devguywilly / data-structure-and-algorithms

Algorithmic Complexity and Common Operations

1. Representing Complexity

Asymptotic Notation

When analyzing algorithms, understanding asymptotic notations is crucial for describing their time and space complexity.

1.1 Big-O Notation (Worst Case Complexity)

Time Complexity

• Constant: O(1)
• Linear: O(n)
• Quadratic: O(n^2)
• Cubic: O(n^3)
• Logarithmic: O(log n)

Space Complexity

1.2 Omega Notation (Best Case Complexity)

1.3 Theta Notation (Average Case Complexity)

2. Objects and Array Operations

Understanding common operations on objects and arrays is crucial for efficient algorithm design.

• Insert / Remove at End
• Insert / Remove at Beginning
• Access
• Search
• Push / Pop
• Shift / Unshift / Concat / Slice / Splice
• forEach / map / filter / reduce

3. Mathematics Algorithms

1. Fibonacci Sequence

   • Explanation: Series of numbers where each number is the sum of the two preceding ones.
   • Code Example: (JavaScript)

     function fibonacci(n) {
         if (n <= 1) return n;
         return fibonacci(n - 1) + fibonacci(n - 2);
     }

2. Factorial of a Number

   • Explanation: Product of all positive integers up to a given number.
   • Code Example: (JavaScript)

     function factorial(n) {
         return n === 0 ? 1 : n * factorial(n - 1);
     }

3. Prime Number

   • Explanation: A number greater than 1 not divisible by any other numbers except 1 and itself.
   • Code Example: (JavaScript)

     function isPrime(n) {
         // Implementation
     }

4. Power of Two

   • Explanation: Numbers that can be expressed as 2^n.
   • Code Example: (JavaScript)

     function isPowerOfTwo(n) {
         // Implementation
     }

5. Recursion

   • Explanation: A programming technique where a function calls itself.
   • Code Example: (JavaScript)

     function recursiveFunction() {
         // Implementation
         recursiveFunction(); // Call itself
     }

6. Fibonacci Sequence with Recursion

   • Explanation: Calculating Fibonacci sequence using recursion.
   • Code Example: (JavaScript)

     function fibonacciRecursive(n) {
         // Implementation
     }

7. Factorial of a Number with Recursion

   • Explanation: Calculating factorial using recursion.
   • Code Example: (JavaScript)

     function factorialRecursive(n) {
         // Implementation
     }