Search a 2D Matrix II

Write an efficient algorithm that searches for a value in anmxnmatrix. This matrix has the following properties:

• Integers in each row are sorted in ascending from left to right.
• Integers in each column are sorted in ascending from top to bottom.

For example,

Consider the following matrix:

[
  [1,   4,  7, 11, 15],
  [2,   5,  8, 12, 19],
  [3,   6,  9, 16, 22],
  [10, 13, 14, 17, 24],
  [18, 21, 23, 26, 30]
]

Given target=5, returntrue.

Given target=20, returnfalse.

Solution:

We start search the matrix from top right corner, initialize the current position to top right corner, if the target is greater than the value in current position, then the target can not be in entire row of current position because the row is sorted, if the target is less than the value in current position, then the target can not in the entire column because the column is sorted too. We can rule out one row or one column each time. Not really a binary search problem.

Time complexity:

O(m+n).

public boolean searchMatrix (int[][] matrix, int target) {
    if (matrix == null || matrix.length == 0 ||
        matrix[0] == null || matrix[0].length == 0) {
            return false;
    }
    int row = 0,
        col = matrix[0].length - 1;
    while (row < matrix.length && col >= 0) {
        if (matrix[row][col] == target) {
            return true;
        } else if (matrix[row][col] > target) {
            col--;
        } else if (matrix[row][col] < target) {
            row++;
        }
    }
    return false;
}