Divide and Conquer is an algorithmic paradigm in which the problem is solved using the Divide, Conquer, and Combine strategy.
A typical divide-and-conquer algorithm solves a problem using the following three steps:
- Divide: This involves dividing the problem into smaller sub-problems.
- Conquer: Solve sub-problems by calling recursively until solved.
- Combine: Combine the sub-problems to get the final solution of the whole problem.
Below image illustrate the working of divide and conquer algorithm used in Merge Sort:
Illustration of Merge Sort
Advantages of Divide and Conquer:
- Efficiency: Divide and conquer algorithms typically have a time complexity of O(n log n), which is more efficient than many other algorithms for large datasets.
- Simplicity: Divide and conquer algorithms are often easy to understand and implement.
- Parallelizability: Divide and conquer algorithms can be easily parallelized, as each subproblem can be solved independently.
- Cache-friendliness: Divide and conquer algorithms tend to have good cache performance, as they access data in a predictable pattern.
Disadvantages of Divide and Conquer:
- Recursion overhead: Divide and conquer algorithms use recursion, which can lead to significant overhead in terms of stack space and function calls.
- Not suitable for all problems: Divide and conquer algorithms are not suitable for all types of problems. They are most effective for problems that can be recursively divided into smaller subproblems.
- Limited memory efficiency: Divide and conquer algorithms can require a significant amount of memory, as they create multiple copies of the input data.
- Difficult to analyze: The time and space complexity of divide and conquer algorithms can be difficult to analyze, especially for complex problems.