Leetcode:Largest Rectangle in Histogram 最大矩形面积

Largest Rectangle in Histogram

Given n non-negative integers representing the histogram‘s bar height where the width of each bar is 1, find the area of largest rectangle in the histogram.

Above is a histogram where width of each bar is 1, given height = [2,1,5,6,2,3].

The largest rectangle is shown in the shaded area, which has area = 10 unit.

For example,
Given height = [2,1,5,6,2,3],
return 10.

解题分析：

园友博文分析

申请一个辅助栈，stack里面只存放单调递增的索引

class Solution {
public:
    int largestRectangleArea(vector<int> &height) {
        if (height.size() == 0) return 0;
        height.push_back(0);   // 便于最后计算所有的矩形面积
        std::stack<int> stk;   // 存放的是数组索引下标
        int  result = 0;
        for (int i = 0; i < height.size(); ) {
            if (stk.empty() || height.at(i) > height.at(stk.top())) {
                stk.push(i);
                ++i;
            } else {
                int idx = stk.top();
                stk.pop();
                int area = height.at(idx) * (stk.empty() ? i : i - stk.top() - 1);
                result = std::max(result, area);
            }
        }
        return result;
    }
};

时间复杂度T(n) = O(n)