#11. Container With Most Water
- Solved
Description
You are given an integer array height of length n. There are n vertical lines drawn such that the two endpoints of the ith line are (i, 0) and (i, height[i]).
Find two lines that together with the x-axis form a container, such that the container contains the most water.
Return the maximum amount of water a container can store.
Notice that you may not slant the container.
Example 1:
Input: height = [1,8,6,2,5,4,8,3,7]
Output: 49
Explanation: The above vertical lines are represented by array [1,8,6,2,5,4,8,3,7]. In this case, the max area of water (blue section) the container can contain is 49.
Example 2:
Input: height = [1,1] Output: 1
Constraints:
- n == height.length
- 2 <= n <= 105
- 0 <= height[i] <= 104
My Solution
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public class Solution {
public int MaxArea(int[] height) {
int max = 0;
for(int i = 0; i < height.Length - 1; i++) {
for (int j = i + 1; j < height.Length; j++) {
int width = j - i;
int length = Math.Min(height[i], height[j]);
max = Math.Max(width * length, max);
}
}
return max;
}
}
Runtime
Time Limit Exceeded
Memory
Time Limit Exceeded
Big O Notation
Time complexity: O(n^2)
Space complexity: O(1)
Best Solution
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public class Solution {
public int MaxArea(int[] height) {
int max = 0;
int left = 0;
int right = height.Length - 1;
while(left < right) {
max = Math.Max((right - left) * Math.Min(height[left], height[right]), max);
if(height[left] > height[right]) {
right--;
}
else {
left++;
}
}
return max;
}
}
Runtime
1 ms / Beats 98.94%
Memory
61.87 MB / Beats 75.86%
Big O Notation
Time complexity: O(n)
Space complexity: O(1)