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### Replies to This Discussion

1..For all primes p and all integers a, b, if p | ab, then p | a or p | b (or p divides both and b).

2...for any nonnegative integer a and any positive integer b, gcd(a, b) = gcd(b, a mod b).
3... BFS algo
4.. .Write down pseudo code of road trip problem.
5... Write down pseudo code of transition function?
6... . Use the Backtracking algorithm for the 0-1 Knapsack problem to maximize the

profit for the following problem instance. Show actions step by steps.

Maximum Capacity = 8
7.. Prove that in a graph there are even number of vertices of odd degree.
8.. . Write the pseudo code of Fast Fourier Transform (FFT) recursive algorithm

LCS algo
back tracking qustion
Clique NP complete
gcd ( a, b) = gcd (b,a mod a)
binary tree cnnot fully
naive string matcher algo
Bellman
a|o

Prove that a binary tree that is not full cannot correspond to an optimal prefix code.

1. pseudo code of longest common subsequence

2. prove that every connected graph has a spanning tree

3. Where greedy algo do not work

4. Prove that if a/b and b/a then a=+_b

5. Prove that CLIQUE is NP complete

6. Prove that gcd(a,b)= gcd(b, a mod b)

7. Prove that gcd(a,m) , where m>1 has a unique inverse a'(modoulo m) 8. 0-1 knapsack problem to calculate maximum profit when maximum capacity is 8

Binary tree which is not full,doesn't corresponds to prefix code.

8m +1 is the square form of an odd integer m

BFS path algo

Prim's algo

Finite State machine matcher

Huffman code algorithm

Clique is NPC prove.

if p ,prime number, divides n then p doesn't divide n+1

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