A method of solving a problem where the solution depends on solutions to smaller instances of the same problem. A function calls itself with a smaller version of the original problem.

A condition in a recursive method that terminates the recursive calls and provides a direct solution.

When a function calls itself with a modified version of the original problem, usually after checking the base case.

A search algorithm that finds the position of a target value within a sorted array by repeatedly dividing the search interval in half.

An efficient, general-purpose, comparison-based sorting algorithm that divides an array into two halves, sorts each half, and then merges the sorted halves back together.

1. Identify the base case(s). 2. Define the recursive call to solve a smaller subproblem. 3. Ensure the recursive call moves towards the base case.

1. Find the middle element. 2. Compare the target to the middle element. 3. If target equals middle, return index. 4. If target is less than middle, search the left half. 5. If target is greater than middle, search the right half. 6. Repeat until found or search space is empty.

1. Divide the array into two halves. 2. Recursively sort the two halves. 3. Merge the sorted halves.

In algorithms like tree traversal, graph searching, and in compilers for parsing code.

Searching for a word in a dictionary, finding a contact in a sorted list, or locating data in a sorted database index.

Used in external sorting (sorting large datasets that don't fit in memory), and as a building block in other algorithms.