21.Search a 2D Matrix II

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 in ascending from left to right.

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

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]
]

Solution:

Approach: Start searching from the top right corner If the target if greater then its not present in that row If the target if smaller we check that row

class Solution
{
public:
    bool searchMatrix(vector<vector<int>> &matrix, int target)
    {

        int n = matrix.size();
        if (n == 0)
        {
            return false;
        }
        int m = matrix[0].size();

        int i = 0, j = m - 1;

        while (i < n && j >= 0)
        {

            if (matrix[i][j] == target)
            {
                return true;
            }

            if (target > matrix[i][j])
            {
                i++;
            }
            else if (target < matrix[i][j])
            {
                j--;
            }
        }

        return false;
    }
};

Time Complexity: O(n)