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LeetCode 519, Medium. Topics: Hash Table, Math, Reservoir Sampling, Randomized. View on LeetCode. Generate this problem as a practice environment: tested reference solution, 18 parametrized pytest cases, and a playground notebook:

Problem

There is an m x n binary grid matrix with all the values set 0 initially. Design an algorithm to randomly pick an index (i, j) where matrix[i][j] == 0 and flips it to 1. All the indices (i, j) where matrix[i][j] == 0 should be equally likely to be returned. Optimize your algorithm to minimize the number of calls made to the built-in random function of your language and optimize the time and space complexity. Implement the Solution class:
  • Solution(int m, int n) Initializes the object with the size of the binary matrix m and n.
  • int[] flip() Returns a random index [i, j] of the matrix where matrix[i][j] == 0 and flips it to 1.
  • void reset() Resets all the values of the matrix to be 0.

Examples

Constraints

  • 1 <= m, n <= 10^4
  • There will be at least one free cell for each call to flip.
  • At most 1000 calls will be made to flip and reset.

Solution

Reference implementation from solution.py on GitHub, full suite in test_solution.py:

Complexity

Tags

Last modified on September 7, 2026