714120. Max min Height
Max Min Height
Summary
Given an array of integers, find the maximum and minimum height that can be achieved by placing a fence at each position in the array. The height at a particular position is defined as the difference between the maximum element to its left and the minimum element to its right.
This problem involves dynamic programming and binary search, with key concepts including arrays, data structures, and algorithms.
Detailed Explanation
The approach to this problem is to use dynamic programming to calculate the maximum and minimum height for each position in the array. The idea is to maintain two arrays: max_height and min_height. For each position i, we calculate the maximum and minimum height by considering the elements on both sides of the fence at that position.
The step-by-step breakdown of the solution is as follows:
- Initialize
max_heightandmin_heightarrays with all elements set to 0. - Iterate through the array from left to right:
- For each position
i, calculate the maximum height by considering the elements on the left side of the fence at that position:max_height[i] = max(0, max(arr[:i]) - arr[i]). - Similarly, calculate the minimum height by considering the elements on the right side of the fence at that position:
min_height[i] = min(0, min(arr[i+1:]) - arr[i]).
- For each position
- The maximum and minimum heights for the entire array are then calculated as follows:
- Maximum height:
max_max_height = max(max_height). - Minimum height:
min_min_height = min(min_height).
- Maximum height:
The time complexity of this solution is O(n), where n is the length of the array, since we only need to iterate through the array once. The space complexity is also O(n) due to the dynamic programming arrays.
Optimized Solutions
Java
public class MaxMinHeight {
public static int[] maxMinHeight(int[] arr) {
int n = arr.length;
int[] max_height = new int[n];
int[] min_height = new int[n];
for (int i = 0; i < n; i++) {
if (i == 0) {
max_height[i] = arr[0];
min_height[i] = -arr[0];
} else if (i == n - 1) {
max_height[i] = -arr[n - 1];
min_height[i] = arr[n - 1];
} else {
max_height[i] = Math.max(0, max(arr[:i]) - arr[i]);
min_height[i] = Math.min(0, min(arr[i+1:]) - arr[i]);
}
}
int max_max_height = Arrays.stream(max_height).max().getAsInt();
int min_min_height = Arrays.stream(min_height).min().getAsInt();
return new int[] {max_max_height, min_min_height};
}
}