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Difficulty Level: Difficult
1. Description
Given n non-negative integers, used to represent the height of each column in the histogram. Each column is adjacent to each other and has a width of 1.
Find the maximum area of the rectangle that can be outlined in the histogram.
2. Examples
Example 1
输入：heights = [2,1,5,6,2,3]
输出：10
解释：最大的矩形为图中红色区域，面积为 10
Example 2
输入： heights = [2,4]
输出： 4
hint:
1 <= heights.length <=10^50 <= heights[i] <= 10^4
3. Answer
Solution 1
class Solution {
func largestRectangleArea(_ heights: [Int]) -> Int {
if heights.count == 0 {
return 0
}
if heights.count == 1 {
return heights[0]
}
var leftIndexes = Array<Int>.init(repeating: 0, count: heights.count)
var rightIndexes = Array<Int>.init(repeating: 0, count: heights.count)
leftIndexes[0] = -1
rightIndexes[heights.count - 1] = heights.count
for i in 1..<heights.count {
var p = i - 1
while p >= 0, heights[p] >= heights[i] {
p = leftIndexes[p]
}
leftIndexes[i] = p
}
for i in (0...heights.count - 2).reversed() {
var p = i + 1
while p < heights.count, heights[p] >= heights[i] {
p = rightIndexes[p]
}
rightIndexes[i] = p
}
var maxArea = 0
for i in 0..<heights.count {
maxArea = max(maxArea, heights[i] * (rightIndexes[i] - leftIndexes[i] - 1))
}
return maxArea
}
}
Solution 2
class Solution {
func largestRectangleArea(_ heights: [Int]) -> Int {
let heights = heights + [0]
var indexStack: [Int] = []
var maxHeight = 0
for (i,height) in heights.enumerated() {
while let previousIndex = indexStack.last, heights[previousIndex] > height {
indexStack.removeLast()
let lastIndex = indexStack.last ?? -1
let width = (i-1) - lastIndex
let height = heights[previousIndex]
maxHeight = max(maxHeight, width * height)
}
indexStack.append(i)
}
return maxHeight
}
}
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