algoadvance

Given an integer array nums and an integer k, return the maximum sum of k elements from the array nums where every element in the array can be chosen only once.

Clarifying Questions

1. Range of Input Length
   • What is the size range of the input list nums?
2. Element Values
   • What range of values can the elements in nums have?
3. Exact K Elements
   • Should the sum always be computed using exactly k elements? (assuming the answer is yes)

Example

If nums = [1, 2, 3, 4, 5] and k = 2, the maximum sum obtained by choosing exactly 2 elements is 4 + 5 = 9.

Strategy

To maximize the sum using exactly k elements from the array nums:

1. Sort the Array: First, sort the nums array in non-decreasing (ascending) order.
2. Select Largest Elements: Select the largest k elements from the sorted array. These will be the last k elements after sorting.
3. Sum the Selected Elements: Sum these k largest elements to get the required maximum sum.

Time Complexity

• Time Complexity: The time complexity is dominated by the sorting step, which is (O(n \log n)), where (n) is the number of elements in nums.
• Space Complexity: The space complexity is (O(1)) if you do in-place sorting, (O(n)) if the sorting creates a new list.

Code

Here is the implementation of the described strategy:

def maxSumWithKElements(nums, k):
    # Sort the array in ascending order
    nums.sort()
    # Sum of the largest k elements
    return sum(nums[-k:])

# Test case
nums = [1, 2, 3, 4, 5]
k = 2
print(maxSumWithKElements(nums, k))  # Output: 9

Explanation

1. Sorting the Array: We first sort the array nums to arrange the elements in ascending order.
2. Selecting K Elements: Using nums[-k:], we extract the last k elements from the sorted array, which are the largest k elements.
3. Summing Up: Finally, we sum up these selected elements to get the maximum sum.

This approach ensures that we efficiently compute the maximum sum using exactly k elements from the given array.

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