lintcode: 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.

方法一

O(n^2)
对于每个bar，找出bar是最矮的范围，求出一个面积；遍历所有bar，得到max面积。
超时

class Solution {public:    /**     * @param height: A list of integer     * @return: The area of largest rectangle in the histogram     */    int largestRectangleArea(vector<int> &height) {        // write your code here        int maxArea=0;        for(int i=0;i<height.size();i++){            int left;            if(i==0){                left=i;            }else{                left=i-1;                while(left>=0 && height[left]>=height[i]) left--;                left++;            }            int right;            if(i==height.size()-1){                right=i;            }else{                right=i+1;                while(right<=height.size()-1 && height[right]>=height[i]) right++;                right--;            }            int area=(right-left+1)*height[i];            if(area>maxArea){                maxArea=area;            }        }        return maxArea;    }};

方法2

用递增栈
http://www.cnblogs.com/lichen782/p/leetcode_Largest_Rectangle_in_Histogram.html

class Solution {public:    /**     * @param height: A list of integer     * @return: The area of largest rectangle in the histogram     */    int largestRectangleArea(vector<int> &height) {        // write your code here        stack<int> stk;        int maxArea=0;        int i=0;        vector<int> h(height);        //后面加个0        h.push_back(0);        while(i<h.size()){            if(stk.empty() || h[i]>=h[stk.top()]){                stk.push(i);                i++;            }else{                int t=stk.top();                stk.pop();                int area=h[t]*(stk.empty()?i:(i-stk.top()-1));                if(area>maxArea){                    maxArea=area;                }            }        }        return maxArea;    }};