# Exercise 2.43

**Note** : *my solution may be extremely wrong as comparing the times doesnâ€™t give expected ratios, maybe because the safe? procedure takes more time when as the number of queens on the board increase. This question is not trivial. My analyze may not be 100% false though, queen-cols is called too many times.*

The original `queens`

procedure calls `queen-cols`

only \(n+1\) times. Louisâ€™s procedure calls the `queen-cols`

procedure for both each `new-row`

and each column, hence for a board of size \(n\) the procedure `queen-cols`

is called \(n^n\) times in contrary to only \(n+1\) times from the original procedure.\ So if the original procedure solves the puzzle in time \(T\), Louisâ€™s procedure may solves the puzzle in approximately time \(T^T\).