Iterative Algorithms

Bubble sort is the simplest sorting algorithm that works by repeatedly swapping adjacent elements if they are in the wrong order. A list with n elements requires n-1 passes for sorting. In each pass, element a[i] is compared with a[i+1] and swapped if they ...

Insertion Sort works by picking each element and inserting it into its correct position among the already-sorted elements to its left. Steps: 1. Start with the array A of n elements. 2. Pick the element at position i (starting from i = 1). 3. Store it in a ...

Idea: Repeatedly compare adjacent elements and swap them if they are in the wrong order. After each pass, the largest unsorted element "bubbles up" to its correct position. 1. Start from the beginning of the array. 2. Compare adjacent elements A[j] and A[j+...

Selection Sort is a simple comparison-based sorting algorithm that works by repeatedly selecting the minimum element from the unsorted portion of the array and placing it at the correct position. --- 1. Start. 2. Let array A have n elements (index 0 to n-1)...

--- Sequential search (also called linear search) compares the search element with each element in the list one by one from the beginning. Case Condition Complexity ----------------------------- Best Case Element found at the first position O(1) Average Cas...

The Fibonacci sequence is defined as: - F(0) = 0 - F(1) = 1 - F(n) = F(n-1) + F(n-2) for n = 2 --- --- Iteration temp = first + second first second i --------------------------------------------------- Initial - 0 1 2 1 0 + 1 = 1 1 1 3 2 1 + 1 = 2 1 2 4 3 1...

The GCD (Greatest Common Divisor) of two numbers is found using the iterative Euclidean algorithm based on the property that GCD(m, n) = GCD(n, m mod n). Steps: Pseudocode: --- Find GCD(48, 18): Step m n r = m mod n --------------------------- 1 48 18 48 mo...