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?微信公眾號：山青詠芝（shanqingyongzhi）
?博客園地址：山青詠芝（https://www.cnblogs.com/strengthen/）
?GitHub地址：https://github.com/strengthen/LeetCode
?原文地址：https://www.cnblogs.com/strengthen/p/9929505.html?
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Write an efficient algorithm that searches for a value in an?m?x?n?matrix. This matrix has the following properties:

• Integers in each row are sorted from left to right.
• The first integer of each row is greater than the last integer of the previous row.

Example 1:

Input: matrix = [[1, 3, 5, 7],[10, 11, 16, 20],[23, 30, 34, 50] ] target = 3 Output: true

Example 2:

Input: matrix = [[1, 3, 5, 7],[10, 11, 16, 20],[23, 30, 34, 50] ] target = 13 Output: false

---

編寫一個高效的算法來判斷?m?x?n?矩陣中，是否存在一個目標值。該矩陣具有如下特性：

• 每行中的整數從左到右按升序排列。
• 每行的第一個整數大于前一行的最后一個整數。

示例?1:

輸入: matrix = [[1, 3, 5, 7],[10, 11, 16, 20],[23, 30, 34, 50] ] target = 3 輸出: true

示例?2:

輸入: matrix = [[1, 3, 5, 7],[10, 11, 16, 20],[23, 30, 34, 50] ] target = 13 輸出: false

---

16ms 1 class Solution { 2 func searchMatrix(_ matrix: [[Int]], _ target: Int) -> Bool { 3 guard matrix.count > 0 else { 4 return false 5 } 6 7 let rows = matrix.count 8 let columns = matrix[0].count 9 10 var first = 0 11 var last = rows*columns-1 12 13 while first <= last { 14 let mid = first + (last-first)/2 15 16 if matrix[mid/columns][mid%columns] == target { 17 return true 18 } 19 20 if matrix[mid/columns][mid%columns] > target { 21 last = mid-1 22 } 23 else { 24 first = mid+1 25 } 26 } 27 28 return false 29 } 30 }

---

16ms

1 class Solution { 2 func searchMatrix(_ matrix: [[Int]], _ target: Int) -> Bool { 3 if matrix.count == 0 || matrix[0].count == 0 { 4 return false 5 } 6 7 let n = matrix.count 8 let m = matrix[0].count 9 var left = 0 10 var right = m * n - 1 11 12 while left < right { 13 let middle = left + (right - left - 1) / 2 14 if matrix[middle / m][middle % m] < target { 15 left = middle + 1 16 } else { 17 right = middle 18 } 19 } 20 21 return matrix[right / m][right % m] == target 22 } 23 }

---

20ms

1 class Solution { 2 func searchMatrix(_ matrix: [[Int]], _ target: Int) -> Bool { 3 if matrix.count == 0 || matrix.first!.count <= 0 { 4 return false 5 } 6 // 邊界判斷 7 if target < matrix.first!.first! || target > matrix.last!.last! { 8 return false 9 } 10 // 因為矩陣的每行都有序, 可將矩陣看作"一個數組"進行二分查找 11 var low = 0 12 var high = matrix.count * matrix.first!.count - 1 13 var mid = 0 14 while low <= high { 15 mid = (low + high) / 2 16 let coords = convertIndex(mid, in: matrix) // index轉換為坐標 17 let value = matrix[coords.row][coords.column] 18 if value == target { 19 return true 20 } else if target < value { 21 high = mid - 1 22 } else { 23 low = mid + 1 24 } 25 } 26 return false 27 } 28 29 private func convertIndex(_ index: Int, in matix: [[Any]]) -> (row: Int, column: Int) { 30 return (row: index / matix.first!.count, 31 column: index % matix.first!.count) 32 } 33 }

---

80ms

1 class Solution { 2 func searchMatrix(_ matrix: [[Int]], _ target: Int) -> Bool { 3 guard !matrix.isEmpty else { return false } 4 5 let lastRowIndex = matrix.count - 1 6 7 for (index, row) in matrix.enumerated() { 8 guard !row.isEmpty else { continue } 9 guard target >= row[0] else { continue } 10 11 if lastRowIndex != index && target >= matrix[index + 1][0] { 12 continue 13 } 14 15 for n in row { 16 if n == target { 17 return true 18 } 19 } 20 21 } 22 23 return false 24 } 25 }

---

100ms

1 class Solution { 2 func searchMatrix(_ matrix: [[Int]], _ target: Int) -> Bool { 3 let arr = matrix.flatMap{$0} 4 return binarySearch(arr, 0, arr.count - 1, target) 5 } 6 7 func binarySearch(_ arr: [Int], _ start: Int, _ end: Int, _ target: Int) -> Bool { 8 let mid = (start + end ) / 2 9 guard start <= end else { return false } 10 if target == arr[mid] { return true} 11 if target < arr[mid] { 12 return binarySearch(arr, start, mid - 1, target) 13 } else { 14 return binarySearch(arr, mid + 1, end, target) 15 } 16 } 17 }

---

104ms

1 class Solution { 2 func searchMatrix(_ matrix: [[Int]], _ target: Int) -> Bool { 3 let arr = matrix.flatMap{$0} 4 return binarySearch(arr, 0, arr.count - 1, target) 5 } 6 7 func divide(_ arr: [[Int]], _ start: Int, _ end:Int, _ target: Int) -> Bool { 8 guard start <= end else { return false } 9 if start == end { 10 return binarySearch(arr[start], 0, arr[start].count - 1, target) 11 } 12 13 let mid = (start + end ) / 2 14 let localArr = arr[mid] 15 let high = localArr[localArr.count - 1] 16 if target == high { return true} 17 if high < target { 18 return divide(arr, mid + 1, end, target) 19 } else { 20 return divide(arr, start, mid, target) 21 } 22 } 23 24 func binarySearch(_ arr: [Int], _ start: Int, _ end: Int, _ target: Int) -> Bool { 25 let mid = (start + end ) / 2 26 guard start <= end else { return false } 27 if target == arr[mid] { return true} 28 if target < arr[mid] { 29 return binarySearch(arr, start, mid - 1, target) 30 } else { 31 return binarySearch(arr, mid + 1, end, target) 32 } 33 } 34 }

?

轉載于:https://www.cnblogs.com/strengthen/p/9929505.html

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