240 lines
6.1 KiB
TeX
240 lines
6.1 KiB
TeX
\documentclass[12pt,a4paper]{article}
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\usepackage[utf8]{inputenc}
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\usepackage{amsmath, amssymb}
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\usepackage{geometry}
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\usepackage{fancyhdr}
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\usepackage{listings}
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\usepackage{xcolor}
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\usepackage{enumitem}
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\usepackage{comment}
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% Page layout
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\geometry{margin=1in}
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\pagestyle{fancy}
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\fancyhf{}
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\fancyhead[L]{Programming Competition Test}
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\fancyhead[R]{\today}
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\fancyfoot[C]{\thepage}
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% Listings style for code
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\lstset{
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language=Java,
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basicstyle=\ttfamily\small,
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keywordstyle=\color{blue},
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commentstyle=\color{green!60!black},
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stringstyle=\color{red},
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numbers=left,
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numberstyle=\tiny,
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stepnumber=1,
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numbersep=5pt,
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showstringspaces=false,
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breaklines=true,
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frame=single,
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rulecolor=\color{black!30},
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backgroundcolor=\color{black!2}
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}
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% Custom commands
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\newcommand{\problem}[1]{\section*{#1}}
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\newcommand{\inputformat}{\textbf{Input format:}}
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\newcommand{\outputformat}{\textbf{Output format:}}
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\newcommand{\examples}{\textbf{Example(s):}}
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\begin{document}
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\begin{center}
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{\LARGE \textbf{Programming Competition Test}}\\[2mm]
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{\large Duration: 2 hours \quad Total Marks: 100}
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\end{center}
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\section*{Instructions}
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\begin{enumerate}[label=\arabic*.]
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\item This test contains algorithmic problems similar to those found on LeetCode or HackerRank.
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\item Use efficient algorithms to avoid timeouts; naive solutions may not receive full marks.
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\item Submit solutions in C++, Python, or Java.
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\item For each problem, write a function or program according to the specified input/output format.
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\item Clearly comment your code if necessary.
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\end{enumerate}
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\begin{comment}
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% ========================= Problem 1 =========================
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\problem{Problem 1: Two Sum}
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\textit{Difficulty: Easy}
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Given an array of integers \texttt{nums} and an integer \texttt{target}, return indices of the two numbers such that they add up to \texttt{target}. Assume exactly one solution exists.
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\inputformat
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\begin{itemize}
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\item First line contains an integer $n$ ($2 \leq n \leq 10^5$), the size of the array.
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\item Second line contains $n$ integers, the elements of the array.
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\item Third line contains the integer \texttt{target}.
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\end{itemize}
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\outputformat
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\begin{itemize}
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\item Print two integers, the indices of the elements adding up to \texttt{target}.
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\end{itemize}
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\examples
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\begin{verbatim}
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Input:
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4
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2 7 11 15
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9
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Output:
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0 1
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\end{verbatim}
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% ========================= Problem 2 =========================
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\problem{Problem 2: Longest Substring Without Repeating Characters}
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\textit{Difficulty: Medium}
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Given a string \texttt{s}, find the length of the longest substring without repeating characters.
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\inputformat
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\begin{itemize}
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\item A single line containing the string \texttt{s} ($1 \leq |s| \leq 10^5$).
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\end{itemize}
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\outputformat
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\begin{itemize}
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\item A single integer, the length of the longest substring without repeated characters.
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\end{itemize}
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\examples
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\begin{verbatim}
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Input:
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abcabcbb
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Output:
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3
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\end{verbatim}
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% ========================= Problem 3 =========================
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\problem{Problem 3: Merge Intervals}
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\textit{Difficulty: Hard}
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Given a collection of intervals, merge all overlapping intervals.
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\inputformat
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\begin{itemize}
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\item First line contains an integer $n$ ($1 \leq n \leq 10^4$), the number of intervals.
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\item Next $n$ lines contain two integers each, representing the start and end of each interval.
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\end{itemize}
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\outputformat
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\begin{itemize}
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\item Print the merged intervals in ascending order of start times.
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\end{itemize}
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\examples
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\begin{verbatim}
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Input:
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4
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1 3
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2 6
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8 10
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15 18
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Output:
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1 6
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8 10
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15 18
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\end{verbatim}
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\end{comment}
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% ========================= Problem 6 =========================
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\problem{Problem 6(.7): Six Seven}
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\textit{Difficulty: Easy}
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\begin{itemize}
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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:
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\item 6 - add a 6 to the end of the sequence
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\item 7 - if the sequence is non-empty and its last chracter is ‘6', remove that last ‘6', otherwise, add ‘7' to the end of the sequence
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\item A - reverse the sequence
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\item B - add a duplicate of the current sequence to the end of it
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\item \# - clear the sequence
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\end{itemize}
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\inputformat
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\begin{itemize}
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\item The first line consists of the string S. The string consists only of the characters 6, 7, A, B, and \#.
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\end{itemize}
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\outputformat
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\begin{itemize}
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\item Output a single line containig the final form of the sequence. If the sequence is empty at the end, output “EMPTY” (without the quotations).
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\end{itemize}
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\examples
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\begin{verbatim}
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Input 1:
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67A6
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Output 1:
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6
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Input 2:
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66B7
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Output 2:
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666
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Input 3:
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7A7#
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Output 3:
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EMPTY
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\end{verbatim}
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% ========================= Problem 7 =========================
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\problem{Problem 7: Limited Jumps}
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\textit{Difficulty: Medium}
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You are given a grid of size N x M, where each cell contains either 6 or 7. You start at the top-left corner (1,1) and want to reach the bottom-right corner (N,M). You can move right, down, or jump diagonally (right+down). The maze has these rules:
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\begin{itemize}
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\item You can step on a 6 any number of times
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\item You can step on a 7 at most once in your path
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\item You can make at most one diagonal move in your path
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\end{itemize}
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Your task is to determine if there exists any valid path from (1,1) to (N,M) obeying the rules.
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\inputformat
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\begin{itemize}
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\item The first line consists 2 integers N and M ($1 \leq N, M \leq 10^9$), the number of rows and columns, respectively
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\item The next N lines will consist of strings of length M, containing 6 or 7
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\end{itemize}
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\outputformat
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\begin{itemize}
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\item Output a single line. If there exists a valid path, print ``Sixxx sevennn" (without the quotations). If there does not exist a valid path, print ``Six was afraid of seven after all" (without the quotations).
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\end{itemize}
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\examples
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\begin{verbatim}
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Input 1:
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2 2
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66
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67
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Output 1:
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Sixxx sevennn
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Input 2:
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2 2
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77
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77
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Output 2:
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Six was afraid of seven after all
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Input 3:
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3 3
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666
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676
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666
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Output 3:
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Sixxx sevennn
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\end{verbatim}
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\end{document}
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