[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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