algorothm,
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The document introduces an algorithm design presentation by a group called Study 360°. It defines an algorithm and discusses criteria algorithms must satisfy like having clear instructions and terminating after a finite number of steps. It presents conventions for writing pseudocode and analyzes the time complexity of a Fibonacci algorithm using asymptotic notation like Big O(n), Omega(n), and Theta(n). Finally, it defines randomized algorithms as making random choices during runtime for potential benefits in speed, simplicity, or leading to deterministic algorithms.
![ASYMPTOTIC NOTATION
1. Big Oh (O)
2. Omega (Ω)
3. Theta (θ)
BIG OH [O]
Big Oh (O): Big Oh O(n) is called worst case of a
algorithm.
an + c = O(n)
If an + c ≤ (a+1)n for all n ≥ c
Example: 3n+2 = O(n)
if. 3n + c ≤ 4n for all n ≥ 2
n = 2 ; 8 ≤ 8
n = 3 ; 11 ≤ 12](https://image.slidesharecdn.com/e1379c7e-4a11-452f-ac69-1dfff2e481d2-170124143615/85/algorothm-10-320.jpg)
![OMEGA [Ω]
Omega (Ω) is called best case of an
algorithm
an + c = Ω (n)
Iff an + c ≥ an for all n ≥1
Example : 3n + 2 = Ω (n)
Iff 3n + 2 ≥ 3n for all n ≥ 1
THETA [Θ]
Theta (θ) is called precise case /
average case of an algorithm
an + c = θ(n)
1. Iff an + c ≥ an for all n ≥ c](https://image.slidesharecdn.com/e1379c7e-4a11-452f-ac69-1dfff2e481d2-170124143615/85/algorothm-11-320.jpg)
algorothm,
- 2. Welcome ToThe Presentation of Algorithm Design
- 3. Group Name: Study 360° Group Members Sohan Ahmed ID:1589 Md Sallahuddin ID:1587 SM Tashdeed ID:1575 Ahsanul Adeeb ID:1562
- 4. Content •Definition of algorithm •Criteria to Satisfy •Convention for writing Pseudocode •Performance analysis of algorithm •Asymptotic Notation 1. Big Oh (O) 2. Omega (Ω) 3. Theta (θ) •Randomized Algorothm
- 5. Definition of algorithm An Algorithm is composed of a finite set of step each of which may require one or more operations. It is a finite set of instructions that if followed, accomplished a particular task
- 6. Criteria to Satisfy •Input : Zero or more quantity are externally supplied. •Output : At least one quantity is produced. •Definiteness : Each Instructions is clear an unambiguous •Finiteness : If we trace out the instructions of an algorithm, then for all cases, the algorithm terminate often a finite number of steps. •Effectiveness :Every instruction must be very basic so that it can be carried out in principle by a person
- 7. Conventions for Pseudocode 1.Comments begin with // and contain until the end of line Ex ://………….Sohan is boss…..// 2:Blocks are indicated with matching braces {and} 3:An Identifier begins with a letter, compound data types can be formed with record here is example Node=record { Datatype_1 data_1 : Datatype_2 datatype_2 node * link; }
- 8. Performance analysis of algorithm >> Algorithm Fibonacci (A,n) { F: = 0; S: = 1; for i = 0 to n do { T = F + S; F: = S; S: = T; } write (F); }
- 9. TiTtle Sequence Frequency Total steps Algorithm Fibonacci (A,n) 0 0 0 { 0 1 1 F: = 0 ; 1 1 0 S: = 1 ; 1 1 1 for i = 0 to n do 1 n+1 n+1 { 0 1 0 T = F + S; 1 n n F: = S; 1 n n S: = T; 1 n n } 0 1 0 write (F); 1 1 1 } 0 1 0 TIME COMPLEXITY OF FIBONACCI Total = 4n+4 Time Complexity
- 10. ASYMPTOTIC NOTATION 1. Big Oh (O) 2. Omega (Ω) 3. Theta (θ) BIG OH [O] Big Oh (O): Big Oh O(n) is called worst case of a algorithm. an + c = O(n) If an + c ≤ (a+1)n for all n ≥ c Example: 3n+2 = O(n) if. 3n + c ≤ 4n for all n ≥ 2 n = 2 ; 8 ≤ 8 n = 3 ; 11 ≤ 12
- 11. OMEGA [Ω] Omega (Ω) is called best case of an algorithm an + c = Ω (n) Iff an + c ≥ an for all n ≥1 Example : 3n + 2 = Ω (n) Iff 3n + 2 ≥ 3n for all n ≥ 1 THETA [Θ] Theta (θ) is called precise case / average case of an algorithm an + c = θ(n) 1. Iff an + c ≥ an for all n ≥ c
- 12. Randomized Algorithm Randomized algorithms: make random choices during run. Main benefits: ➢Speed: may be faster than any deterministic. ➢Even if not faster, often simpler ( quicksort) ➢Sometimes, randomized idea leads to deterministic algorithm