398 Random Pick Index

1. Question

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

(1) Reservoir Sampling
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class Solution {
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Random rand;
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int[] nums;
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public Solution(int[] nums) {
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this.nums = nums;
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rand = new Random();
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}
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public int pick(int target) {
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int res = -1;
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int count = 0;
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for (int i = 0; i < nums.length; i++) {
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if (nums[i] == target && rand.nextInt(++count) == 0) {
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res = i;
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}
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}
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return res;
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}
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}
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/**
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* Your Solution object will be instantiated and called as such:
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* Solution obj = new Solution(nums);
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* int param_1 = obj.pick(target);
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*/
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3. Time & Space Complexity

Reservoir Sampling: 时间复杂度O(n), 空间复杂度O(n)