Binary Search in 2D Array 3 - c++

Question

I need to find a number in the 2D array.
Columns are sorted (from smallest value to the biggest).
Here is my code:
const int SIZE = 4;
const int NOT_FOUND = 1;
int binarySearch(int mat[][SIZE], int &line , int num);
void main()
{
int num, index, mat[SIZE][SIZE] = { 11,1,5,11,
11,6,7,2,
8,7,7,7,
0,12,9,10 };
int line = sizeof(mat) / sizeof(mat[0][0]);
cout << "please type a number to search: " << endl;
cin >> num;
index = binarySearch(mat, line, num);
if (index == NOT_FOUND) {
cout << "The value: " << num << "doesn't exist in the array\n";
}
else {
cout << "The value: " << num << " exists in line " << line+1
<<" and column: " << index+1 << endl;
}
system("pause");
}
int binarySearch(int mat[][SIZE], int &line, int num)
{
for (int j = 0; j < SIZE; j++)
{
int low = 0;
int high = SIZE - 1;
int middle;
while (low <= high)
{
middle = (low + high) / 2;
if (num == mat[middle][j])
{
line = middle;
return j;
}
else if (num < mat[middle][j]) {
high = middle - 1;
{
else {
low = middle + 1;
}
}
}
return NOT_FOUND;
}
The program doesn't find all the numbers in the array.
Something doesn't work.
What is the problem?

Answer 1

Your binarySearch doesn't go through all the numbers, it checks the first number, so in your case 11, then it moves to the next number, but it skips the whole row of numbers (1, 5, 11) and the first number in second row and then moves to the next second number which will be 6 in second row.
Since you have a Matrix of number it consists of Rows and Columns, that means you have to create two loops for(...), once for the Rows and one for the Columns so you can go through all the numbers in your 2D array.
I recommend setting a Break point on the binarySearch function and going through with that, it'll help you a lot.

Answer 2

A few things that I see wrong in your code are ::
1) It appears that you are applying binary search to every column in your input array, and if the number is not found in the corresponding column, you increment j and move to the next column.
The most important thing about binary search is "The array in which you are searching should always be sorted". Since here you are searching columns, all your columns shall be sorted! Which appears unsorted in the code above! Which is a major reason why you don't find most elements. So, your input array shall look something like this (if you want to apply binary search) ::
int mat[SIZE][SIZE] = { 0,1,5,2,
8,6,7,7,
11,7,7,10,
11,12,9,11 }
All columns sorted in ascending order here!
2) The value of the variable NOT_FOUND you have set it to 1 and from your function you return the column number from where you found the element. So, if you found the element in the 2D array in column 1 your program will print Element Not Found because the condition if (index == NOT_FOUND) evaluates to true if the element was found in column 1. So, a better solution would be to change the value of NOT_FOUND to some negative value, since it can never be the column number in a valid case. Something like this ::
const int NOT_FOUND = -1;
Ideone link of code :: http://ideone.com/9cwHnY