The sliding window technique is used to find the longest subarray where elements can be incremented to make them equal using at most k increments. We sort the array first to ensure it's easier to increment elements to become equal. We then use two pointers: one for the current end of the subarray and the other to represent the start. By checking the cost to transform the current subarray into an equal value using the difference between values and leveraging the sorted property, we can determine the maximum frequency we can achieve.
Time Complexity: O(n log n), due to sorting the array.
Space Complexity: O(1), as no extra space is used apart from variable allocations.
1class Solution:
2 def maxFrequency(self, nums, k):
3 nums.sort()
4 sum = 0
5 left = 0
6 res = 0
7 for right in range(len(nums)):
8 sum += nums[right]
9 while nums[right] * (right - left + 1) > sum + k:
10 sum -= nums[left]
11 left += 1
12 res = max(res, right - left + 1)
13 return res
14
15# Sample Usage
16sol = Solution()
17print(sol.maxFrequency([1, 2, 4], 5))The Python solution sorts the list and maintains a sliding window using sum calculations to determine the possible maximum equal frequency within a boundary condition constrained by k. It effectively tracks and updates the maximum range by adjusting the left pointer as necessary.
This approach makes use of binary search in combination with prefix sums to efficiently find the maximum frequency possible by transforming elements. We first sort the array. For a given target frequency, we check through calculating the required increment operations using a prefix sum array and binary searching over possible solutions. This allows us to leverage efficient range queries and reduce time complexity.
Time Complexity: O(n log n), because of sorting and binary search iterations.
Space Complexity: O(n), due to additional space for prefix sums.
1function maxFrequency(nums, k) {
2 nums.sort((a, b) => a - b);
3 const prefixSum = new Array(nums.length).fill(0);
4 nums.reduce((sum, num, idx) => {
5 prefixSum[idx] = sum + num;
6 return prefixSum[idx];
7 }, 0);
8
9 function canAchieveFrequency(freq) {
10 for (let end = freq - 1; end < nums.length; end++) {
11 const totalNeeded = nums[end] * freq;
12 const currentSum = prefixSum[end] - (end >= freq ? prefixSum[end - freq] : 0);
13 if (totalNeeded - currentSum <= k) return true;
14 }
15 return false;
16 }
17
18 let left = 1, right = nums.length, res = 1;
19 while (left <= right) {
20 const mid = Math.floor((left + right) / 2);
21 if (canAchieveFrequency(mid)) {
22 res = mid;
23 left = mid + 1;
24 } else {
25 right = mid - 1;
26 }
27 }
28 return res;
29}
30
31// Sample Usage
32console.log(maxFrequency([1, 2, 4], 5));JavaScript solutions leverage native array sorting and inclusion of a prefix sum-based mechanism to drastically cut down checks on possible frequential transformations. The binary search enables efficient determinations on how many total operations yield within their respective ranges.