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
.
此题难度很大,个人并未想出来。第一反应是F(i,j)但是超时错误。此处借鉴他人。并理解了下代码。以及相关题目Maximal Rectangle,利用此题结论。先做的Maximal Rectangle,直接被打击,后面度娘下,发现此题很刁钻,利用了本题的思路。否则有的超时!!
借鉴自:http://blog.csdn.net/sbitswc/article/details/33451347
int largestRectangleArea(vector<int> &height)
{
stack<int> st;
int max_area = 0;
height.push_back(0);//技巧
for(int i = 0;i < height.size();)
{
if(st.empty() || height[i] > height[st.top()])
{
st.push(i);
i++;
}
else
{
int temp_index = st.top();
st.pop();
max_area = max(max_area, height[temp_index]*(st.empty()? i:i-st.top()-1));
//cout<<height[temp_index]*(st.empty()? i:i-st.top()-1)<<endl;
//此题关键的地方 最后一句索引与高度的获取。在栈里面的是最小递增序列(当前)
}
}
return max_area;
}