<p>Given <code>n</code> non-negative integers representing an elevation map where the width of each bar is <code>1</code>, compute how much water it can trap after raining.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img src="https://assets.leetcode.com/uploads/2018/10/22/rainwatertrap.png" style="width: 412px; height: 161px;" />
<pre>
<strong>Input:</strong> height = [0,1,0,2,1,0,1,3,2,1,2,1]
<strong>Output:</strong> 6
<strong>Explanation:</strong> The above elevation map (black section) is represented by array [0,1,0,2,1,0,1,3,2,1,2,1]. In this case, 6 units of rain water (blue section) are being trapped.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> height = [4,2,0,3,2,5]
<strong>Output:</strong> 9
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == height.length</code></li>
	<li><code>1 &lt;= n &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>0 &lt;= height[i] &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution {
public:
    int trap(vector<int>& height) {
        int n = height.size();
    if (n == 0) return 0;
    
    stack<int> st;
    int trapped_water = 0;
    
    for (int i = 0; i < n; ++i) {
        // While the stack is not empty and the current height is greater than
        // the height at the index stored in the stack's top
        while (!st.empty() && height[i] > height[st.top()]) {
            int top = st.top();
            st.pop();
            
            // If stack is empty, it means there is no left boundary, so continue
            if (st.empty()) break;
            
            // Calculate the distance to the next higher bar
            int distance = i - st.top() - 1;
            // Calculate the bounded height
            int bounded_height = min(height[i], height[st.top()]) - height[top];
            // Add to the total trapped water
            trapped_water += distance * bounded_height;
        }
        
        // Push current index to stack
        st.push(i);
    }
    
    return trapped_water;
    }
};
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