leetcode_398

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);

Solutions

1. Reservoir Sampling

2. reference: https://leetcode-cn.com/problems/random-pick-index/solution/xu-shui-chi-chou-yang-wen-ti-by-an-xin-9/

3. Sample each element with probability 1 / n;

4. Suppose there are 4 items, following the rule of selecting each encountered index with probability of 1 / numseen(include self). we have:

5. the prob of selected the first element at last is: 3/4 * 2/3 * 1/2 == 1/4

6. second 3/4 * 2/3 * 1/2 == 1/4

7. third 3/4 * 1/3 == 1/4

8. fourth 1/4 == 1/4

class Solution {
public:
    vector<int> nums;
    Solution(vector<int>& nums) : nums(nums) {
    }

    int pick(int target) {
        int cnt = 0, index = -1;
        for (int i = 0; i < nums.size(); i++)
            if (nums[i] == target) {
                cnt++;
                // (1 / cnt) prob to slect the current index 
                if (rand() % cnt == 0)
                    index = i;
            }
        return index;
    }
};