[LeetCode]Largest Rectangle in Histogram

题目解析:(链接)

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

.

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解题思路：

O(n^2)的代码很好写，下面是copy来的O(n)的解题思路：

原帖地址：http://www.cnblogs.com/lichen782/p/leetcode_Largest_Rectangle_in_Histogram.html

class Solution {
public:
int largestRectangleArea(vector<int>& height) {
stack<int> cache;
int result = 0;
height.push_back(0);
for (int i = 0; i < height.size(); ) {
if (cache.empty() || height[i] >= height[cache.top()]) {
cache.push(i++);
} else {
int index = cache.top();
cache.pop();
int muliply = cache.empty()? i : i - cache.top() - 1;
result = max(result, height[index] * muliply);
}
}

return result;
}
};