Can you explain the Trapping Rain Water problem and its solution?

DSA
Hard
126.2K views

This problem calculates the amount of water trapped between bars of different heights after raining. It tests dynamic programming and two-pointer strategies.

Why Interviewers Ask This

This is a challenging problem that evaluates advanced problem-solving skills and mathematical intuition. Interviewers assess whether you can derive the water level at each position based on the maximum height to its left and right. It tests the ability to optimize a brute-force O(n^2) solution to O(n). The question also gauges how you handle complex constraints and visualize the problem geometrically.

How to Answer This Question

Start by explaining that water at any index depends on the minimum of the max height to its left and right. Describe the pre-computation approach using two arrays to store these max values. Then, introduce the optimized two-pointer approach that reduces space complexity to O(1). Explain how moving the pointer with the smaller max height guarantees the water calculation is correct.

Key Points to Cover

  • Min of max left and right
  • Two-pointer optimization
  • Space complexity reduction
  • Geometric visualization

Sample Answer

The key insight is that the water trapped at any bar is determined by the shorter of the tallest bars to its left and right. A simple DP approach stores these max heights in arrays, allowing O(n) calculation. However, we can optimize space by using two pointers from both ends. By tracking the max height seen so far from both sides, we only process the side with the smaller max height, ensuring correctness while using constant extra space.

Common Mistakes to Avoid

  • Ignoring boundary conditions
  • Incorrectly calculating max heights
  • Using O(n) space unnecessarily

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