在二维数组上进行二进制搜索

Question

I have a 2D array which is fully sorted. The arrays below are examples

    1  2  3  
    5  6  7  
    9 10 11 

and

    1  2  3  4  5
    6  7  8  9  10

I would like to use binary search on these array. Let rows be the number of rows and cols be the number of columns

Initially start = 0 and end = rows * cols -1

In the 3 X 3 array above, midpoint works out to be four [9 elements]. Now how do I find out the corresponding row and column with the midpoint ? Is there any standard formula for that ?

Answer 1

The formula is pretty simple:

row = number/cols_per_row;
col = number%cols_per_row;

Answer 2

Let size = rows * cols

mid = size // 2 (integer division)

row = mid // cols

col = mid % cols (rest for integer division)