[LeetCode] 040: Largest Rectangle in Histogram

[Problem]

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.

[Solution]

class Solution {
public:
    int largestRectangleArea(vector<int> &height) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function

        // empty vector
        if(height.size() == 0)return 0;
        
        // init leftH
        int *leftH = new int[height.size()];
        leftH[0] = 0;
        for(int i = 1; i < height.size(); ++i){
            if(height[i] > height[i-1]){
                leftH[i] = i;
            }
            else{
                int j = leftH[i-1];
                while(true){
                    if(j != leftH[j]){
                        j = leftH[j];
                    }
                    else{
                        if(j > 0 && height[j-1] >= height[i]){
                            j--;
                        }
                        else{
                            leftH[i] = j;
                            break;
                        }
                    }
                }
            }
        }
        
        // init rightH
        int *rightH = new int[height.size()];
        rightH[height.size()-1] = height.size()-1;
        for(int i = height.size()-2; i >= 0; --i){
            if(height[i] > height[i+1]){
                rightH[i] = i;
            }
            else{
                int j = rightH[i+1];
                while(true){
                    if(j != rightH[j]){
                        j = rightH[j];
                    }
                    else{
                        if(j < height.size() - 1 && height[i] <= height[j+1]){
                            j++;
                        }
                        else{
                            rightH[i] = j;
                            break;
                        }
                    }
                }
            }
        }
        
        // get result
        int res = 0, area;
        for(int i = 0; i < height.size(); ++i){
            area = height[i] * (rightH[i] - leftH[i] + 1);
            res = max(res, area);
        }
        return res;
    }
};

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