Algorithm

Problem Name: 519. Random Flip Matrix

Problem Link: https://leetcode.com/problems/random-flip-matrix/


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.

 

Example 1:

Input
["Solution", "flip", "flip", "flip", "reset", "flip"]
[[3, 1], [], [], [], [], []]
Output
[null, [1, 0], [2, 0], [0, 0], null, [2, 0]]

Explanation
Solution solution = new Solution(3, 1);
solution.flip();  // return [1, 0], [0,0], [1,0], and [2,0] should be equally likely to be returned.
solution.flip();  // return [2, 0], Since [1,0] was returned, [2,0] and [0,0]
solution.flip();  // return [0, 0], Based on the previously returned indices, only [0,0] can be returned.
solution.reset(); // All the values are reset to 0 and can be returned.
solution.flip();  // return [2, 0], [0,0], [1,0], and [2,0] should be equally likely to be returned.

 

Constraints:

  • 1 <= m, n <= 104
  • There will be at least one free cell for each call to flip.
  • At most 1000 calls will be made to flip and reset.
 

Code Examples

#1 Code Example with Javascript Programming

Code - Javascript Programming


const Solution = function(n_rows, n_cols) {
  this.r = n_rows
  this.c = n_cols
  this.total = n_rows * n_cols
  this.m = new Map()
}

Solution.prototype.flip = function() {
  const r = (Math.random() * this.total--) >> 0
  const i = this.m.get(r) || r
  this.m.set(r, this.m.get(this.total) || this.total)
  return [(i / this.c) >> 0, i % this.c]
}

Solution.prototype.reset = function() {
  this.m.clear()
  this.total = this.c * this.r
}
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Input

x
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+
cmd
["Solution", "flip", "flip", "flip", "reset", "flip"] [[3, 1], [], [], [], [], []]

Output

x
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cmd
[null, [1, 0], [2, 0], [0, 0], null, [2, 0]]

#2 Code Example with Python Programming

Code - Python Programming


class Solution:

    def __init__(self, n_rows, n_cols):
        self.rows, self.cols, self.used = n_rows, n_cols, set()
        
    def flip(self):
        while True:
            r, c = random.randint(1, self.rows), random.randint(1, self.cols)
            if (r, c) not in self.used:
                self.used.add((r, c))
                return [r - 1, c - 1]
            
    def reset(self):
        self.used = set()
Copy The Code & Try With Live Editor

Input

x
–
+
cmd
["Solution", "flip", "flip", "flip", "reset", "flip"] [[3, 1], [], [], [], [], []]

Output

x
–
+
cmd
[null, [1, 0], [2, 0], [0, 0], null, [2, 0]]
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