LeetCode-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.

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

暴力求解：

public int LargestRectangleArea(int[] heights)
        {
           int maxArea = 0;
           int len = heights.Length;
           int[] min = new int[len];
           for(int i = 0; i < len; i++)
            {
               if(heights[i] != 0 && maxArea/heights[i] >= (len - i))
                   continue;
               for(int j = i; j < len; j++)
               {
                   if(i == j)
                        min[j] = heights[j];
                   else
                   {
                       if(heights[j] < min[j - 1])
                           min[j] = heights[j];
                        else
                           min[j] = min[j-1];
                   }
                   int tentativeArea = min[j] * (j - i + 1);
                   if(tentativeArea > maxArea)
                       maxArea = tentativeArea;
               }
           }
           return maxArea;
        }

方法二：

使用一个栈，存放递增的bar

public int LargestRectangleArea(int[] heights) 
    {
        int len = heights.Length;
        if (len == 0)
            return 0;
        Stack<int> stack = new Stack<int>();
        int i = 0;
        int maxArea = 0;
        int[] h = new int[len + 1];
        Array.Copy(heights, h, len);
        while (i < len + 1)
        {
            if (stack.Count == 0 || h[stack.Peek()] <= h[i])
                stack.Push(i++);
            else
            {
                int t = stack.Pop();
                maxArea = Math.Max(maxArea, h[t] * (stack.Count == 0 ? i : i - stack.Peek() - 1));
            }
        }
        return maxArea;
    }

参考：

http://www.cnblogs.com/lichen782/p/leetcode_Largest_Rectangle_in_Histogram.html

http://blog.csdn.net/linhuanmars/article/details/20524507