Random Pick Index

Random Pick Index


Given an array of integers with possible duplicates, randomly output the index of a given target number. You can assume that the given target number must exist in the array.
Note:
The array size can be very large. Solution that uses too much extra space will not pass the judge.
Example:
int[] nums = new int[] {1,2,3,3,3};
Solution solution = new Solution(nums);

// pick(3) should return either index 2, 3, or 4 randomly. Each index should have equal probability of returning.
solution.pick(3);

// pick(1) should return 0. Since in the array only nums[0] is equal to 1.
solution.pick(1);

class Solution {
    int[] nums;
    Random rand;

    public Solution(int[] nums) {
        this.nums = nums;
        this.rand = new Random();
    }
    
    public int pick(int target) {
        int count = 0;
        int sample = -1;
        for(int i = 0; i < nums.length; i++){
            if(nums[i] == target){
                count++;
                int x = rand.nextInt(count);
                if(x == 0){
                    sample = i;
                }
            }
        }
        return sample;
    }
}


a  b c c c

c

sample =  2   3 ½  3 ⅓ 
                      2 ½  2 ⅓ 
                               4 ⅓
      
counter = 3; [0, 3)
i = 3


index = 2,   3
counter = 1  2
sample = 2

0, 1, 2
sample   0  0 ½ 0 ½ * ⅔ = ⅓ 
            1 ½
                 2 ⅓
counter  1,  2,  3
产生一个随机数，如果这个随机数等于0, 替换掉原来的index, 不然保留

sample = 0
counter = 1
for (int i = 1; i < … ;i++) {
    counter++;
    int random = randint(0, counter);
    if (random == 0) {  1/counter 替换掉原来的数字
        sample = i;
    }
}

P(第三步保留的是0) = P(第二步是0

 

Given an array of integers with possible duplicates, randomly output the index of a given target number. You can assume that the given target number must exist in the array.

Note:
The array size can be very large. Solution that uses too much extra space will not pass the judge.

Example:

int[] nums = new int[] {1,2,3,3,3};
Solution solution = new Solution(nums);

// pick(3) should return either index 2, 3, or 4 randomly. Each index should have equal probability of returning.
solution.pick(3);

// pick(1) should return 0. Since in the array only nums[0] is equal to 1.
solution.pick(1);