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.
Move from brute-force thinking to an efficient approach using array strategy.
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 <= 1051 <= nums[i] <= 105Problem 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.
Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.
Pattern signal: Array · Hash Map · Greedy
[3,1,3,2,4,3]
[1,2,2,2,2]
minimum-deletions-to-make-array-beautiful)minimum-number-of-flips-to-make-the-binary-string-alternating)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)};
}
}
// Accepted solution for LeetCode #2170: Minimum Operations to Make the Array Alternating
func minimumOperations(nums []int) int {
f := func(i int) [4]int {
cnt := make(map[int]int)
for ; i < len(nums); i += 2 {
cnt[nums[i]]++
}
k1, k2 := 0, 0
for k, v := range cnt {
if cnt[k1] < v {
k2, k1 = k1, k
} else if cnt[k2] < v {
k2 = k
}
}
return [4]int{k1, cnt[k1], k2, cnt[k2]}
}
a := f(0)
b := f(1)
n := len(nums)
if a[0] != b[0] {
return n - (a[1] + b[1])
}
return n - max(a[1]+b[3], a[3]+b[1])
}
# Accepted solution for LeetCode #2170: Minimum Operations to Make the Array Alternating
class Solution:
def minimumOperations(self, nums: List[int]) -> int:
def f(i: int) -> Tuple[int, int, int, int]:
k1 = k2 = 0
cnt = Counter(nums[i::2])
for k, v in cnt.items():
if cnt[k1] < v:
k2, k1 = k1, k
elif cnt[k2] < v:
k2 = k
return k1, cnt[k1], k2, cnt[k2]
a, b = f(0), f(1)
n = len(nums)
if a[0] != b[0]:
return n - (a[1] + b[1])
return n - max(a[1] + b[3], a[3] + b[1])
// Accepted solution for LeetCode #2170: Minimum Operations to Make the Array Alternating
/**
* [2170] Minimum Operations to Make the Array Alternating
*
* 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,<u>1</u>,<u>3</u>,<u>1</u>].
* 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,<u>1</u>,2,<u>1</u>].
* The number of operations required in this case is 2.
* Note that the array cannot be converted to [<u>2</u>,2,2,2,2] because in this case nums[0] == nums[1] which violates the conditions of an alternating array.
*
*
* Constraints:
*
* 1 <= nums.length <= 10^5
* 1 <= nums[i] <= 10^5
*
*/
pub struct Solution {}
// problem: https://leetcode.com/problems/minimum-operations-to-make-the-array-alternating/
// discuss: https://leetcode.com/problems/minimum-operations-to-make-the-array-alternating/discuss/?currentPage=1&orderBy=most_votes&query=
// submission codes start here
impl Solution {
pub fn minimum_operations(nums: Vec<i32>) -> i32 {
0
}
}
// submission codes end
#[cfg(test)]
mod tests {
use super::*;
#[test]
#[ignore]
fn test_2170_example_1() {
let nums = vec![3, 1, 3, 2, 4, 3];
let result = 3;
assert_eq!(Solution::minimum_operations(nums), result);
}
#[test]
#[ignore]
fn test_2170_example_2() {
let nums = vec![1, 2, 2, 2, 2];
let result = 2;
assert_eq!(Solution::minimum_operations(nums), result);
}
}
// Accepted solution for LeetCode #2170: Minimum Operations to Make the Array Alternating
function minimumOperations(nums: number[]): number {
const f = (i: number): [number, number, number, number] => {
const cnt: Map<number, number> = new Map();
for (; i < nums.length; i += 2) {
cnt.set(nums[i], (cnt.get(nums[i]) || 0) + 1);
}
let [k1, k2] = [0, 0];
for (const [k, v] of cnt) {
if ((cnt.get(k1) || 0) < v) {
k2 = k1;
k1 = k;
} else if ((cnt.get(k2) || 0) < v) {
k2 = k;
}
}
return [k1, cnt.get(k1) || 0, k2, cnt.get(k2) || 0];
};
const a = f(0);
const b = f(1);
const 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]);
}
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: 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.
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.