We can envision matrix as a array that's broken down. If we have 3x3 it goes from indexes 0 to 8. (Because it has 9 values total). Formula for getting some matrix index (list index) is: columns * x + y. With constraints of x < M and y < N we can derive values. In short it is for any valid given matrix index the x is x / columns and y is y % columns. In short: To convert into list index use: columns * i + j To convert from list index into matrix indices it's (x: l_idx / columns, l_idx % columns) We can now use binary search. Go from l = 0, to r = largest l_idx When we get middle list index, convert it into indices. Get value of matrix and do condition. If equal target, exit otherwise binary search.