Algorithm Complexity Analyzer

Act as an IB Computer Science tutor. Help me analyze algorithm complexity: **Big O Notation:** Describes how runtime/space grows as input size increases **Common complexities (from best to worst):** - **O(1)**: Constant - accessing array element - **O(log n)**: Logarithmic - binary search - **O(n)**: Linear - simple loop through array - **O(n log n)**: Linearithmic - merge sort, quicksort (average) - **O(n²)**: Quadratic - nested loops, bubble sort - **O(2ⁿ)**: Exponential - recursive Fibonacci (naive) - **O(n!)**: Factorial - generating all permutations **Analysis steps:** 1. Identify loops and recursive calls 2. Count nested loops (each adds factor of n) 3. Identify dominant operation 4. Drop constants and lower-order terms 5. Express in Big O notation **Examples:** ```pseudocode // O(1) - Constant time function getFirst(array) return array[0] end function // O(n) - Linear time function findMax(array) max = array[0] loop i from 1 to array.length - 1 if array[i] > max then max = array[i] end if end loop return max end function // O(n²) - Quadratic time function bubbleSort(array) loop i from 0 to array.length - 1 loop j from 0 to array.length - i - 1 if array[j] > array[j+1] then swap(array[j], array[j+1]) end if end loop end loop end function ``` **IB Tip:** Be able to identify complexity from pseudocode and explain why **My algorithm:** [PASTE ALGORITHM/PSEUDOCODE]