# Question

Formatted question description: https://leetcode.ca/all/398.html

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.

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.


Constraints:

• 1 <= nums.length <= 2 * 104
• -231 <= nums[i] <= 231 - 1
• target is an integer from nums.
• At most 104 calls will be made to pick.

# Algorithm

Define two variables, counter cnt and return result res.

Traverse the entire array,

• If the value of the array is not equal to target, skip directly;
• If it is equal to target, the counter is increased by 1,

Then we randomly generate a number in the range of [0,cnt). If this number is 0, we assign res.

# Code

• import java.util.Random;

public class Random_Pick_Index {

// ref: https://leetcode.com/problems/random-pick-index/discuss/88072/Simple-Reservoir-Sampling-solution
class Solution {

int[] nums;
Random rnd;

public Solution(int[] nums) {
this.nums = nums;
this.rnd = new Random();
}

public int pick(int target) {

int resultIndex = -1;
int count = 0;

for (int i = 0; i < nums.length; i++) {
if (nums[i] != target) {
continue;
}

count++;

if (rnd.nextInt(count) == 0) {
resultIndex = i;
// first time nextInt is always 0, so set as first index
// for the rest, probobility issue
}
}

return resultIndex;
}
}

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

############

class Solution {
private int[] nums;
private Random random = new Random();

public Solution(int[] nums) {
this.nums = nums;
}

public int pick(int target) {
int n = 0, ans = 0;
for (int i = 0; i < nums.length; ++i) {
if (nums[i] == target) {
++n;
int x = 1 + random.nextInt(n);
if (x == n) {
ans = i;
}
}
}
return ans;
}
}

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

• class Solution:
def __init__(self, nums: List[int]):
self.nums = nums

def pick(self, target: int) -> int:
n = ans = 0
for i, v in enumerate(self.nums):
if v == target:
n += 1
x = random.randint(1, n)
if x == n:
ans = i
return ans

# Your Solution object will be instantiated and called as such:
# obj = Solution(nums)
# param_1 = obj.pick(target)

############

class Solution(object):

def __init__(self, nums):
"""

:type nums: List[int]
:type numsSize: int
"""
self.nums = nums

def pick(self, target):
"""
:type target: int
:rtype: int
"""
count = 0
ans = -1
for i in range(0, len(self.nums)):
if self.nums[i] == target:
count += 1
if random.randrange(0, count) == 0:
ans = i
return ans

# Your Solution object will be instantiated and called as such:
# obj = Solution(nums)
# param_1 = obj.pick(target)


• class Solution {
public:
vector<int> nums;

Solution(vector<int>& nums) {
this->nums = nums;
}

int pick(int target) {
int n = 0, ans = 0;
for (int i = 0; i < nums.size(); ++i) {
if (nums[i] == target) {
++n;
int x = 1 + rand() % n;
if (n == x) ans = i;
}
}
return ans;
}
};

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

• type Solution struct {
nums []int
}

func Constructor(nums []int) Solution {
return Solution{nums}
}

func (this *Solution) Pick(target int) int {
n, ans := 0, 0
for i, v := range this.nums {
if v == target {
n++
x := 1 + rand.Intn(n)
if n == x {
ans = i
}
}
}
return ans
}

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