Binary Search in 2D Array

Question

I wonder, can binary search be applied on a 2D array?

• What would the conditions on the array be? Sorted on 2D??

Answer 1

You can transform 2D array into 1D array and do the binary search here. Complexity is O(log(m * n)) for mxn array.

Answer 2

Binary Search works in the divide and conquer way,

int r = arr.length; // ROW Count
int c = arr[0].length; // Column Count
int start = 0; // Initialize with the 0
int end = r*c-1; // Last Index

We will keep iterating the while loop, each time we updating the start and end index as per requirements..
while(start <= end){

int mid = (start+end)/2;
int midX = mid/c;
int midY = mid%c;

If the current value is equals to the search element then we just have to print and return it.

if(arr[midX][midY] == searchElement){
return true;
}

If the current value is smaller then the search element then we just have to update the mid value by mid = mid + 1

if(arr[midX][midY] < searchElement){
start = mid+1;
}

If the current value is grater than the search element then we just have to update the mid value by mid = mid - 1

else{
end = mid-1;
}