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);

解析：一个概率题，假如数组中一个有k个target,则每个target的概率相同即为1/k，rand()%k==0的概率即为1/k，当遍历到第i个与target相同的元素时,且最后pick的下标为i时的概率p=1/i*(i/(i+1))*...*(k-1)/k=1/k；即每次遍历到target时，把结果更新为当前i时的概率为rand()%i==0的概率。注：本题由于数组很大

代码：

class Solution {
public:

    vector<int> num;

    Solution(vector<int> nums) {
        num=nums;
    }
    
    int pick(int target) {
        int length=num.size();
       
        int indexnum=-1;
        int count=0;
        for (int i=0; i<num.size(); i++)
        {
            
            if (num[i]==target)
            { 
                count++;
                if (indexnum==-1)
                indexnum=i;
                else
                {
                    indexnum=rand()%count?(indexnum):i;
                }
                
            }
        }
        
         return indexnum;
        
    }
};

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