Largest Rectangle in Histogram
阿新 • • 發佈:2019-01-03
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
For example,
Given height = [2,1,5,6,2,3]
,
return 10
.
遍歷陣列,每找到一個區域性峰值,然後向前遍歷所有的值,算出共同的矩形面積,每次對比保留最大值,程式碼如下:
// 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; } };
也可用棧來維護一個高度遞增序列,每次遇到較小的高度就開始計算矩形面積,程式碼如下
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; } };