Google interview questions: Find the largest rectangle in the bar chart

Find the largest rectangle in the column chart: Give a group of non-negative integers to represent a column chart, design an algorithm to find the largest area of the rectangle that can fit into the column chart. For example, there are two possible solutions for the number of groups, 1 2 3 4 1, one is suitable for the rectangle within 2 3 4, and the area is 2*3; the other is a rectangle suitable for up to 3 4, with an area of 3*2. Do you think there are any O (n) algorithms?

This is a Google interview question. The following shows my solution. My setting is that the height of all bar charts is between 0 and 10.

 1 #include <iostream> 2 #include <vector> 3  4 using namespace std; 5  6 int MaxRectBarChart(vector<int> barChart) 7 { 8     int i_areaArray[11] = {}; 9     int i_tempareaArray[11] = {};10     vector<int>::iterator iter = barChart.begin();11     int max = 0;12     for (; iter != barChart.end(); iter++)13     {14         for (int i = 1; i <= *iter; i++)15         {16             i_tempareaArray[i] += i;17         }18         for (int i = *iter + 1; i < 11; i++)19         {20             if (i_tempareaArray[i] > i_areaArray[i])21                 i_areaArray[i] = i_tempareaArray[i];22             i_tempareaArray[i] = 0;23         }24     }25     for (int i = 1; i < 11; i++)26     {27         if (max < i_areaArray[i])28             max = i_areaArray[i];29     }30     return max;31 }32 33 int main()34 {35     vector<int> iv_highArray;36     int i_insert;37     while (cin >> i_insert)38     {39         iv_highArray.push_back(i_insert);40     }41     cout << "Max Rectangle area is " << MaxRectBarChart(iv_highArray) << endl;42     return 0;43 }

There is also a similar Google interview question that can be extended as the last question:

Find the largest White Rectangle in a single map: Give You a n * n black/white bitmap, find the largest white rectangle. Note that it is a rectangle, not any white area. Can your algorithm reach O (N * n?