diff --git a/exam/packet.tex b/exam/packet.tex index 4c1397f..3b621d8 100644 --- a/exam/packet.tex +++ b/exam/packet.tex @@ -143,7 +143,7 @@ Output: \end{comment} \newpage % ========================= Problem 6 ========================= -\problem{Problem 6(.7): Six Seven} +\problem{Problem 6(.7): Sequencing} \textit{Difficulty: Easy} \begin{itemize} You are given a string S composed of only the characters ‘6', ‘7’, ‘A', ‘B', and ‘\#' (without the quotation marks). This string is processed from left to right, and you must maintain a sequence of chracters that changes according to these rules: @@ -237,5 +237,59 @@ Input 3: Output 3: Sixxx sevennn \end{verbatim} + +% ========================= Problem 8 ========================= +\newpage +\problem{Problem 8: Staircase} +\textit{Difficulty: Medium} + +There is a staircase with N steps. Each step is labelled with a 6 or a 7. Simon starts at step 1 and wishes to reach the top step (Step N). If a step is labelled with a 6, Simon may go up 1 or 2 steps. If a step is labelled with a 7, Simon can move up exactly 1 step. Your job is to find the total number of distinct ways Simon can reach the top step N, given these rules. + +\inputformat +\begin{itemize} + \item The first line consists an integer N($1 \leq N \leq 10^5$), the number of steps + \item The second line will consist of N integers, the label of each step (either 6 or 7) +\end{itemize} + +\outputformat +\begin{itemize} + \item Output the number of distinct ways Simon can reach the top step N. Note that Simon starts at step 1. +\end{itemize} + +\examples +\begin{verbatim} +Input 1: +5 +66766 + +Output 1: +3 + +Explanation 1: +Case 1: Step 1->2->3->4->5 +Case 2: Step 1->2->4->5 +Case 3: Step 1->3->4->5 + +Input 2: +3 +677 + +Output 2: +2 + +Explanation 2: +Case 1: 1->2->3 +Case 2: 1->3 + +Input 3: +1 +6 + +Output 3: +1 + +Explanation 3: +There is only one way to get to the top (which Simon is already at). +\end{verbatim} \end{document}