![TABULATION
Function Of fibonacci series:
int fib(int n){
if (n<=1) {
return n;
F[0]=0;F[1]=1;
}
for(int i=2; i<=n; i++){
F[i] = F[i-2]+F[i-1];
}
return F[n];
}
0 1 1 2 3
F0 F1 F2 F3 F4
F =
Time Complexity= O(n)
Global Array
Bottom-up
approach
F1 F0
F2](https://image.slidesharecdn.com/dynamicprogramming-240909083819-dc0f77bd/85/DYNAMIC_________________________PROGRAMMING-pptx-9-320.jpg)
DYNAMIC_________________________PROGRAMMING.pptx
- 1. DYNAMIC PROGRAMMING •Presented By Group : 4 •Group Members : •Md.Nazmus Shakib -220320852 •Tanvin Sadik Dhrubo -220320860 •Khan Waziur Rahman -220320861 •Arghya Saha -200120456
- 2. INTRODUCTION TO DYNAMIC PROGRAMMING • Dynamic Programming is a method for solving complex problems by breaking them down into simpler sub problems. It is applicable where the problem can be divided into overlapping subproblems and has optimal substructure. It is also known as divide and conquer technique
- 3. Why We Choose Dynamic Programming Over Greedy Method? Dynamic programming (DP) is often preferred over the greedy method for solving optimization problems where future decisions are affected by earlier ones. In greedy algorithms, the approach is to make the locally optimal choice at each stage in hopes of finding the global optimum. However, this doesn't always lead to the best solution for all problems, as greedy methods may miss key subproblems or fail to consider how earlier decisions affect the later ones.
- 4. DYNAMIC PROGRAMMING APPROACHES Top Down(Memoization): Starts By Solving Main Problems & Breaks It down Into Smaller Parts Saves The Answers To These Smaller Parts In A Table To Avoid Doing The Same Work Twice Works Well When There Are Smaller Parts
- 5. DYNAMIC PROGRAMMING APPROACHES Bottom-Up(Tabulation): Begins by solving the smallest parts of the problem first Uses these small solutions to build up the final answer step by step Works well when there are fewer smaller parts,& the final answer can be easily found by using these smaller solutions
- 6. MEMOIZATION VS TABULATION Memoization:Top- down approach. Uses recursion. Stores results of subproblems as they are solved Tabulation:Bottom- up approach. Iterative solution. Builds solutions to all subproblems and uses them
- 7. MEMOIZATION F4 F2 F1 F0 F1 F1 F0 F2 F3 0 1 1 2 3 F0 F1 F2 F3 F4 F = Time Complexity= O(n) Fn F(n-2) F(n-1) Global Array
- 8. MEMOIZATION The Fibonacci sequence is defined as: F(n)=F(n−1)+F(n−2) with base cases: F(0)=0, F(1)=1 Function Of fibonacci series : int fib(int n){ if (n<=1) { return n; } else { return fib(n-2) + fib(n- 1); } Top-down approach
- 9. TABULATION Function Of fibonacci series: int fib(int n){ if (n<=1) { return n; F[0]=0;F[1]=1; } for(int i=2; i<=n; i++){ F[i] = F[i-2]+F[i-1]; } return F[n]; } 0 1 1 2 3 F0 F1 F2 F3 F4 F = Time Complexity= O(n) Global Array Bottom-up approach F1 F0 F2
- 10. KEY CONCEPTS OF DYNAMIC PROGRAMMING Optimal Substructure: The optimal solution to the problem can be constructed from the optimal solutions of its subproblems. Overlapping Subproblems: Subproblems are reused multiple times.
- 11. STEPS TO APPLY DYNAMIC PROGRAMMING Define Define the subproblems. Identify Identify the recursive relation. Choose Choose between memoization or tabulation. Solve Solve the base cases. Build Build the solution from subproblem results.
- 12. ADVANTAGES OF DYNAMIC PROGRAMMING EFFICIENT FOR SOLVING OPTIMIZATION PROBLEMS. REDUCES TIME COMPLEXITY BY STORING INTERMEDIATE RESULTS. HELPS AVOID REDUNDANT CALCULATIONS.
- 13. DISADVANTAGES May require a lot of memory. Requires identifying overlapping subproblems and optimal substructure, which may not be straightforward
- 14. THANK YOU!