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:
matrix will be a 2D array of integers.
matrix will have a number of rows and columns in range [1, 20].
matrix[i][j] will be integers in range [0, 99].
Solutions
My solution
class Solution {
public:
bool isToeplitzMatrix(vector<vector<int>>& matrix) {
int m = matrix.size();
int n = matrix[0].size();
// line equations: j = i + k, k \in [1 - m, n - 1]
for(int k = 1 - m; k < n; ++k){
// i < m, j = i + k < n ==> i < min(m, n - k)
for(int i = 1 + max(0, -k) ; i < min(m, n - k); ++i){
if(matrix[i][i + k] != matrix[i - 1][i - 1 + k])
return false;
}
}
return true;
}
};
A better solution
class Solution {
public:
bool isToeplitzMatrix(vector<vector<int>>& matrix) {
int m = matrix.size();
int n = matrix[0].size();
for(int i = 1; i < m; ++i){
for(int j = 1; j < n; ++j){
if(matrix[i][j] != matrix[i - 1][j - 1])
return false;
}
}
return true;
}
};
