398. Random Pick Index

1. Description

Given an integer array nums 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.
Implement the Solution class:

• Solution(int[] nums) Initializes the object with the array nums.
• int pick(int target) Picks a random index i from nums where nums[i] == target. If there are multiple valid i’s, then each index should have an equal probability of returning.

2. Example

Example 1

Input
[“Solution”, “pick”, “pick”, “pick”]
[[[1, 2, 3, 3, 3]], [3], [1], [3]]
Output
[null, 4, 0, 2]

Explanation
Solution solution = new Solution([1, 2, 3, 3, 3]);
solution.pick(3); // It should return either index 2, 3, or 4 randomly. Each index should have equal probability of returning.
solution.pick(1); // It should return 0. Since in the array only nums[0] is equal to 1.
solution.pick(3); // It should return either index 2, 3, or 4 randomly. Each index should have equal probability of returning.

3. Constraints

• 1 <= nums.length <= 2 * 10$^4$
• -2$^{31}$ <= nums[i] <= 2$^{31}$ - 1
• target is an integer from nums.
• At most 10$^4$ calls will be made to pick.

4. Solutions

Hash Table

n is the number of elements in nums
Solution(nums): O(n) time, O(n) space
pick(target): O(1) time, O(1) space

class Solution {
public:
    Solution(vector<int> &nums) {
        for (int i = 0, n = nums.size(); i < n; ++i) {
            indexes[nums[i]].push_back(i);
        }
    }

    int pick(int target) {
        return indexes[target][rand() % indexes[target].size()];
    }

private:
    unordered_map<int, vector<int>> indexes;
};