Question

input --> NxN matrix of integers where every row and column strictly increasing.

How can I design a search algorithm to determine whether matrix contains a element x?

Can you also analyze it? PLEASE make efficient as possible.

Answer 1

Please find the pseudocode/algorithm below.

Let x be the  element we’re trying to search for in the matrix, and e be the current element we’re processing in the array.

1) We would need to start with top right element.
2) Loop for each row and for each row, loop for each column:

....i) compare this element e with x
…ii) if e = x, then return position of e, since we found x in the given matrix.
…iii) if e > x then move left to check elements smaller than e (if out of bound of matrix, then break and return false)
…iv) if e < x then move below to check elements greater than e (if out of bound of matrix, then break and return false)
3) repeat the i), ii) and iii) until you find the element or return false

Time Complexity: O(n)