Minimum Number of Visited Cells in a Grid — LeetCode 2617 Python Solution

HardStackBreadth-First SearchUnion FindArrayDynamic ProgrammingMatrixMonotonic StackHeap (Priority Queue)
Problem
#2617
Pattern
Union-Find
Reading time
4 min

The problem

You are given a 0-indexed m x n integer matrix grid. Your initial position is at the top-left cell (0, 0).

Example

Input
grid = [[3,4,2,1],[4,2,3,1],[2,1,0,0],[2,4,0,0]]
Output
4
Explanation
The image above shows one of the paths that visits exactly 4 cells.

Python solution

Python
class Solution:
    def minimumVisitedCells(self, grid: List[List[int]]) -> int:
        m, n = len(grid), len(grid[0])
        dist = [[-1] * n for _ in range(m)]
        dist[0][0] = 1
        row = [[] for _ in range(m)]
        col = [[] for _ in range(n)]
        for i in range(m):
            for j in range(n):
                while row[i] and grid[i][row[i][0][1]] + row[i][0][1] < j:
                    heappop(row[i])
                if row[i] and (dist[i][j] == -1 or dist[i][j] > row[i][0][0] + 1):
                    dist[i][j] = row[i][0][0] + 1
                while col[j] and grid[col[j][0][1]][j] + col[j][0][1] < i:
                    heappop(col[j])
                if col[j] and (dist[i][j] == -1 or dist[i][j] > col[j][0][0] + 1):
                    dist[i][j] = col[j][0][0] + 1
                if dist[i][j] != -1:
                    heappush(row[i], (dist[i][j], j))
                    heappush(col[j], (dist[i][j], i))
        return dist[-1][-1]

Complexity

MeasureComplexity
TimeO(m \times n \times \log (m \times n))
SpaceO(m \times n) auxiliary

Pattern: Union-Find

Merge groups and ask whether two things are connected, both in near-constant time. LeetCode 2617. Minimum Number of Visited Cells in a Grid is filed here because LeetCode tags it Union Find, which is the vocabulary this hub collects.

The union-find guide has the Python template for the pattern and the 83 LeetCode problems that use it.

Related problems

Frequently asked questions

How hard is LeetCode 2617. Minimum Number of Visited Cells in a Grid?
LeetCode 2617. Minimum Number of Visited Cells in a Grid is rated Hard on LeetCode.
What is the time complexity of LeetCode 2617. Minimum Number of Visited Cells in a Grid?
The Python solution on this page runs in O(m \times n \times \log (m \times n)).
What is the space complexity of LeetCode 2617. Minimum Number of Visited Cells in a Grid?
The Python solution on this page uses O(m \times n) auxiliary space.
What topics does LeetCode 2617. Minimum Number of Visited Cells in a Grid cover?
LeetCode 2617. Minimum Number of Visited Cells in a Grid is tagged Stack, Breadth-First Search, Union Find, Array, Dynamic Programming, Matrix, Monotonic Stack and Heap (Priority Queue) on LeetCode.

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