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Container With Most Water

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 12

Write a C# program to solve the Container With Most Water problem. You are given an array of positive integers where each integer represents the height of a vertical line on a chart. Find two lines that together with the x-axis form a container that holds the most water. Return the maximum amount of water the container can hold.

Example 1
    
  
  • Input: height = [1,8,6,2,5,4,8,3,7]
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  • Output: 49
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  • Explanation: The maximum area is obtained by selecting the heights at indices 1 and 8 (heights 8 and 7), with a distance of 7 between them, giving an area of min(8, 7) * 7 = 7 * 7 = 49.
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Example 2
    
  
  • Input: height = [4,3,2,1,4]
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  • Output: 16
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  • Explanation: The maximum area is obtained by selecting the heights at indices 0 and 4 (both height 4), with a distance of 4 between them, giving an area of min(4, 4) * 4 = 4 * 4 = 16.
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Constraints
    
  
  • n == height.length
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  • 2 ≤ n ≤ 10^5
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  • 0 ≤ height[i] ≤ 10^4
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  • Time Complexity: O(n)
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  • Space Complexity: O(1)
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ArraysControl StructuresLTIMindtreeD. E. Shaw
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Hint
Solution

Solution Hints

    
  
  • A brute force approach would be checking all pairs, but it would be O(n²)
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  • Use the two-pointer technique for an optimal approach
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  • Start with the widest possible container (pointers at both ends)
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  • Move the pointer with the smaller height inward
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  • Keep track of the maximum area seen so far
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Steps to solve by this approach:

 Step 1: Initialize two pointers, left at the beginning and right at the end of the array.
 Step 2: Initialize a variable to keep track of the maximum area.
 Step 3: While left pointer is less than right pointer, calculate the current area.
 Step 4: The area is determined by the width (difference between indices) and the minimum height of the two lines.
 Step 5: Update the maximum area if the current area is greater.
 Step 6: Move the pointer that points to the smaller height inward, as this might lead to a larger area.
 Step 7: Return the maximum area found.

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