84. 柱状图中最大的矩形(单调栈)(LeetCode)

84. 柱状图中最大的矩形
单调栈可以解决找到一个数左边或者右边离他最近的比他还要小的数

class Solution {
public:
    int largestRectangleArea(vector<int>& heights) {
        int n = heights.size();
        //存储最多能到达的左边或者右边的下标
        vector<int> left(n), right(n);
        stack<int> stk;

        for(int i = 0; i < n; ++i){
            while(stk.size() && heights[stk.top()] >= heights[i]) stk.pop();
            if(stk.empty()) left[i] = -1;
            else left[i] = stk.top();
            stk.push(i);
        }
        stk = stack<int>();
        for(int i = n - 1; i >= 0; --i){
            while(stk.size() && heights[stk.top()] >= heights[i]) stk.pop();
            if(stk.empty()) right[i] = n;
            else right[i] = stk.top();
            stk.push(i);
        }

        int res = 0;
        for(int i = 0; i < n; ++i){
            res = max(res, (right[i] - left[i] - 1) * heights[i]);
        }

        return res;
    }
};