Intuition

A subarray is "good" when every value appears at most k times. Goodness is monotonic under shrinking: if a window is good, any sub-window is also good. This is the classic setup for a sliding window — grow the right end greedily, and only shrink from the left when the window becomes invalid.

Approach: Sliding Window + Frequency Map

Maintain a window [left, right] and a hash map freq of value counts inside it.

1. Extend right one step at a time, incrementing freq[nums[right]].
2. If the newly added value now exceeds k (freq[nums[right]] > k), shrink from the left — decrement freq[nums[left]] and advance left — until the window is good again. Only the just-added value can violate the constraint, so checking it is sufficient.
3. After each step the window is good, so update the answer with its length right - left + 1.

Each index enters and leaves the window at most once, giving linear time.

Complexity

• Time complexity: $$O(n)$$, where n is the length of nums — each element is added and removed from the window at most once.
• Space complexity: $$O(n)$$ for the frequency map in the worst case (all distinct values).

Code

Go

func maxSubarrayLength(nums []int, k int) int {
    ans, left := 0, 0
    freq := map[int]int{}
    for right, num := range nums {
        freq[num]++
        for freq[num] > k {
            freq[nums[left]]--
            left++
        }
        ans = max(ans, right - left + 1)
    }
    return ans
}

Rust

use std::collections::HashMap;
impl Solution {
    pub fn max_subarray_length(nums: Vec<i32>, k: i32) -> i32 {
        let mut freq = HashMap::new();
        let mut ans = 0;
        let mut left = 0;
        for right in 0..nums.len() {
            let num = nums[right];
            *freq.entry(num).or_insert(0) += 1;
            while freq[&num] > k {
                if let Some(count) = freq.get_mut(&nums[left]) {
                    *count -= 1;
                }
                left += 1;
            }
            ans = ans.max(right - left + 1);
        }
        ans as i32
    }
}