题目链接 : https://leetcode-cn.com/problems/largest-rectangle-in-histogram/
题目描述:
给定 n 个非负整数,用来表示柱状图中各个柱子的高度。每个柱子彼此相邻,且宽度为 1 。
求在该柱状图中,能够勾勒出来的矩形的最大面积。
以上是柱状图的示例,其中每个柱子的宽度为 1,给定的高度为 [2,1,5,6,2,3]。
图中阴影部分为所能勾勒出的最大矩形面积,其面积为 10 个单位。
示例:
输入: [2,1,5,6,2,3]
输出: 10
思路:
首先,想找到第i
位置最大面积是什么?
是以i
为中心,向左找第一个小于heights[i]
的位置left_i
;向右找第一个小于于heights[i]
的位置right_i
,即最大面积为heights[i] * (right_i - left_i -1)
,如下图所示:
所以,我们的问题就变成如何找right_i
和left_i
?
最简单的思路就是,就是暴力法,直接分别在i
左右移动
class Solution:
def largestRectangleArea(self, heights: List[int]) -> int:
res = 0
n = len(heights)
for i in range(n):
left_i = i
right_i = i
while left_i >= 0 and heights[left_i] >= heights[i]:
left_i -= 1
while right_i < n and heights[right_i] >= heights[i]:
right_i += 1
res = max(res, (right_i - left_i - 1) * heights[i])
return res
但是,这是一个时间复杂度为\(O(n^2)\),超时
接下来想办法优化.
思路一:
当我们找i
左边第一个小于heights[i]
如果heights[i-1] >= heights[i]
其实就是和heights[i-1]
左边第一个小于heights[i-1]
一样.依次类推,右边同理.
思路二:栈
利用单调栈,我写过关于它一篇文章
维护一个单调递增的栈,就可以找到left_i
和right_i
代码:
思路一:
class Solution:
def largestRectangleArea(self, heights: List[int]) -> int:
if not heights:
return 0
n = len(heights)
left_i = [0] * n
right_i = [0] * n
left_i[0] = -1
right_i[-1] = n
for i in range(1, n):
tmp = i - 1
while tmp >= 0 and heights[tmp] >= heights[i]:
tmp = left_i[tmp]
left_i[i] = tmp
for i in range(n - 2, -1, -1):
tmp = i + 1
while tmp < n and heights[tmp] >= heights[i]:
tmp = right_i[tmp]
right_i[i] = tmp
# print(left_i)
# print(right_i)
res = 0
for i in range(n):
res = max(res, (right_i[i] - left_i[i] - 1) * heights[i])
return res
java
class Solution {
public int largestRectangleArea(int[] heights) {
if (heights == null || heights.length == 0) return 0;
int n = heights.length;
int[] left_i = new int[n];
int[] right_i = new int[n];
left_i[0] = -1;
right_i[n - 1] = n;
int res = 0;
for (int i = 1; i < n; i++) {
int tmp = i - 1;
while (tmp >= 0 && heights[tmp] >= heights[i]) tmp = left_i[tmp];
left_i[i] = tmp;
}
for (int i = n - 2; i >= 0; i--) {
int tmp = i + 1;
while (tmp < n && heights[tmp] >= heights[i]) tmp = right_i[tmp];
right_i[i] = tmp;
}
for (int i = 0; i < n; i++) res = Math.max(res, (right_i[i] - left_i[i] - 1) * heights[i]);
return res;
}
}
思路二:
class Solution:
def largestRectangleArea(self, heights: List[int]) -> int:
stack = []
heights = [0] + heights + [0]
res = 0
for i in range(len(heights)):
#print(stack)
while stack and heights[stack[-1]] > heights[i]:
tmp = stack.pop()
res = max(res, (i - stack[-1] - 1) * heights[tmp])
stack.append(i)
return res
java
class Solution {
public int largestRectangleArea(int[] heights) {
int res = 0;
Deque<Integer> stack = new ArrayDeque<>();
int[] new_heights = new int[heights.length + 2];
for (int i = 1; i < heights.length + 1; i++) new_heights[i] = heights[i - 1];
//System.out.println(Arrays.toString(new_heights));
for (int i = 0; i < new_heights.length; i++) {
//System.out.println(stack.toString());
while (!stack.isEmpty() && new_heights[stack.peek()] > new_heights[i]) {
int cur = stack.pop();
res = Math.max(res, (i - stack.peek() - 1) * new_heights[cur]);
}
stack.push(i);
}
return res;
}
}
原文地址:https://www.cnblogs.com/powercai/p/10987169.html
时间: 2024-10-11 17:39:51