Algorithm Complexity Analyzer

Big O notation is a mathematical representation used in computer science to describe the performance characteristics of algorithms. It expresses how the runtime or space requirements of an algorithm grow as the input size increases, providing a standardized way to compare algorithm efficiency and predict scalability.

The "O" in Big O stands for "order of" and represents the worst-case scenario of an algorithm's complexity. When we say an algorithm has O(n) time complexity, we mean that in the worst case, the execution time grows linearly with the input size. This notation helps developers make informed decisions about which algorithms to use based on expected data sizes and performance requirements.

function findDuplicates(arr) {
  const duplicates = [];
  for (let i = 0; i < arr.length; i++) {
    for (let j = i + 1; j < arr.length; j++) {
      if (arr[i] === arr[j]) {
        duplicates.push(arr[i]);
      }
    }
  }
  return duplicates;
}
// Time Complexity: O(n²)
// Space Complexity: O(n)

function findDuplicates(arr) {
  const seen = new Set();
  const duplicates = [];
  for (const item of arr) {
    if (seen.has(item)) {
      duplicates.push(item);
    }
    seen.add(item);
  }
  return duplicates;
}
// Time Complexity: O(n)
// Space Complexity: O(n)

Common Time Complexities

• •O(1) Constant: Instant execution regardless of input size (array access, hash table lookup)
• •O(log n) Logarithmic: Execution time grows slowly (binary search, balanced tree operations)
• •O(n) Linear: Execution time grows proportionally with input (single loop, array traversal)
• •O(n log n) Linearithmic: Common in efficient sorting algorithms (merge sort, quick sort average case)
• •O(n²) Quadratic: Execution time grows with square of input (nested loops, bubble sort)
• •O(2ⁿ) Exponential: Execution time doubles with each additional input (recursive Fibonacci without memoization)
• •O(n!) Factorial: Execution time grows factorially (generating all permutations)

Understanding Big O notation is essential for writing efficient code, especially when dealing with large datasets. An algorithm that works fine with 100 items might become unusable with 1 million items if it has poor time complexity. Our algorithm complexity analyzer helps you identify these potential bottlenecks before they become production issues.

In coding interviews at companies like Google, Amazon, and Facebook, candidates are expected to analyze and optimize algorithm complexity. Being able to identify O(n²) patterns and suggest O(n) alternatives demonstrates strong problem-solving skills and algorithmic thinking that employers value.