We have some permutation A
of [0, 1, ..., N - 1]
, where N
is the length of A
.
The number of (global) inversions is the number of i < j
with 0 <= i < j < N
and A[i] > A[j]
.
The number of local inversions is the number of i
with 0 <= i < N
and A[i] > A[i+1]
.
Return true
if and only if the number of global inversions is equal to the number of local inversions.
Example 1:
Input: A = [1,0,2] Output: true Explanation: There is 1 global inversion, and 1 local inversion.
Example 2:
Input: A = [1,2,0] Output: false Explanation: There are 2 global inversions, and 1 local inversion.
Note:
A
will be a permutation of[0, 1, ..., A.length - 1]
.A
will have length in range[1, 5000]
.- The time limit for this problem has been reduced.
数组
A
是 [0, 1, ..., N - 1]
的一种排列,N
是数组 A
的长度。全局倒置指的是 i,j
满足 0 <= i < j < N
并且 A[i] > A[j]
,局部倒置指的是 i
满足 0 <= i < N
并且 A[i] > A[i+1]
。
当数组 A
中全局倒置的数量等于局部倒置的数量时,返回 true
。
示例 1:
输入: A = [1,0,2] 输出: true 解释: 有 1 个全局倒置,和 1 个局部倒置。
示例 2:
输入: A = [1,2,0] 输出: false 解释: 有 2 个全局倒置,和 1 个局部倒置。
注意:
A
是[0, 1, ..., A.length - 1]
的一种排列A
的长度在[1, 5000]
之间- 这个问题的时间限制已经减少了。
Runtime: 380 ms
Memory Usage: 19.1 MB
1 class Solution { 2 func isIdealPermutation(_ A: [Int]) -> Bool { 3 for i in 0..<A.count 4 { 5 if abs(A[i] - i) > 1 6 { 7 return false 8 } 9 } 10 return true 11 } 12 }
476ms
1 class Solution { 2 func isIdealPermutation(_ A: [Int]) -> Bool { 3 var leftMax = Int.min 4 for i in 0..<A.count - 1 { 5 if A[i] > A[i + 1] && leftMax > A[i + 1] { 6 return false 7 } 8 leftMax = max(leftMax, A[i]) 9 } 10 var rightMin = Int.max 11 for i in (1..<A.count).reversed() { 12 if A[i - 1] > A[i] && rightMin < A[i - 1] { 13 return false 14 } 15 rightMin = min(rightMin, A[i]) 16 } 17 return true 18 } 19 }
656ms
1 class Solution { 2 func merge_sort(_ array: inout[Int], _ global: inout Int, _ local: inout Int, _ start: Int, _ end: Int) { 3 //print("[\(start), \(end))") 4 guard end - start > 1 else { return } 5 let mid = (start + end) / 2 6 if mid - 1 >= start { 7 local += array[mid - 1] > array[mid] ? 1 : 0 8 } 9 merge_sort(&array, &global, &local, start, mid) 10 merge_sort(&array, &global, &local, mid, end) 11 12 let copy = Array(array[start..<mid]) 13 var i = copy.startIndex, j = mid, k = start 14 while i < copy.endIndex { 15 if j >= end || copy[i] <= array[j] { 16 array[k] = copy[i] 17 i += 1 18 } else { 19 array[k] = array[j] 20 j += 1 21 global += copy.endIndex - i 22 } 23 k += 1 24 } 25 } 26 func isIdealPermutation(_ A: [Int]) -> Bool { 27 var global = 0, local = 0 28 var array = A 29 merge_sort(&array, &global, &local, 0, array.count) 30 return global == local 31 } 32 }
8688ms
1 class Solution { 2 func isIdealPermutation(_ A: [Int]) -> Bool { 3 for i in 0..<A.count-1 { 4 var k = i - 1 5 if A[i] <= A[i+1] { 6 while k >= 0 { 7 if A[k] > A[i+1] { return false } 8 k -= 1 9 } 10 } 11 else { 12 while k >= 0 { 13 if A[k] >= A[i] { return false } 14 if A[k] < A[i] && A[k] > A[i+1] { return false } 15 k -= 1 16 } 17 } 18 } 19 return true 20 } 21 }
原文地址:https://www.cnblogs.com/strengthen/p/10541664.html
时间: 2024-10-09 21:05:19