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Problem · Array

Count Possible Winners (All About Rewards :)

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Problem statement

SDE II

Amazon Shopping is running a reward collection event for its customers.

There are n customers and the i-th customer has collected initialRewards[i] points so far.

One final tournament is to take place where:

The champion earns n additional points

The second place earns n - 1 points

The third place earns n - 2 points

… and the last place earns 1 point

Given an integer array initialRewards of length n, representing the initial reward points of the customers before the final tournament:

Find the number of customers i (1 ≤ i ≤ n) such that, if the i-th customer wins the final tournament, they would have the highest total points.

Note -

The total points = initialRewards[i] + n (if they win). Other customers also get points in the tournament depending on their ranks (from n - 1 to 1). You must check if the i-th customer, upon winning, ends up with the highest total score, regardless of how others place.

Function

countPossibleWinners(initialRewards: int[], n: int) → int

Examples

Example 1

initialRewards = [1, 3, 4]n = 3return = 2

Let's analyze for each customer if they win the final tournament, would they have the highest total points or not:

If the 1st customer wins the final tournament, their total points would be: 1 + 3 = 4, but this is not the highest possible points in this case.
For example, if the 3rd customer with an initial reward of 4 comes 2nd, then they would achieve a total of: 4 + 2 = 6 points which is the higher than 1st customer points.
If the 2nd customer wins the final tournament, their total points would be: 3 + 3 = 6, and this is the highest total points in this case.
Even if the 3rd customer with an initial reward of 4 comes 2nd, then they would achieve a total of: 4 + 2 = 6 points which is not greater than 2nd customer points.
If the 3rd customer wins the final tournament, their total points would be: 4 + 3 = 7, and this is the highest total points, as there are no other customers that can achieve the total point of 7 in this case.

Thus, the customers 2 and 3 are the ones such that, if they win the final tournament, they would have the highest total points.

Hence the answer is 2.

Example 2

initialRewards = [5, 7, 9, 11]n = 4return = 1

Only the 4th customer is the one such that, if they win the final tournament, they would have the highest total points.

Example 3

initialRewards = [8, 10, 9]n = 3return = 2

Only the 2nd and the 3rd customers are the ones such that, if they win the final tournament, they would have the highest total points.

If the 2nd customer wins the final tournament, their total points would be: 10 + 3 = 13, and this is the highest total points, as there are no other customers that can achieve the total point of 13 in this case.
If the 3rd customer wins the final tournament, their total points would be: 9 + 3 = 12, and this is the highest total points in this case.
Even if the 2nd customer with an initial reward of 10 comes 2nd, then they would achieve a total of: 10 + 2 = 12 points which is not greater than 2nd customer points.

Constraints

1 ≤ n ≤ 10^5
0 ≤ initialRewards[i] ≤ 10^5
Complete constraints added on 06-18-2025