Question

Give an nxn array of elements such that each row is in ascending order and each column is in ascending order, devise an O(n) algorithm to determine if a given element x in the array. You may assume all elements in the nxn array are distinct.

Please tell me if somebody knows the solution to this problem.

Answer 1

Start at 1st row last column i.e. i=0, j = n-1

while true {
if (j< 0 || i > (n-1) )
 break; // element not found
if (array[i][j] == x)
 return i,j
else if (x < array[i][j])
 j = j -1; // and repeat
else 
 i = i+1; // and repeat
}

This is O(n). Explanation:

Start at first row and last column. i=0;j=n-1 Everytime x is less than currElement decrement j else increment i.