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.
Example:
Input: [2,1,5,6,2,3] Output: 10
思路:
两种方案:1 递归;2 堆栈
1 递归
我们按照最小的数将输入分为前后两部分,如此递归的寻找最大值。但是这样会导致内存使用过大,有些用例会溢出,代码如下:
void getMaxRec(vector<int> heights, int &maxRec){
if (heights.size() == 0) return;
auto minHeight = min_element(heights.begin(), heights.end());
int rec = *minHeight*heights.size();
maxRec = max(maxRec, rec);
int minIdx = distance(heights.begin(), minHeight);
if (heights.size() == 1) return;
vector<int> leftHeights, rightHeights;
leftHeights.assign(heights.begin(), heights.begin() + minIdx);
getMaxRec(leftHeights, maxRec);
rightHeights.assign(heights.begin()+minIdx+1, heights.end());
getMaxRec(rightHeights, maxRec);
}
int largestRectangleArea(vector<int>& heights) {
int maxRec = 0;
getMaxRec(heights, maxRec);
return maxRec;
}
2 堆栈
这种方法非常靠技巧,需要细致的思考,但是实现方法很简单:我们维持一个stack,里面的数只能是升序,当遇到降序时就记录下前面升序的序列所围成的矩形面积。代码如下:
int largestRectangleArea2(vector<int>& heights){
stack<int> records; int maxRec = 0;
heights.push_back(0);
for (int i = 0; i < heights.size(); i++){
if (records.size() == 0 || heights[records.top()] <= heights[i]){
records.push(i); continue;
}
int top = records.top(); records.pop();
int rec = records.size() ? (i - records.top()-1)*heights[top] : i*heights[top];
maxRec = max(maxRec, rec);
i--;
}
return maxRec;
}