题目： 
给定 n个非负整数表示每个宽度为 1 的柱子的高度图，计算按此排列的柱子，下雨之后能接多少雨水。

上面是由数组 [0,1,0,2,1,0,1,3,2,1,2,1] 表示的高度图，在这种情况下，可以接 6 个单位的雨水（蓝色部分表示雨水）

//暴力
int trap(vector<int>& height)
{
    int ans = 0;
    int size = height.size();
    for (int i = 1; i < size - 1; i++) {
        int max_left = 0, max_right = 0;

        //左边最大值
        for (int j = i; j >= 0; j--) { //Search the left part for max bar size
            max_left = max(max_left, height[j]);
        }

        //右边最大值
        for (int j = i; j < size; j++) { //Search the right part for max bar size
            max_right = max(max_right, height[j]);
        }
        ans += min(max_left, max_right) - height[i];
    }

    return ans;
}

//动态编程
int trap(vector<int>& height)
{
    if (height == null)
        return 0;
    int ans = 0;
    int size = height.size();
    vector<int> left_max(size), right_max(size);

    //把左边最大值和右边最大值不放在循环内部求解
    left_max[0] = height[0];
    for (int i = 1; i < size; i++) {
        left_max[i] = max(height[i], left_max[i - 1]);
    }

    right_max[size - 1] = height[size - 1];
    for (int i = size - 2; i >= 0; i--) {
        right_max[i] = max(height[i], right_max[i + 1]);
    }

    for (int i = 1; i < size - 1; i++) {
        ans += min(left_max[i], right_max[i]) - height[i];
    }
    return ans;
}

//栈的应用,将数组元素代入就能明白过程 
int trap(vector<int>& height)
{
    int ans = 0, current = 0;
    stack<int> st;

    while (current < height.size()) {
        //当前元素大于栈顶元素
        while (!st.empty() && height[current] > height[st.top()]) {
            int top = st.top();
            st.pop();
            if (st.empty())
                break;
            int distance = current - st.top() - 1;
            int bounded_height = min(height[current], height[st.top()]) - height[top];
            ans += distance * bounded_height;
        }

        //入栈
        st.push(current++);
    }

    return ans;
}

//代入值
int trap(vector<int>& height)
{
    int left = 0, right = height.size() - 1;
    int ans = 0;
    int left_max = 0, right_max = 0;

    while (left < right) {

        if (height[left] < height[right]) {
            height[left] >= left_max ? (left_max = height[left]) : ans += (left_max - height[left]);
            ++left;
        }else {
            height[right] >= right_max ? (right_max = height[right]) : ans += (right_max - height[right]);
            --right;
        }

    }
    return ans;
}