four matrices (left, right, up, down) to store the count of consecutive 1's in each direction for each cell.
2Step 2: Populate these matrices by iterating through the grid in all four directions.
3Step 3: For each cell, calculate the possible order of the plus sign as the minimum of the counts from the four matrices.
4Step 4: Track the maximum order found.

solution.py24 lines

1def orderOfLargestPlusSign(n, mines):
2    grid = [[1] * n for _ in range(n)]
3    for x, y in mines:
4        grid[x][y] = 0
5    left = [[0] * n for _ in range(n)]
6    right = [[0] * n for _ in range(n)]
7    up = [[0] * n for _ in range(n)]
8    down = [[0] * n for _ in range(n)]
9    for r in range(n):
10        for c in range(n):
11            if grid[r][c] == 1:
12                left[r][c] = (left[r][c-1] + 1) if c > 0 else 1
13                up[r][c] = (up[r-1][c] + 1) if r > 0 else 1
14    for r in range(n-1, -1, -1):
15        for c in range(n-1, -1, -1):
16            if grid[r][c] == 1:
17                right[r][c] = (right[r][c+1] + 1) if c < n-1 else 1
18                down[r][c] = (down[r+1][c] + 1) if r < n-1 else 1
19    max_order = 0
20    for r in range(n):
21        for c in range(n):
22            if grid[r][c] == 1:
23                max_order = max(max_order, min(left[r][c], right[r][c], up[r][c], down[r][c]))
24    return max_order

ℹ

Complexity note: The time complexity remains O(n²) due to the need to process each cell in the grid, but we use additional space for the four direction matrices.

1The center of the plus sign must be a 1, and the arms must extend in all four directions without hitting a 0.
2Using preprocessing (direction counts) allows for efficient calculation of the plus sign order.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.