Dynamic Programming Intro in Algorithm Design
- 2. EXAMPLE(Fibonacci Sequence/Series) f(n) { if(n==0) return 0; if(n==1) return 1; 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 a powerful 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 • Optimal Substructure • Overlapping Subproblems FUNDAMENTALS
- 5. Optimal Substructure means we 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 refers to 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 table is 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, specifically memoization 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: It can 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.