Problem Description
You are given an integer array rewardValues of length n, representing the values of rewards. Initially, your total reward x is 0, and all indices are unmarked. You are allowed to perform the following operation any number of times: Choose an unmarked index i from the range [0, n - 1]. If rewardValues[i] is greater than your current total reward x, then add rewardValues[i] to x, and mark the index i. Return an integer denoting the maximum total reward you can collect by performing the operations optimally.
Key Insights
- The total reward can only increase if we choose rewards that are greater than the current total reward.
- The strategy involves selecting rewards in a way that maximizes the total reward.
- Sorting the rewards helps in easily determining which rewards can be added based on the current total reward.
- A greedy approach can be applied where we always try to take the next possible maximum reward.
Space and Time Complexity
Time Complexity: O(n log n) due to sorting the array.
Space Complexity: O(1) if we consider the sorting in-place, otherwise O(n) for storing the sorted array.
Solution
To solve the problem, we can use a greedy algorithm approach. We will first sort the rewardValues array in ascending order. Starting from a total reward x initialized to 0, we iterate through the sorted list and add each reward to x only if it is greater than the current x. We also mark the index as used by simply iterating through the sorted list without needing a separate data structure for marking.