Algorithms & Data Structures — Assignment 1 (AITU)

Overview

Eleven standalone Java programs solving classic algorithmic problems using recursion. Each solution includes a documented Big-O analysis in the Javadoc. Written as a lab series for the Algorithms & Data Structures course at Astana IT University.

What it implements

• Recursive minimum (FirstProblem) — finds the minimum element in an array recursively; O(n).
• Recursive average (SecondProblem) — sums an array recursively then divides; O(n).
• Primality test (ThirdProblem) — trial division up to √n; O(√n).
• Factorial (Fourthproblem) — standard recursive factorial; O(n).
• Fibonacci (FifthProblem) — naive recursive Fibonacci; O(2ⁿ), complexity noted explicitly.
• Power (SixthProblem) — recursive exponentiation aⁿ; O(n).
• Reverse print (SeventhProblem) — reads N integers and prints them in reverse using the call stack; O(n).
• All-digits check (EigthProblem) — recursive character scan to verify a string is all digits; O(n).
• Binomial coefficient (NinethProblem) — Pascal's rule recursion C(n,k); O(2ⁿ).
• GCD (TenthProblem) — Euclidean algorithm via recursion; O(log min(a,b)).
• Palindrome check (Eleventh) — recursive two-pointer comparison; O(n).

Project structure

src/
├── Main.java                  # Entry point (reverse-print demo)
└── tasks/
    ├── FirstProblem.java      # Recursive minimum
    ├── SecondProblem.java     # Recursive average
    ├── ThirdProblem.java      # Primality test
    ├── Fourthproblem.java     # Factorial
    ├── FifthProblem.java      # Fibonacci
    ├── SixthProblem.java      # Power
    ├── SeventhProblem.java    # Reverse print
    ├── EigthProblem.java      # All-digits check
    ├── NinethProblem.java     # Binomial coefficient
    ├── TenthProblem.java      # GCD (Euclidean)
    └── Eleventh.java          # Palindrome check

How to run

Each task has its own main method. Compile and run any one individually:

# From the src/ directory
javac tasks/FifthProblem.java
java -cp . tasks.FifthProblem
# Enter n at the prompt, e.g. 10

Or compile everything at once:

javac -d out src/tasks/*.java src/Main.java
java -cp out tasks.TenthProblem

---

Adil Ormanov — GitHub