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exam/packet.tex

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+\documentclass[12pt,a4paper]{article}
+\usepackage[utf8]{inputenc}
+\usepackage{amsmath, amssymb}
+\usepackage{geometry}
+\usepackage{fancyhdr}
+\usepackage{listings}
+\usepackage{xcolor}
+\usepackage{enumitem}
+
+% Page layout
+\geometry{margin=1in}
+\pagestyle{fancy}
+\fancyhf{}
+\fancyhead[L]{Programming Competition Test}
+\fancyhead[R]{\today}
+\fancyfoot[C]{\thepage}
+
+% Listings style for code
+\lstset{
+    language=Java,
+    basicstyle=\ttfamily\small,
+    keywordstyle=\color{blue},
+    commentstyle=\color{green!60!black},
+    stringstyle=\color{red},
+    numbers=left,
+    numberstyle=\tiny,
+    stepnumber=1,
+    numbersep=5pt,
+    showstringspaces=false,
+    breaklines=true,
+    frame=single,
+    rulecolor=\color{black!30},
+    backgroundcolor=\color{black!2}
+}
+
+% Custom commands
+\newcommand{\problem}[1]{\section*{#1}}
+\newcommand{\inputformat}{\textbf{Input format:}}
+\newcommand{\outputformat}{\textbf{Output format:}}
+\newcommand{\examples}{\textbf{Example(s):}}
+
+\begin{document}
+
+\begin{center}
+    {\LARGE \textbf{Programming Competition Test}}\\[2mm]
+    {\large Duration: 2 hours \quad Total Marks: 100}
+\end{center}
+
+\section*{Instructions}
+\begin{enumerate}[label=\arabic*.]
+    \item This test contains algorithmic problems similar to those found on LeetCode or HackerRank.
+    \item Use efficient algorithms to avoid timeouts; naive solutions may not receive full marks.
+    \item Submit solutions in C++, Python, or Java.
+    \item For each problem, write a function or program according to the specified input/output format.
+    \item Clearly comment your code if necessary.
+\end{enumerate}
+
+% ========================= Problem 1 =========================
+\problem{Problem 1: Two Sum}
+\textit{Difficulty: Easy}
+
+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.
+
+\inputformat
+\begin{itemize}
+    \item First line contains an integer $n$ ($2 \leq n \leq 10^5$), the size of the array.
+    \item Second line contains $n$ integers, the elements of the array.
+    \item Third line contains the integer \texttt{target}.
+\end{itemize}
+
+\outputformat
+\begin{itemize}
+    \item Print two integers, the indices of the elements adding up to \texttt{target}.
+\end{itemize}
+
+\examples
+\begin{verbatim}
+Input:
+4
+2 7 11 15
+9
+
+Output:
+0 1
+\end{verbatim}
+
+% ========================= Problem 2 =========================
+\problem{Problem 2: Longest Substring Without Repeating Characters}
+\textit{Difficulty: Medium}
+
+Given a string \texttt{s}, find the length of the longest substring without repeating characters.
+
+\inputformat
+\begin{itemize}
+    \item A single line containing the string \texttt{s} ($1 \leq |s| \leq 10^5$).
+\end{itemize}
+
+\outputformat
+\begin{itemize}
+    \item A single integer, the length of the longest substring without repeated characters.
+\end{itemize}
+
+\examples
+\begin{verbatim}
+Input:
+abcabcbb
+
+Output:
+3
+\end{verbatim}
+
+% ========================= Problem 3 =========================
+\problem{Problem 3: Merge Intervals}
+\textit{Difficulty: Hard}
+
+Given a collection of intervals, merge all overlapping intervals.
+
+\inputformat
+\begin{itemize}
+    \item First line contains an integer $n$ ($1 \leq n \leq 10^4$), the number of intervals.
+    \item Next $n$ lines contain two integers each, representing the start and end of each interval.
+\end{itemize}
+
+\outputformat
+\begin{itemize}
+    \item Print the merged intervals in ascending order of start times.
+\end{itemize}
+
+\examples
+\begin{verbatim}
+Input:
+4
+1 3
+2 6
+8 10
+15 18
+
+Output:
+1 6
+8 10
+15 18
+\end{verbatim}
+
+\end{document}
+