LeetCode 3357: Minimize the Maximum Adjacent Element Difference Solution

Master LeetCode problem 3357 (Minimize the Maximum Adjacent Element Difference), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

3357. Minimize the Maximum Adjacent Element Difference

Hard

Array Binary Search Greedy

Problem Explanation

Explanation

To solve this problem, we can use binary search to find the minimum possible maximum absolute difference between adjacent elements after replacements. We can define a function check that will check if it's possible to minimize the maximum absolute difference to a given value mid.

Within the check function, we will iterate through all possible pairs of numbers within the given constraints and check if we can replace the missing elements in the array such that the maximum absolute difference between adjacent elements is less than or equal to mid.

If it is possible to achieve this for a given mid, we update our answer and continue with the binary search for a smaller mid value. Otherwise, we search for a larger mid value.

This approach allows us to find the minimum possible maximum absolute difference that can be achieved by choosing the optimal pair of integers.

Time Complexity

The time complexity of this approach is O(n log M), where n is the length of the input array and M is the maximum possible difference between adjacent elements.

Space Complexity

The space complexity of this approach is O(1) as we are using constant extra space.

Solution Code

class Solution {
    public int minimizeTheMaxDifference(int[] nums) {
        int left = 1, right = 1000000000;
        int res = right;
        while (left <= right) {
            int mid = left + (right - left) / 2;
            if (check(nums, mid)) {
                res = mid;
                right = mid - 1;
            } else {
                left = mid + 1;
            }
        }
        return res;
    }

    private boolean check(int[] nums, int diff) {
        int maxDiff = 0;
        for (int i = 1; i < nums.length; i++) {
            if (nums[i] == -1 || nums[i - 1] == -1) {
                continue;
            }
            maxDiff = Math.max(maxDiff, Math.abs(nums[i] - nums[i - 1]));
        }
        for (int i = 1; i < nums.length; i++) {
            if (nums[i] == -1 || nums[i - 1] == -1) {
                int val = Math.abs(nums[i] == -1 ? nums[i - 1] : nums[i - 1]);
                if (val + diff <= 1000000000 && val - diff >= 1) {
                    return true;
                }
            }
        }
        return maxDiff <= diff;
    }
}

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