LeetCode #2829 — MEDIUM

Determine the Minimum Sum of a k-avoiding Array

Move from brute-force thinking to an efficient approach using math strategy.

Solve on LeetCode
The Problem

Problem Statement

You are given two integers, n and k.

An array of distinct positive integers is called a k-avoiding array if there does not exist any pair of distinct elements that sum to k.

Return the minimum possible sum of a k-avoiding array of length n.

Example 1:

Input: n = 5, k = 4
Output: 18
Explanation: Consider the k-avoiding array [1,2,4,5,6], which has a sum of 18.
It can be proven that there is no k-avoiding array with a sum less than 18.

Example 2:

Input: n = 2, k = 6
Output: 3
Explanation: We can construct the array [1,2], which has a sum of 3.
It can be proven that there is no k-avoiding array with a sum less than 3.

Constraints:

  • 1 <= n, k <= 50
Patterns Used

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: You are given two integers, n and k. An array of distinct positive integers is called a k-avoiding array if there does not exist any pair of distinct elements that sum to k. Return the minimum possible sum of a k-avoiding array of length n.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Math · Greedy

Example 1

5
4

Example 2

2
6
Step 02

Core Insight

What unlocks the optimal approach

  • <div class="_1l1MA">Try to start with the smallest possible integers.</div>
  • <div class="_1l1MA">Check if the current number can be added to the array.</div>
  • <div class="_1l1MA">To check if the current number can be added, keep track of already added numbers in a set.</div>
  • <div class="_1l1MA">If the number <code>i</code> is added to the array, then <code>i + k</code> can not be added.</div>
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Upper-end input sizes
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #2829: Determine the Minimum Sum of a k-avoiding Array
class Solution {
    public int minimumSum(int n, int k) {
        int s = 0, i = 1;
        boolean[] vis = new boolean[n + k + 1];
        while (n-- > 0) {
            while (vis[i]) {
                ++i;
            }
            if (k >= i) {
                vis[k - i] = true;
            }
            s += i++;
        }
        return s;
    }
}
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(n + k)
Space
O(n + k)

Approach Breakdown

EXHAUSTIVE
O(2ⁿ) time
O(n) space

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
O(n log n) time
O(1) 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.

Shortcut: Sort + single pass → O(n log n). If no sort needed → O(n). The hard part is proving it works.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Overflow in intermediate arithmetic

Wrong move: Temporary multiplications exceed integer bounds.

Usually fails on: Large inputs wrap around unexpectedly.

Fix: Use wider types, modular arithmetic, or rearranged operations.

Using greedy without proof

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.