[Swift]LeetCode766. 托普利茨矩阵 | Toeplitz Matrix

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A matrix is Toeplitz if every diagonal from top-left to bottom-right has the same element.

Now given an M x N matrix, return True if and only if the matrix is Toeplitz. 

Example 1:

Input:
matrix = [
  [1,2,3,4],
  [5,1,2,3],
  [9,5,1,2]
]
Output: True
Explanation:
In the above grid, the diagonals are:
"[9]", "[5, 5]", "[1, 1, 1]", "[2, 2, 2]", "[3, 3]", "[4]".
In each diagonal all elements are the same, so the answer is True.

Example 2:

Input:
matrix = [
  [1,2],
  [2,2]
]
Output: False
Explanation:
The diagonal "[1, 2]" has different elements.

Note:

1. matrix will be a 2D array of integers.
2. matrix will have a number of rows and columns in range [1, 20].
3. matrix[i][j] will be integers in range [0, 99].

---

如果一个矩阵的每一方向由左上到右下的对角线上具有相同元素，那么这个矩阵是托普利茨矩阵。

给定一个 M x N 的矩阵，当且仅当它是托普利茨矩阵时返回 True。

示例 1:

输入: 
matrix = [
  [1,2,3,4],
  [5,1,2,3],
  [9,5,1,2]
]
输出: True
解释:
在上述矩阵中, 其对角线为:
"[9]", "[5, 5]", "[1, 1, 1]", "[2, 2, 2]", "[3, 3]", "[4]"。
各条对角线上的所有元素均相同, 因此答案是True。

示例 2:

输入:
matrix = [
  [1,2],
  [2,2]
]
输出: False
解释: 
对角线"[1, 2]"上的元素不同。

说明:

1.  matrix 是一个包含整数的二维数组。
2. matrix 的行数和列数均在 [1, 20]范围内。
3. matrix[i][j] 包含的整数在 [0, 99]范围内。

进阶:

1. 如果矩阵存储在磁盘上，并且磁盘内存是有限的，因此一次最多只能将一行矩阵加载到内存中，该怎么办？
2. 如果矩阵太大以至于只能一次将部分行加载到内存中，该怎么办？

---

Runtime: 28 ms

Memory Usage: 19 MB

class Solution {
    func isToeplitzMatrix(_ matrix: [[Int]]) -> Bool {
        for i in 0..<matrix.count - 1
        {
            for j in 0..<matrix[i].count - 1
            {
                if matrix[i][j] != matrix[i + 1][j + 1]
                {
                    return false
                }
            }
        }
        return true
    }
}

---

28ms

class Solution {
    func isToeplitzMatrix(_ matrix: [[Int]]) -> Bool {
        var temp: [Int] = matrix[0]
        for i in 1..<matrix.count {
            let smallMatrix = matrix[i]
            for j in 0..<smallMatrix.count {
                if j == 0 {
                    temp.insert(smallMatrix[j], at: 0)
                } else {
                    if smallMatrix[j] != temp[j] {
                        return false
                    }
                }
            }
        }
        return true
    }
}

---

32ms

class Solution {
    func isToeplitzMatrix(_ matrix: [[Int]]) -> Bool {
        var result = true

        for i in 0..<matrix.count {
            for j in 0..<matrix[0].count {
                if i > 0 && j > 0 {
                    break;
                }
                var pointR = i + 1
                var pointC = j + 1

                let val1 = matrix[i][j];
                let count = matrix[0].count

                while pointR < matrix.count {
                    if pointC < count {
                        let val2 = matrix[pointR][pointC]
                        if val1 != val2 {
                            result = false;
                        }
                        pointR += 1;
                        pointC += 1;
                    } else {
                        break;
                    }
                }
            }
        }
        return result;
    }
}

---

68ms

class Solution {
    func isToeplitzMatrix(_ matrix: [[Int]]) -> Bool {
for i in 0..<matrix[0].count{
            var val = -1
            var rowIndex = 0
            var columnIndex = i
            
            while rowIndex < matrix.count && columnIndex < matrix[0].count{
                if val != -1 && val != matrix[rowIndex][columnIndex]{
                    return false
                }
                val = matrix[rowIndex][columnIndex]
                rowIndex += 1
                columnIndex += 1
            }
        }
       
        for i in 0..<matrix.count{
            var val = -1
            
            var rowIndex = i
            var columnIndex = 0
            
            while rowIndex < matrix.count && columnIndex < matrix[0].count{
                if val != -1 && val != matrix[rowIndex][columnIndex]{
                    return false
                }
                val = matrix[rowIndex][columnIndex]
                rowIndex += 1
                columnIndex += 1
            }            
        }
        return true
    }
}

---

88ms

class Solution {
    func isToeplitzMatrix(_ matrix: [[Int]]) -> Bool {
        guard matrix.count > 0 else {
            return false
        }
        if matrix.count == 1 {
            return true
        }
        
        var row = matrix[0]
        for i in 1..<matrix.count {
            row = matrix[i-1]
            if !matrix[i][1...].elementsEqual(row[0..<row.count - 1]) {
                return false
            }
        }
        return true
    }
}