We use cookies (including Google cookies) to personalize ads and analyze traffic. By continuing to use our site, you accept our Privacy Policy.

SimplyLeet
TagsDisclaimersPrivacyTermsContactAbout Us

Maximum Total Reward Using Operations II

Difficulty: Hard

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 (i.e., x = x + rewardValues[i]), and mark the index i. Return an integer denoting the maximum total reward you can collect by performing the operations optimally.

Key Insights

  • The greedy approach is optimal for this problem as we want to maximize the total reward.
  • We can only add a reward if it is greater than the current total reward x.
  • Sorting the array helps in efficiently selecting the maximum rewards that can be added without violating the condition.
  • After sorting, we can iterate through the rewards and keep adding them to x while ensuring the condition is met.

Space and Time Complexity

Time Complexity: O(n log n) - due to sorting the array.
Space Complexity: O(1) - as we are using a constant amount of extra space.

Solution

To solve this problem, we will use a greedy algorithm. First, we sort the rewardValues array in ascending order. Then, we iterate through the sorted array and maintain a variable x that tracks the total reward. For each reward in the sorted list, we check if it is greater than x. If it is, we add it to x and mark it as included. This ensures that we are always maximizing our total reward by only adding rewards that can be added according to the rules.

Code Solutions

def maxTotalReward(rewardValues):
    # Sort the reward values in ascending order
    rewardValues.sort()
    total_reward = 0  # Initialize total reward
    for reward in rewardValues:
        # If the current reward is greater than total_reward, add it
        if reward > total_reward:
            total_reward += reward
    return total_reward
← Back to All Questions