题目描述

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.

样例

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);

算法

(蓄水池抽样)

利用一个unordered_map<int, vector<int>> um存储每个数值对应的下标，那么随机返回一个索引，其实就是生成一个0-um[target].size() - 1的一个随机数，这样如果存在多次pick，那么每次都是$O(1)$的效率。

C++ 代码

class Solution {
    unordered_map<int, vector<int>> um;
public:
    Solution(vector<int>& nums) {
        std::ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout.tie(NULL);

        int n = nums.size();
        for (int i = 0; i < n; ++i) {
            um[nums[i]].push_back(i);
        }
    }

    int pick(int target) {
        int len = um[target].size();
        int pos = rand() % len;
        return um[target][pos];
    }
};

/**
 * Your Solution object will be instantiated and called as such:
 * Solution* obj = new Solution(nums);
 * int param_1 = obj->pick(target);
 */