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
  • They broke into non-overlapping sub-problems
  • Example: factorial numbers i.e. fact(n) = n*fact(n-1)

fact(5) = 5* fact(4) = 5 * (4 * fact(3))= 5 * 4 * (3 *fact(2))= 5 * 4 * 3 * 2 * (fact(1))

As we can see above, no fact(x) is repeated so factorial has non overlapping problems.

• Dynamic Programming
  • They Broke into overlapping sub-problems
  • Example: Fibonacci numbers i.e. fib(n) = fib(n-1) + fib(n-2)

fib(5) = fib(4) + fib(3) = (fib(3)+fib(2)) + (fib(2)+fib(1))

As we can see above, fib(4) and fib(3) both use fib(2). similarly so many fib(x) gets repeated. that's why Fibonacci has overlapping sub-problems.

• As a result of the repetition of sub-problem in DP, we can keep such results in a table and save computation effort. this is called as memoization