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Trapping Rain Water

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15

Write a C# program to solve the Trapping Rain Water problem. Given n non-negative integers representing an elevation map where the width of each bar is 1, compute how much water it can trap after raining.

Example 1
    
  
  • Input: height = [0,1,0,2,1,0,1,3,2,1,2,1]
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  • Output: 6
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  • Explanation: 
    
      
      
    • The elevation map is represented by the array [0,1,0,2,1,0,1,3,2,1,2,1].
      • 
      
    • In this case, 6 units of rain water are being trapped.
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Example 2
    
  
  • Input: height = [4,2,0,3,2,5]
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  • Output: 9
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  • Explanation: 
    
      
      
    • The elevation map is represented by array [4,2,0,3,2,5].
      • 
      
    • In this case, 9 units of rain water are being trapped.
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Constraints
    
  
  • n == height.length
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  • 1 ≤ n ≤ 2 * 10^4
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  • 0 ≤ height[i] ≤ 10^5
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  • Time Complexity: O(n)
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  • Space Complexity: O(1)
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Hint
Solution

Solution Hints

    
  
  • Consider using two pointers approach to avoid extra space
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  • For each position, the water trapped depends on the minimum of maximum heights to its left and right
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  • Keep track of the left and right maximum heights as you traverse the array
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  • Calculate the water amount at each position by finding the difference between the minimum of the two maxima and the current height
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Steps to solve by this approach:

 Step 1: Initialize two pointers - left at the start of the array and right at the end of the array.
 Step 2: Initialize two variables leftMax and rightMax to track the maximum heights from the left and right ends.
 Step 3: Initialize a result variable to store the total trapped water.
 Step 4: Use a two-pointer approach, moving inward from both ends of the array.
 Step 5: At each step, compare leftMax and rightMax and move the pointer from the side with the smaller maximum height.
 Step 6: Update the maximum height for that side and add the trapped water at the current position.
 Step 7: Continue until the two pointers meet.

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