[Swift]LeetCode960. 删列造序 III | Delete Columns to Make Sorted III

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We are given an array A of N lowercase letter strings, all of the same length.

Now, we may choose any set of deletion indices, and for each string, we delete all the characters in those indices.

For example, if we have an array A = ["babca","bbazb"] and deletion indices {0, 1, 4}, then the final array after deletions is ["bc","az"].

Suppose we chose a set of deletion indices D such that after deletions, the final array has every element (row) in lexicographic order.

For clarity, A[0] is in lexicographic order (ie. A[0][0] <= A[0][1] <= ... <= A[0][A[0].length - 1]), A[1] is in lexicographic order (ie. A[1][0] <= A[1][1] <= ... <= A[1][A[1].length - 1]), and so on.

Return the minimum possible value of D.length.

Example 1:

Input: ["babca","bbazb"] Output: 3 Explanation: After deleting columns 0, 1, and 4, the final array is A = ["bc", "az"]. Both these rows are individually in lexicographic order (ie. A[0][0] <= A[0][1] and A[1][0] <= A[1][1]). Note that A[0] > A[1] - the array A isn't necessarily in lexicographic order. 

Example 2:

Input: ["edcba"] Output: 4 Explanation: If we delete less than 4 columns, the only row won't be lexicographically sorted. 

Example 3:

Input: ["ghi","def","abc"] Output: 0 Explanation: All rows are already lexicographically sorted.

Note:

1. 1 <= A.length <= 100
2. 1 <= A[i].length <= 100

---

给定由 N 个小写字母字符串组成的数组 A，其中每一个字符串长度相等。

选取一个删除索引序列，对于 A 中的每一个字符串，删除对应每一个索引处的字符。

好比，有 A = ["babca","bbazb"]，删除索引序列 {0, 1, 4}，删除后 A 为["bc","az"]。

假设，咱们选择了一组删除索引 D，那么在执行删除操做以后，最终获得的数组的行中的每一个元素都是按字典序排列的。

清楚起见，A[0] 是按字典序排列的（即，A[0][0] <= A[0][1] <= ... <= A[0][A[0].length - 1]），A[1] 是按字典序排列的（即，A[1][0] <= A[1][1] <= ... <= A[1][A[1].length - 1]），依此类推。

请你返回 D.length 的最小可能值。

示例 1：

输入：["babca","bbazb"]
输出：3
解释：
删除 0、1 和 4 这三列后，最终获得的数组是 A = ["bc", "az"]。
这两行是分别按字典序排列的（即，A[0][0] <= A[0][1] 且 A[1][0] <= A[1][1]）。
注意，A[0] > A[1] —— 数组 A 不必定是按字典序排列的。

示例 2：

输入：["edcba"]
输出：4
解释：若是删除的列少于 4 列，则剩下的行都不会按字典序排列。

示例 3：

输入：["ghi","def","abc"]
输出：0
解释：全部行都已按字典序排列。

提示：

1. 1 <= A.length <= 100
2. 1 <= A[i].length <= 100

---

108ms

 1 class Solution {  2     func minDeletionSize(_ A: [String]) -> Int {  3         let n = A.count  4         if (n == 0) {  5             return 0
 6  }  7         let m = A.first!.count  8         if (m == 0) {  9             return 0
10  } 11         
12         let Chars = A.map{Array<UInt8>($0.utf8)} 13         
14         var compare = Array<Array<Bool>>(repeating: Array<Bool>(repeating: false, count: m), count: m) 15         for i in 0..<m { 16             one: for j in i+1..<m { 17                 for l in 0..<n { 18                     if Chars[l][i] > Chars[l][j] { 19                         continue one 20  } 21  } 22                 compare[i][j] = true
23  } 24  } 25         
26         var f :[Int] = Array<Int>(repeating: 0, count: m) 27         
28         var i = m - 2; 29         while  i >= 0 { 30             var max = 0
31             for j in i+1..<m { 32                 let tempMax = (compare[i][j] ? (1 + f[j]): 0) 33                 if (tempMax > max) { 34                     max = tempMax 35  } 36  } 37             f[i] = max 38             i -= 1
39  } 40         var max = 0
41         for fe in f { 42             if max < fe { 43                 max = fe 44  } 45  } 46         return m - (max + 1) 47  } 48 }

---

160ms

 1 class Solution {  2     func minDeletionSize(_ A: [String]) -> Int {  3     let count = A[0].count  4     guard count > 1 else { return 0 }  5     
 6     let chars: [[Character]] = A.map { Array($0) }  7     var dp = [Int](repeating: 1, count: count)  8     
 9     for r in 1..<count { 10         var longest = 0
11         
12         next: for l in 0..<r { 13             for row in chars { 14                 if row[l] > row[r] { 15                     continue next 16  } 17  } 18             if dp[l] > longest { 19                 longest = dp[l] 20  } 21  } 22         
23         dp[r] = longest + 1
24  } 25     return count - dp.max()!
26 } 27 }

---

512ms

 1 class Solution {  2     func minDeletionSize(_ A: [String]) -> Int {  3         var A = A  4         var n:Int = A.count  5         var m:Int = A[0].count  6         var f:[Int] = [Int](repeating:0,count:102)  7         var maxd = -1
 8         for i in 0..<m  9  { 10             f[i] = 1
11             for j in 0..<i 12  { 13                 if smaller(j, i, &A, n) 14  { 15                     f[i] = max(f[i], f[j] + 1) 16  } 17  } 18             maxd = max(maxd, f[i]) 19  } 20         return m - maxd 21  } 22     
23     func smaller(_ i:Int,_ j:Int,_ A:inout [String],_ n:Int) -> Bool 24  { 25         for k in 0..<n 26  { 27             if A[k][i] > A[k][j] 28  { 29                 return false
30  } 31  } 32         return true
33  } 34 } 35 
36 extension String { 37     //subscript函数能够检索数组中的值 38     //直接按照索引方式截取指定索引的字符
39     subscript (_ i: Int) -> Character { 40         //读取字符
41         get {return self[index(startIndex, offsetBy: i)]} 42  } 43 }

---

1488ms

 1 class Solution {  2     func minDeletionSize(_ A: [String]) -> Int {  3         let count = A[0].count  4     guard count > 1 else { return 0 }  5     
 6     var dp = [Int](repeating: 1, count: count)  7     
 8     for r in 1..<count {  9         var longest = 0
10         
11         next: for l in 0..<r { 12             for row in A { 13                 let chars = Array(row) 14                 if chars[l] > chars[r]{ 15                     continue next 16  } 17  } 18             if dp[l] > longest { 19                 longest = dp[l] 20  } 21  } 22         
23         dp[r] = longest + 1
24  } 25     
26     return count - dp.max()!
27  } 28 }