42. Receiving rainwater (difficulty)

Ideas:

Observation shows that if the height of the current column is greater than the height of the previous column, it will be popped out of the stack, and the height of one column will be obtained further, that is, 3 columns will be used. Get the area between the two higher pillars. As you can see, you need to use a monotonic stack

 

class Solution {
    public int trap(int[] height) {
		int n=height.length;
		Deque<Integer> stack=new ArrayDeque<>();
		int sum=0;
		
		for(int i=0;i<n;i++){
			//分为了3个柱子
			while(!stack.isEmpty()&&height[i]>height[stack.peekLast()]){
				//第二根柱子
				int pop=stack.pollLast();
				//若前面没有了（第一根柱子），就退出循环，必须要满足3个柱子
				if(stack.isEmpty()) break;
				
				//这里的stack.peekLast()表示第一根柱子
				//high表示头尾2根较矮一根的高度-中间柱子的高度
				int high=Math.min(height[i],height[stack.peekLast()])-height[pop];
				int width=i-stack.peekLast()-1;
				sum+=high*width;
			}
			stack.addLast(i);
		}
		
		return sum;
    }
}

break down:

Here not only compares the current column to be higher than the previous column, but also obtains the height of the previous column.

In this way, the rainwater area of ​​the following shape can be obtained cleverly