Algorithm

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2. Dr. Omprakash Chandrakar
Associate Professor (Computer Science)

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1. ALGORITHM
2. FLOWCHART
3. PSEUDOCODE
4. PROGRAM
F i r s t t h i n g f i r s t

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C h a r a c t e r i s t i c s o f A l g o r i t h m
INPUT, OUTPUT, DEFINITE, FINITE, CORRECT

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A l g o r i t h m A n d D a t a S t r u c t u r e s
DEPENDS ON
INPUT DATA,
ACCURACY,
ENVIRONMENT,
PROBLEM DOMAIN

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T h e R o l e o f A l g o r i t h m i n C o m p u t i n g
An algorithm is thus a sequence of computational steps
that transform the input into the output.
An Instance of a problem consists of the input needed to
compute a solution to the problem.

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W h a t k i n d s o f p r o b l e m s a r e s o l v e d b y
a l g o r i t h m s ?
The Human Genome Project
 Identifying 100,000 genes in human DNA
 determining the sequences of the 3 billion chemical
base pairs that make up human DNA
 storing this information in databases

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W h a t k i n d s o f p r o b l e m s a r e s o l v e d b y
a l g o r i t h m s ?
E-Commerce
 public-key cryptography and digital signatures
 recommendation system
 logistics

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W h a t k i n d s o f p r o b l e m s a r e s o l v e d b y
a l g o r i t h m s ?

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W h a t k i n d s o f p r o b l e m s a r e s o l v e d b y
a l g o r i t h m s ?
If you can show that the problem is NP-complete, you can instead
spend your time developing an efficient algorithm that gives a good, but not
the best possible, solution.

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Don’t you wish that
all NP can be reduced into P
???

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Efficiency of an Algorithm

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Finding factorial of integer n
int factorial(int n)
{
int i, fact = 1;
for (i = 2; i <= n; i++)
{
fact *= i;
}
return fact;
}
}

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Finding factorial of integer n
int factorial(int n)
{
int i, fact = 1;
for (i = 2; i <= n; i++)
{
fact *= i;
}
return fact;
}
}
int factorial(int n)
{
int i, fact = 1;
if (n<=1) return 1;
else return n*factorial(n-1);
}

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Fibonacci Series: Algorithm I
int fun(int x)
{
int f;
if (x==1) return(0);
else
if (x==2) return(1);
else
f= fun(x-1)+fun(x-2);
return(f);
}

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Fibonacci Series: Algorithm II
int fun(int x)
{
int A[x+1];
A[0]=0;
A[1]=1;
for (i=0; i<=x, i++)
{
A[i] = A[i-1]+A[i-2];
}
return A[i];
}

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Fibonacci Series: Algorithm III
int fun(int x)
{
int pre=0, curr-1, next;
for (i=2; i<=x, i++)
{
next=pre+curr;
p=curr;
curr=next;
}
return next;
}

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Evaluating algorithms
Two questions we ask about an algorithm
1. Is it correct?
2. Is it efficient?
Correctness is of utmost importance.
highly efficient but incorrect algorithm ???
Efficiency with respect to:
1. Running time
2. Space (amount of memory used)
3. Network traffic
4. Other features (e.g. number of times secondary storage is
accessed)

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Loop-invariant approach to correctness proof
Initialization: true before the first execution of the loop.
Maintenance: If true before an iteration of the loop, it should be
true also after the iteration.
Termination: Prove that when the loop terminates, the invariant,
and the reason that the loop terminates, imply the correctness
of the loop-construct.
Temporarily be false during the body of the loop

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int j = 9;
for(int i=0; i<10; i++)
j--;
Loop invariant: i + j == 9.
A weaker invariant: i >= 0 && i <= 10.

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Subarray A[0 to i-1] is always sorted
Insertion Sort:

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41. Thank You