Difference between Divide and Conquer Algo and Dynamic Programming

Question

What is the difference between Divide and Conquer Algorithms and Dynamic Programming Algorithms? How are the two terms different? I do not understand the difference between

Answer 1

Divide and Conquer involves three steps at each level of recursion:

1. Divide the problem into subproblems.
2. Conquer the subproblems by solving them recursively.
3. Combine the solution for subproblems into the solution for original problem.
   
   • It is a top-down approach.
     
   • It does more work on subproblems and hence has more time consumption.
   • eg. n-th term of Fibonacci series can be computed in O(2^n) time complexity.
     
     

Dynamic Programming involves the following four steps:

1. Characterise the structure of optimal solutions.
2. Recursively define the values of optimal solutions.
3. Compute the value of optimal solutions.
4. Construct an Optimal Solution from computed information.

• It is a Bottom-up approach.
• Less time consumption than divide and conquer since we make use of the values computed earlier, rather than computing again.
• eg. n-th term of Fibonacci series can be computed in O(n) time complexity.
  
  

For easier understanding, lets see divide and conquer as a brute force solution and its optimisation as dynamic programming.

N.B. divide and conquer algorithms with overlapping subproblems can only be optimised with dp.