欢迎您访问程序员文章站本站旨在为大家提供分享程序员计算机编程知识!
您现在的位置是: 首页

Largest Rectangle in Histogram

程序员文章站 2022-06-17 22:54:53
...

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.

 

Largest Rectangle in Histogram

Above is a histogram where width of each bar is 1, given height = [2,1,5,6,2,3].

 

Largest Rectangle in Histogram

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.

 

遍历数组,每找到一个局部峰值,然后向前遍历所有的值,算出共同的矩形面积,每次对比保留最大值,代码如下:

// Pruning optimize
class Solution {
public:
    int largestRectangleArea(vector<int> &height) {
        int res = 0;
        for (int i = 0; i < height.size(); ++i) {
            if (i + 1 < height.size() && height[i] <= height[i + 1]) {
                continue;
            }
            int minH = height[i];
            for (int j = i; j >= 0; --j) {
                minH = min(minH, height[j]);
                int area = minH * (i - j + 1);
                res = max(res, area);
            }
        }
        return res;
    }
};

 也可用栈来维护一个高度递增序列,每次遇到较小的高度就开始计算矩形面积,代码如下

class Solution {
public:
    int largestRectangleArea(vector<int>& heights) {
        int res = 0;
        stack<int> st;
        heights.push_back(0);
        for (int i = 0; i < heights.size(); ++i) {
            while (!st.empty() && heights[st.top()] >= heights[i]) {
                int cur = st.top(); st.pop();
                res = max(res, heights[cur] * (st.empty() ? i : (i - st.top() - 1)));
            }
            st.push(i);
        }
        return res;
    }
};

 

相关标签: 算法