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Question

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.

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, return true.

Given target = 20, return false.

Solution

Result: Accepted Time: 100 ms

Here should be some explanations.

bool search(int **a, int colnum, int rownum, int k)
{
    if(colnum == 0 || rownum == 0)
        return false;
    int sx = colnum - 1, sy = 0;
    while ( sx >= 0 && sx<colnum && sy >= 0 && sy<rownum)
    {
        if (a[sy][sx]>k)
            --sx;
        else if ( a[sy][sx]<k)
            ++sy;
        else
            return true;
    }
    return false;
}

bool searchMatrix(int** matrix, int matrixRowSize, int matrixColSize, int target) {
    return search(matrix,matrixColSize, matrixRowSize,target);
}

Complexity Analytics

• Time Complexity: $O(n+m)$
• Space Complexity: $O(1)$