519 Random Flip Matrix
519. Random Flip Matrix
1. Question
You are given the number of rowsn_rows
and number of columnsn_cols
of a 2D binary matrix where all values are initially 0. Write a functionflip
which chooses a 0 value uniformly at random, changes it to 1, and then returns the position[row.id, col.id]
of that value. Also, write a functionreset
which sets all values back to 0. Try to minimize the number of calls to system's Math.random()and optimize the time and space complexity.
Note:
1 <= n_rows, n_cols <= 10000
0 <= row.id < n_rows
and0 <= col.id < n_cols
flip
will not be called when the matrix has no 0 values left.the total number of calls to
flip
andreset
will not exceed 1000.
Example 1:
Input:
["Solution","flip","flip","flip","flip"]
[[2,3],[],[],[],[]]
Output: [null,[0,1],[1,2],[1,0],[1,1]]
Example 2:
Input:
["Solution","flip","flip","reset","flip"]
[[1,2],[],[],[],[]]
Output: [null,[0,0],[0,1],null,[0,0]]
Explanation of Input Syntax:
The input is two lists: the subroutines called and their arguments.Solution
's constructor has two arguments,n_rows
andn_cols
. flip
andreset
have no arguments. Arguments are always wrapped with a list, even if there aren't any.
2. Implementation
(1) Fisher-Yate 算法
class Solution {
// 思路: Fisher-Yate的2D版本
Map<Integer, Integer> map;
Random rand;
int rows, cols, total;
public Solution(int n_rows, int n_cols) {
map = new HashMap();
rand = new Random();
rows = n_rows;
cols = n_cols;
total = rows * cols;
}
public int[] flip() {
int index = rand.nextInt(total--);
// Check if we have put anything in this index
int x = map.getOrDefault(index, index);
// swap index with total
map.put(index, map.getOrDefault(total, total));
return new int[] {x / cols, x % cols};
}
public void reset() {
map.clear();
total = rows * cols;
}
}
/**
* Your Solution object will be instantiated and called as such:
* Solution obj = new Solution(n_rows, n_cols);
* int[] param_1 = obj.flip();
* obj.reset();
*/
3. Time & Space Complexity
Fisher-Yate 时间复杂度flip: O(1), 空间复杂度O(m * n), 空间主要是map,m为行,n为列
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