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?微信公眾號：山青詠芝（shanqingyongzhi）
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?原文地址：https://www.cnblogs.com/strengthen/p/10497048.html?
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Given an unsorted array of integers, find the number of longest increasing subsequence.

Example 1:

Input: [1,3,5,4,7] Output: 2 Explanation: The two longest increasing subsequence are [1, 3, 4, 7] and [1, 3, 5, 7].?

Example 2:

Input: [2,2,2,2,2] Output: 5 Explanation: The length of longest continuous increasing subsequence is 1, and there are 5 subsequences' length is 1, so output 5.

Note:?Length of the given array will be not exceed 2000 and the answer is guaranteed to be fit in 32-bit signed int.

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給定一個未排序的整數(shù)數(shù)組，找到最長遞增子序列的個數(shù)。

示例 1:

輸入: [1,3,5,4,7] 輸出: 2 解釋: 有兩個最長遞增子序列，分別是 [1, 3, 4, 7] 和[1, 3, 5, 7]。

示例 2:

輸入: [2,2,2,2,2] 輸出: 5 解釋: 最長遞增子序列的長度是1，并且存在5個子序列的長度為1，因此輸出5。

注意:?給定的數(shù)組長度不超過 2000 并且結(jié)果一定是32位有符號整數(shù)。

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108ms

1 class Solution { 2 func findNumberOfLIS(_ nums: [Int]) -> Int { 3 if nums.count <= 1 { 4 return nums.count 5 } 6 7 var lengths = [Int](repeating: 0, count: nums.count) 8 var rank = [Int : Int]() 9 let uniArr = Array(Set(nums)).sorted() 10 for (k, v) in uniArr.enumerated() { 11 rank[v] = k 12 } 13 14 let n = uniArr.count 15 var binaryIndexed = [Int](repeating: 0, count: n+1) 16 17 func update(_ index: Int, _ val: Int) -> Void { 18 var x = index 19 while x <= n { 20 binaryIndexed[x] = max(binaryIndexed[x], val) 21 x += x&(-x) 22 } 23 } 24 25 func query(fromOneTo index: Int) -> Int { 26 var rval = 0 27 var x = index 28 while x > 0 { 29 rval = max(binaryIndexed[x], rval) 30 x &= x-1 31 } 32 return rval 33 } 34 35 var longestLen = 0 36 for i in 0..<nums.count { 37 let bIndex = rank[nums[i]]! + 1 38 lengths[i] = query(fromOneTo: bIndex-1) + 1 39 longestLen = max(longestLen, lengths[i]) 40 update(bIndex, lengths[i]) 41 } 42 43 if longestLen == nums.count { 44 return 1 45 } else if longestLen == 1 { 46 return nums.count 47 } 48 49 var dp = [Int](repeating: 0, count: nums.count) 50 // table stores the indexes of nums, sort by lengths and then nums 51 var table = Array(0..<nums.count) 52 table.sort{ 53 lengths[$0] == lengths[$1] ? nums[$0] < nums[$1] : lengths[$0] < lengths[$1] 54 } 55 var lengthIndexDict = [Int:Int]() 56 57 for (i, v) in table.enumerated() where i == 0 || lengths[v] != lengths[table[i-1]] { 58 lengthIndexDict[lengths[v]] = i 59 } 60 61 for i in 0..<nums.count { 62 if lengths[i] == i+1 || lengths[i] == 1 { 63 dp[i] = 1 64 } else { 65 let len = lengths[i]-1 66 let tableIndex = lengthIndexDict[len]! 67 for j in tableIndex..<table.count { 68 let index = table[j] 69 if nums[index] >= nums[i] || lengths[index] != len { 70 break 71 } 72 if index < i { 73 dp[i] += dp[index] 74 } 75 } 76 } 77 } 78 79 var ans = 0 80 for i in 0..<dp.count where lengths[i] == longestLen { 81 ans += dp[i] 82 } 83 84 return ans 85 } 86 }

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Runtime:?140 ms Memory Usage:?18.9 MB 1 class Solution { 2 func findNumberOfLIS(_ nums: [Int]) -> Int { 3 var res:Int = 0 4 var mx:Int = 0 5 var n:Int = nums.count 6 var len:[Int] = [Int](repeating:1,count:n) 7 var cnt:[Int] = [Int](repeating:1,count:n) 8 for i in 0..<n 9 { 10 for j in 0..<i 11 { 12 if nums[i] <= nums[j] {continue} 13 if len[i] == len[j] + 1 {cnt[i] += cnt[j]} 14 else if len[i] < len[j] + 1 15 { 16 len[i] = len[j] + 1 17 cnt[i] = cnt[j] 18 } 19 } 20 mx = max(mx, len[i]) 21 } 22 for i in 0..<n 23 { 24 if mx == len[i] 25 { 26 res += cnt[i] 27 } 28 } 29 return res 30 } 31 }

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140ms

1 class Solution { 2 func findNumberOfLIS(_ nums: [Int]) -> Int { 3 return lengthOfLISDP(nums) 4 } 5 6 func lengthOfLISDP(_ nums: [Int]) -> Int { 7 var matrix = Array(repeating: 0, count: nums.count) 8 var matrixCount = Array(repeating: 1, count: nums.count) 9 var maxResult = 0 10 var maxResultCount = 0 11 12 for i in 0..<nums.count { 13 var maxInside = 0 14 var maxInsideCount = 1 15 for j in 0..<i { 16 if nums[i] > nums[j] { 17 if matrix[j] > maxInside { 18 maxInside = matrix[j] 19 maxInsideCount = matrixCount[j] 20 } else if matrix[j] == maxInside { 21 maxInsideCount += matrixCount[j] 22 } 23 } 24 } 25 26 matrix[i] = 1 + maxInside 27 matrixCount[i] = maxInsideCount 28 29 if matrix[i] > maxResult { 30 maxResult = matrix[i] 31 maxResultCount = maxInsideCount 32 } else if matrix[i] == maxResult { 33 maxResultCount += maxInsideCount 34 } 35 } 36 37 return maxResultCount 38 } 39 }

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144ms

1 class Solution { 2 func findNumberOfLIS(_ nums: [Int]) -> Int { 3 guard nums.count > 1 else { 4 return nums.count 5 } 6 7 var LISDP = [Int](repeating: 1, count: nums.count) 8 var count = [Int](repeating: 0, count: nums.count) 9 count[0] = 1 10 var LIS: Int = 1 11 for i in 1..<nums.count { 12 let currentNum = nums[i] 13 for j in 0..<i { 14 let movingNum = nums[j] 15 if currentNum > movingNum { 16 if LISDP[i] < LISDP[j] + 1 { 17 LISDP[i] = LISDP[j] + 1 18 count[i] = count[j] 19 } else if LISDP[i] == LISDP[j] + 1 { 20 count[i] += count[j] 21 } 22 23 } 24 } 25 if count[i] == 0 { count[i] = 1 } 26 LIS = max(LIS, LISDP[i]) 27 } 28 print(count) 29 var result: Int = 0 30 for (index, increasingSequence) in LISDP.enumerated() { 31 if increasingSequence == LIS { 32 result += count[index] 33 } 34 } 35 return result 36 } 37 }

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148ms

1 class Solution { 2 func findNumberOfLIS(_ nums: [Int]) -> Int { 3 if nums.count == 0 { 4 return 0 5 } 6 // 長度 7 var dp = Array(repeating: 1, count: nums.count) 8 // count 9 var count = Array(repeating: 1, count: nums.count) 10 dp[0] = 1 11 dp[0] = 1 12 for (index, num) in nums.enumerated() where index != 0 { 13 for i in 0...index-1 { 14 if nums[i] < num { 15 if dp[i] + 1 > dp[index] { 16 dp[index] = dp[i] + 1 17 count[index] = count[i] 18 } else if dp[i] + 1 == dp[index]{ 19 count[index] += count[i] 20 } 21 } 22 } 23 } 24 var sum = 0 25 let _max = dp.max()! 26 for (index, count) in count.enumerated() { 27 if dp[index] == _max { 28 sum += count 29 } 30 } 31 return sum 32 } 33 }

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172ms

1 class Solution { 2 func findNumberOfLIS(_ nums: [Int]) -> Int { 3 let n = nums.count 4 5 var length = [Int](repeating:1, count:n) 6 var count = [Int](repeating:1, count: n) 7 8 for i in 0..<n { 9 for j in 0..<i { 10 if nums[i] > nums[j] { 11 if length[i] == length[j] + 1 { 12 count[i] += count[j] 13 } 14 if length[i] < length[j] + 1 { 15 length[i] = length[j] + 1 16 count[i] = count[j] 17 } 18 } 19 } 20 } 21 22 var result = 0 23 var maxLength = 0 24 25 length.forEach({ maxLength = max(maxLength, $0) }) 26 27 for i in 0..<n { 28 result += length[i] == maxLength ? count[i] : 0 29 } 30 31 return result 32 } 33 }

---

184ms

1 class Solution { 2 3 func findNumberOfLIS(_ nums: [Int]) -> Int { 4 let n = nums.count 5 6 var result = 0 7 var maxLength = 0 8 9 var length = [Int](repeating:0, count:n) 10 var count = [Int](repeating:0, count: n) 11 12 for i in 0..<n { 13 length[i] = 1 14 count[i] = 1 15 for j in 0..<i { 16 if nums[i] > nums[j] { 17 if length[i] == length[j] + 1 { 18 count[i] += count[j] 19 } 20 if length[i] < length[j] + 1 { 21 length[i] = length[j] + 1 22 count[i] = count[j] 23 } 24 } 25 } 26 if maxLength == length[i] { 27 result += count[i] 28 } 29 if maxLength < length[i] { 30 maxLength = length[i] 31 result = count[i] 32 } 33 } 34 return result 35 } 36 }

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轉(zhuǎn)載于:https://www.cnblogs.com/strengthen/p/10497048.html

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