Time and Space Complexity of Algorithms

The time it takes to solve the Josephus problem is directly proportional to the number of people (n).

The Manacher's algorithm takes linear time, O(n), to find the longest palindromic substring in a string of length n.

Manacher's algorithm uses space proportional to the input string length (n).

The maneuvering algorithm has a time complexity of O(n) for calculating the number of paths in a matrix.

Maze solving algorithms using brute-force have an exponential time complexity (2^(n*n)) in the worst-case scenario, with n being the maze size.

A recursive function that explores a matrix, starting from a given position, marking valid paths as 1 and checking if a destination is reached.

In recursive matrix exploration, the function explores the next positions by calling itself with (i+1, j) and (i, j+1) to check valid paths.

When a path doesn't lead to the destination in recursive matrix exploration, the function unmarks the positions to explore other paths.

In recursive matrix exploration, 'valid paths' are those that conform to the rules of the problem and are marked as 1 in the matrix.

The recursive function checks if the destination position (i, j) is reached during the exploration of the matrix.

A time complexity where the runtime grows proportionally to the square of the input size (n). This means if the input doubles, the runtime quadruples.

This denotes an algorithm with an exponential time complexity. The runtime grows incredibly fast as the input size increases, making it impractical for large inputs.

Linear time complexity. The runtime increases proportionally to the input size (n). Doubling the input doubles the runtime.

Logarithmic time complexity. The runtime grows very slowly as the input size increases. Doubling the input only slightly increases the runtime.

Constant time complexity. The runtime remains the same regardless of the input size.

A measure of how long an algorithm takes to run as a function of the input size.

A measure of how much memory an algorithm uses as a function of the input size.

An arrangement of elements from a set, where the elements are ordered in a specific way.

A simple sorting algorithm that repeatedly selects the minimum element from the unsorted subarray and puts it at the beginning of the sorted subarray.

A highly efficient sorting algorithm that uses a divide-and-conquer strategy to recursively partition the array around a pivot element.

A bitwise operation that swaps the lower and upper nibbles (groups of 4 bits) of a byte.

An operation that swaps two blocks of data within an array or memory.

An efficient algorithm for finding the greatest common divisor (GCD) of two integers.

A divide-and-conquer algorithm for multiplying two integers that is faster than the traditional algorithm for large numbers.