84. 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.

Example:

Input: [2,1,5,6,2,3]
Output: 10

class Solution {
public:
    int largestRectangleArea(vector<int>& heights) {
       
         int sum = 0;
          for (int i = 0; i < heights.size(); ++i) {
             if (i + 1 < heights.size() && heights[i] <= heights[i + 1]) {
                  continue;
              }
             int value = heights[i];
             for (int j = i; j >= 0; --j) {
                value = min(value, heights[j]);
                  int area = value * (i - j + 1);
                  sum = max(sum, area);
              }
          }
          return sum;
        
        /*    
        if(heights.size()==0) return 0;
     else if(heights.size()==1) return heights[0];
        
        int sum=0;
        int num=0;
        int maxval=0;
        for(int i=0;i<heights.size();i++)
            maxval=max(heights[i],maxval);
        for(int i=0;i<heights.size();i++)
            maxval=max(heights[i],maxval);
        
        
         for(int i=1;i<=maxval;i++)
         {     
            for(int j=0;j<heights.size();j++)

              if((heights[j]=heights[j]-1)>=0) num++;
                  else {sum=max(num*i,sum);
                         num=0;}
                  
                  sum=max(num*i,sum);
                  num=0;
             
         }
 
              
        return sum;
        // 第一想法，可惜代码超时了～～～～
        */
    }
};