519. Random Flip Matrix

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LeetCode

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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.

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 <= 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.

Code

384

class Solution {
    Map<Integer, Integer> map;
    int rows;
    int cols;
    int total;
    Random random;
    
    public Solution(int n_rows, int n_cols) {
        map = new HashMap<>();
        random = new Random();
        rows = n_rows; 
        cols = n_cols; 
        total = rows * cols;
    }
    
    public int[] flip() {
        int rand = random.nextInt(total--);
        
        int index = rand;
        if(map.containsKey(rand)) {
            index = map.get(rand);
        }
        
        map.put(rand, total);
        if(map.containsKey(total)) {
            map.put(rand, map.get(total));
        }
        
        return new int[]{index / cols, index % cols};
    }
    
    public void reset() {
        map.clear();
        total = rows * cols;
    }
}