Off-by-one on range boundaries
Wrong move: Loop endpoints miss first/last candidate.
Usually fails on: Fails on minimal arrays and exact-boundary answers.
Fix: Re-derive loops from inclusive/exclusive ranges before coding.
Build confidence with an intuition-first walkthrough focused on array fundamentals.
You are given a 0-indexed integer array nums and an integer k. Your task is to perform the following operation exactly k times in order to maximize your score:
m from nums.m from the array.m + 1 to the array.m.Return the maximum score you can achieve after performing the operation exactly k times.
Example 1:
Input: nums = [1,2,3,4,5], k = 3 Output: 18 Explanation: We need to choose exactly 3 elements from nums to maximize the sum. For the first iteration, we choose 5. Then sum is 5 and nums = [1,2,3,4,6] For the second iteration, we choose 6. Then sum is 5 + 6 and nums = [1,2,3,4,7] For the third iteration, we choose 7. Then sum is 5 + 6 + 7 = 18 and nums = [1,2,3,4,8] So, we will return 18. It can be proven, that 18 is the maximum answer that we can achieve.
Example 2:
Input: nums = [5,5,5], k = 2 Output: 11 Explanation: We need to choose exactly 2 elements from nums to maximize the sum. For the first iteration, we choose 5. Then sum is 5 and nums = [5,5,6] For the second iteration, we choose 6. Then sum is 5 + 6 = 11 and nums = [5,5,7] So, we will return 11. It can be proven, that 11 is the maximum answer that we can achieve.
Constraints:
1 <= nums.length <= 1001 <= nums[i] <= 1001 <= k <= 100Problem summary: You are given a 0-indexed integer array nums and an integer k. Your task is to perform the following operation exactly k times in order to maximize your score: Select an element m from nums. Remove the selected element m from the array. Add a new element with a value of m + 1 to the array. Increase your score by m. Return the maximum score you can achieve after performing the operation exactly k times.
Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.
Pattern signal: Array · Greedy
[1,2,3,4,5] 3
[5,5,5] 2
Source-backed implementations are provided below for direct study and interview prep.
// Accepted solution for LeetCode #2656: Maximum Sum With Exactly K Elements
class Solution {
public int maximizeSum(int[] nums, int k) {
int x = 0;
for (int v : nums) {
x = Math.max(x, v);
}
return k * x + k * (k - 1) / 2;
}
}
// Accepted solution for LeetCode #2656: Maximum Sum With Exactly K Elements
func maximizeSum(nums []int, k int) int {
x := slices.Max(nums)
return k*x + k*(k-1)/2
}
# Accepted solution for LeetCode #2656: Maximum Sum With Exactly K Elements
class Solution:
def maximizeSum(self, nums: List[int], k: int) -> int:
x = max(nums)
return k * x + k * (k - 1) // 2
// Accepted solution for LeetCode #2656: Maximum Sum With Exactly K Elements
impl Solution {
pub fn maximize_sum(nums: Vec<i32>, k: i32) -> i32 {
let mut mx = 0;
for &n in &nums {
if n > mx {
mx = n;
}
}
((0 + k - 1) * k) / 2 + k * mx
}
}
// Accepted solution for LeetCode #2656: Maximum Sum With Exactly K Elements
function maximizeSum(nums: number[], k: number): number {
const x = Math.max(...nums);
return k * x + (k * (k - 1)) / 2;
}
Use this to step through a reusable interview workflow for this problem.
Try every possible combination of choices. With n items each having two states (include/exclude), the search space is 2ⁿ. Evaluating each combination takes O(n), giving O(n × 2ⁿ). The recursion stack or subset storage uses O(n) space.
Greedy algorithms typically sort the input (O(n log n)) then make a single pass (O(n)). The sort dominates. If the input is already sorted or the greedy choice can be computed without sorting, time drops to O(n). Proving greedy correctness (exchange argument) is harder than the implementation.
Review these before coding to avoid predictable interview regressions.
Wrong move: Loop endpoints miss first/last candidate.
Usually fails on: Fails on minimal arrays and exact-boundary answers.
Fix: Re-derive loops from inclusive/exclusive ranges before coding.
Wrong move: Locally optimal choices may fail globally.
Usually fails on: Counterexamples appear on crafted input orderings.
Fix: Verify with exchange argument or monotonic objective before committing.