LeetCode #3712 — EASY

Sum of Elements With Frequency Divisible by K

Build confidence with an intuition-first walkthrough focused on array fundamentals.

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The Problem

Problem Statement

You are given an integer array nums and an integer k.

Return an integer denoting the sum of all elements in nums whose frequency is divisible by k, or 0 if there are no such elements.

Note: An element is included in the sum exactly as many times as it appears in the array if its total frequency is divisible by k.

Example 1:

Input: nums = [1,2,2,3,3,3,3,4], k = 2

Output: 16

Explanation:

  • The number 1 appears once (odd frequency).
  • The number 2 appears twice (even frequency).
  • The number 3 appears four times (even frequency).
  • The number 4 appears once (odd frequency).

So, the total sum is 2 + 2 + 3 + 3 + 3 + 3 = 16.

Example 2:

Input: nums = [1,2,3,4,5], k = 2

Output: 0

Explanation:

There are no elements that appear an even number of times, so the total sum is 0.

Example 3:

Input: nums = [4,4,4,1,2,3], k = 3

Output: 12

Explanation:

  • The number 1 appears once.
  • The number 2 appears once.
  • The number 3 appears once.
  • The number 4 appears three times.

So, the total sum is 4 + 4 + 4 = 12.

Constraints:

  • 1 <= nums.length <= 100
  • 1 <= nums[i] <= 100
  • 1 <= k <= 100

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 an integer array nums and an integer k. Return an integer denoting the sum of all elements in nums whose frequency is divisible by k, or 0 if there are no such elements. Note: An element is included in the sum exactly as many times as it appears in the array if its total frequency is divisible by k.

Baseline thinking

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

Pattern signal: Array · Hash Map

Example 1

[1,2,2,3,3,3,3,4]
2

Example 2

[1,2,3,4,5]
2

Example 3

[4,4,4,1,2,3]
3
Step 02

Core Insight

What unlocks the optimal approach

  • Simulate as described
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 #3712: Sum of Elements With Frequency Divisible by K
class Solution {
    public int sumDivisibleByK(int[] nums, int k) {
        Map<Integer, Integer> cnt = new HashMap<>();
        for (int x : nums) {
            cnt.merge(x, 1, Integer::sum);
        }
        int ans = 0;
        for (var e : cnt.entrySet()) {
            int x = e.getKey(), v = e.getValue();
            if (v % k == 0) {
                ans += x * v;
            }
        }
        return ans;
    }
}
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)
Space
O(1)

Approach Breakdown

BRUTE FORCE
O(n²) time
O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED
O(n) time
O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

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.

Mutating counts without cleanup

Wrong move: Zero-count keys stay in map and break distinct/count constraints.

Usually fails on: Window/map size checks are consistently off by one.

Fix: Delete keys when count reaches zero.