LeetCode Online Judge 题目C# 练习 - 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.
1 public static int LargestRectangleinHistogramOpt(List<int> height) 2 { 3 if (height.Count == 0) 4 return 0; 5 if (height.Count == 1) 6 return height[0]; 7 8 int[] Base = new int[height.Count]; 9 Stack<int> s = new Stack<int>(); 10 int MaxArea = 0; 11 12 //Calculate the base from left to right 13 for (int i = 0; i < height.Count; i++) 14 { 15 while(s.Count > 0 && height[i] < height[s.Peek()]) 16 { 17 Base[s.Peek()] = i - s.Peek(); 18 s.Pop(); 19 } 20 21 s.Push(i); 22 } 23 while (s.Count > 0) 24 { 25 Base[s.Peek()] = height.Count - s.Peek(); 26 s.Pop(); 27 } 28 29 //Add base from right to left 30 for (int i = height.Count - 1; i >= 0; i--) 31 { 32 while (s.Count > 0 && height[i] < height[s.Peek()]) 33 { 34 Base[s.Peek()] += s.Peek() - i - 1; 35 s.Pop(); 36 } 37 38 s.Push(i); 39 } 40 while (s.Count > 0) 41 { 42 Base[s.Peek()] += s.Peek(); 43 s.Pop(); 44 } 45 46 //Find the MaxArea 47 for (int i = 0; i < height.Count; i++) 48 { 49 MaxArea = Math.Max(MaxArea, Base[i] * height[i]); 50 } 51 52 return MaxArea; 53 54 }
代码分析：
上面代码的时间复杂度是O(n)。应该算是比较理想的做法了。
1. 从左往右计算对应高度右边的底的长度。
2. 加上从右往左对应高度左边的地的长度。
3. 通过底×高，计算最大面积
展开1.
使用Stack帮助计算。
例如[2,1,5,6,2,3]
Base[0,0,0,0,0,0] Stack[ )
1.i = 0 Base[0,0,0,0,0,0] Stack[0,)
2.i = 1 下降沿， Base[1,0,0,0,0,0] Stack[0,1,)
3.i = 2 上升沿， Base[1,0,0,0,0,0] Stack[1,2)
4.i = 3 上升沿， Base[1,0,0,0,0,0] Stack[1,2,3)
5.i = 4 下降沿， Base[1,0,2,1,0,0] Satck[1,2,3,4)
6.i = 5 上升沿， Base[1,0,2,1,0,0] Stack[1,4,5)
7.把底算完 Base[1,5,2,1,2,1] Stack[1,4,5)
