Question

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.

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].

Follow up:

1. What if the matrix is stored on disk, and the memory is limited such that you can only load at most one row of the matrix into the memory at once?
2. What if the matrix is so large that you can only load up a partial row into the memory at once?

Difficulty:Easy

Category:Array

Analyze

Solution

class Solution {
 public:
  bool isToeplitzMatrix(vector<vector<int>>& matrix) {
    int m = matrix.size(), n = matrix[0].size();
    if (m <= 1) return true;

    for (int i = m - 1; i >= 0; --i) {
      int val = matrix[i][0];
      int p = 1;
      for (int j = i + 1; j < m && p < n; ++j) {
        if (matrix[j][p++] != val) return false;
      }
    }

    for (int i = 1; i < n; ++i) {
      int val = matrix[0][i];
      int p = 1;
      for (int j = i + 1; j < n && p < m; ++j) {
        if (matrix[p++][j] != val) return false;
      }
    }

    return true;
  }
};