Divide and Conquer-

The "Divide and Conquer" strategy is a fundamental algorithmic technique used to solve complex problems by breaking them down into smaller, more manageable subproblems. It is a widely used approach in computer science and mathematics for designing algorithms to solve a wide range of problems efficiently. The key idea is to divide a problem into smaller instances, solve those instances independently, and then combine their solutions to solve the original problem. Here's a detailed explanation of the Divide and Conquer strategy:

1. Divide:
   • The first step is to break the problem into smaller, more manageable subproblems. These subproblems should ideally be of the same type as the original problem but smaller in size.
   • The process of dividing continues recursively until the subproblems become simple enough to be solved directly. In other words, the problem is divided until it reaches a base case.
2. Conquer:
   • The second step involves solving the subproblems. Each subproblem is solved individually, either directly if it's simple enough (base case), or by applying the same Divide and Conquer strategy recursively.
3. Combine:
   • The final step is to combine the solutions of the subproblems to obtain the solution to the original problem.
   • In some cases, combining the subproblem solutions may involve merging, summing, or other operations that aggregate the results into a single coherent solution.

Characteristic-

The Divide and Conquer strategy is particularly useful for problems that exhibit the following characteristics:

• Overlapping Subproblems: The problem can be broken down into subproblems that are reused or computed multiple times. In such cases, the technique of memoization (storing and reusing intermediate results) can be applied to avoid redundant work.
• Optimal Substructure: The solution to the original problem can be constructed from the solutions of its subproblems. This means that solving subproblems independently will ultimately lead to the correct solution for the original problem.

Advantages of Divide and Conquer

• Divide and Conquer tend to successfully solve one of the biggest problems, such as the Tower of Hanoi, a mathematical puzzle. It is challenging to solve complicated problems for which you have no basic idea, but with the help of the divide and conquer approach, it has lessened the effort as it works on dividing the main problem into two halves and then solve them recursively. This algorithm is much faster than other algorithms.
• It efficiently uses cache memory without occupying much space because it solves simple subproblems within the cache memory instead of accessing the slower main memory.
• It is more proficient than that of its counterpart Brute Force technique.
• Since these algorithms inhibit parallelism, it does not involve any modification and is handled by systems incorporating parallel processing.

Disadvantages of Divide and Conquer

• Since most of its algorithms are designed by incorporating recursion, so it necessitates high memory management.
• An explicit stack may overuse the space.
• It may even crash the system if the recursion is performed rigorously greater than the stack present in the CPU.

Fundamental of Divide & Conquer Strategy: