LeetCode #2170 — MEDIUM

Minimum Operations to Make the Array Alternating

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

Solve on LeetCode
The Problem

Problem Statement

You are given a 0-indexed array nums consisting of n positive integers.

The array nums is called alternating if:

  • nums[i - 2] == nums[i], where 2 <= i <= n - 1.
  • nums[i - 1] != nums[i], where 1 <= i <= n - 1.

In one operation, you can choose an index i and change nums[i] into any positive integer.

Return the minimum number of operations required to make the array alternating.

Example 1:

Input: nums = [3,1,3,2,4,3]
Output: 3
Explanation:
One way to make the array alternating is by converting it to [3,1,3,1,3,1].
The number of operations required in this case is 3.
It can be proven that it is not possible to make the array alternating in less than 3 operations. 

Example 2:

Input: nums = [1,2,2,2,2]
Output: 2
Explanation:
One way to make the array alternating is by converting it to [1,2,1,2,1].
The number of operations required in this case is 2.
Note that the array cannot be converted to [2,2,2,2,2] because in this case nums[0] == nums[1] which violates the conditions of an alternating array.

Constraints:

  • 1 <= nums.length <= 105
  • 1 <= nums[i] <= 105
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 a 0-indexed array nums consisting of n positive integers. The array nums is called alternating if: nums[i - 2] == nums[i], where 2 <= i <= n - 1. nums[i - 1] != nums[i], where 1 <= i <= n - 1. In one operation, you can choose an index i and change nums[i] into any positive integer. Return the minimum number of operations required to make the array alternating.

Baseline thinking

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

Pattern signal: Array · Hash Map · Greedy

Example 1

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

Example 2

[1,2,2,2,2]

Related Problems

  • Minimum Deletions to Make Array Beautiful (minimum-deletions-to-make-array-beautiful)
  • Minimum Number of Flips to Make the Binary String Alternating (minimum-number-of-flips-to-make-the-binary-string-alternating)
Step 02

Core Insight

What unlocks the optimal approach

  • Count the frequency of each element in odd positions in the array. Do the same for elements in even positions.
  • To minimize the number of operations we need to maximize the number of elements we keep from the original array.
  • What are the possible combinations of elements we can choose from odd indices and even indices so that the number of unchanged elements is maximized?
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 #2170: Minimum Operations to Make the Array Alternating
class Solution {
    public int minimumOperations(int[] nums) {
        int[] a = f(nums, 0);
        int[] b = f(nums, 1);
        int n = nums.length;
        if (a[0] != b[0]) {
            return n - (a[1] + b[1]);
        }
        return n - Math.max(a[1] + b[3], a[3] + b[1]);
    }

    private int[] f(int[] nums, int i) {
        int k1 = 0, k2 = 0;
        Map<Integer, Integer> cnt = new HashMap<>();
        for (; i < nums.length; i += 2) {
            cnt.merge(nums[i], 1, Integer::sum);
        }
        for (var e : cnt.entrySet()) {
            int k = e.getKey(), v = e.getValue();
            if (cnt.getOrDefault(k1, 0) < v) {
                k2 = k1;
                k1 = k;
            } else if (cnt.getOrDefault(k2, 0) < v) {
                k2 = k;
            }
        }
        return new int[] {k1, cnt.getOrDefault(k1, 0), k2, cnt.getOrDefault(k2, 0)};
    }
}
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(n)

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.

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.

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.