Dynamic Programming Intro in Algorithm Design

Dynamic Programming Intro in Algorithm Design

• 1.
  Dynamic Programming Ahsan Raza
• 2.
  EXAMPLE(Fibonacci Sequence/Series) f(n) { if(n==0) return 0; if(n==1) return1; if(n>1) return (f(n-1)+f(n-2); } n : 1 2 3 4 5 6 7 8 9 1 0 f(n): 0 1 1 2 3 5 8 13 21 34 55 F(5) F(3) F(4) F(3) F(1) F(2) F(2) F(0) F(1) F(1) F(2) F(0) F(1) F(0) F(1)
• 3.
  • It's apowerful algorithm technique. • •Used for Optimization problems • Solve complex problems by breaking them into smaller subproblems. • Optimal substructure and overlapping subproblems. INTRODUCTION
• 4.
  Two Fundamental Principles • OptimalSubstructure • Overlapping Subproblems FUNDAMENTALS
• 5.
  Optimal Substructure meanswe can break a big problem into smaller subproblems, and if we solve those smaller subproblems optimally, we can combine their solutions to solve the big problem optimally. OPTIMAL SUBSTRUCTURE: EXAMPLE: JIGSAW PUZZLE
• 6.
  Overlapping Subproblems refersto the situation where the same smaller problems are encountered and solved multiple times when solving a larger problem.It's about reusing solutions to avoid redundant work. OVERLAPPING SUBPROBLEMS
• 7.
  Memoization(Top-Down) A lookup tableis maintained and checked before computation of any state.Recursion is involved. WAYS TO HANDLE OVERLAPPING SUBPROBLEMS Tabulation(Bottom-Up) Solution is built from base.It is an iterative process.
• 8.
  Dynamic programming, specificallymemoization or tabulation, helps here by storing the results of these subproblems the first time you solve them.When you need the same result again, you simply look it up, avoiding redundant calculations.This significantly improves efficiency, especially for larger problems.
• 9.
  • Space complexity •Complexity of identifying subproblems • Inability to handle problems without optimal substructure: LIMITATIONS LIMITATIONS
• 10.
  • Efficiency: Itcan improve the efficiency of algorithms by avoiding redundant computations. • Optimality: The algorithms are guaranteed to find optimal solutions to problems with optimal substructure. • Generality: Dynamic programming can be applied to a wide variety of problems. ADVANTAGES ADVANTAGES
• 11.
  Thank you.