Divide and Conquer

An algorithm design paradigm that breaks a problem into smaller sub-problems, solves them independently, and combines their solutions to solve the original problem.

Definition

A strategy that divides a problem into smaller sub-problems, solves each sub-problem independently, and combines their solutions to solve the original problem.

Steps

  1. Divide: Split the problem into smaller sub-problems.
  2. Conquer: Solve each sub-problem recursively.
  3. Combine: Merge the solutions of the sub-problems.

Examples

  • Merge Sort: Divides the array into halves, sorts them, and merges.
  • Quick Sort: Divides the array using a pivot and recursively sorts partitions.
  • Binary Search: Divides the search space in half at each step.

Advantages

  • Simplifies complex problems.
  • Efficient for large datasets.