algorithm_practice.pptzkkxiqdhiwdowhdohwod2hodh2odh2o
- 1. Algorithm: The Fundamental knowledge needed to solve problems using a computer is the notion of an algorithm. “An Algorithm is a precise specification of a seq. of instructions (tells what task is to be executed) to be carried out in order to solve a given problem”. Features of a good algorithm: 1.Finiteness: An algorithm must terminate after a finite number of steps and further each step must be executable in finite amount of time 2.Definiteness (no ambiguity): Each steps of an algorithm must be precisely defined; the action to be carried out must be rigorously and unambiguously specified for each case. 3.Inputs/ Output: An algorithm has zero or more (but only finite), number of inputs and (atleast 1)output. 4.Effectiveness(efficient): An algorithm should be effective. This means that each of the operation to be performed in an algorithm must be sufficiently basic that it can be done exactly and in a finite length of time.
- 2. Write an algorithm to add two numbers entered by user. Step 1: Start Step 2: Declare variables num1, num2 and sum. Step 3: Read (i/p)values num1 and num2. Step 4: Add num1 and num2 and assign the result to sum as: sum←num1+num2 Step 5: Display sum Step 6: Stop
- 3. Flowchart: addition of 2 numbers
- 4. • Write an algorithm to find the largest among three different numbers entered by user. • Step 1: Start • Step 2: Declare variables a,b and c. • Step 3: Read variables a,b and c. • Step 4: compare a & b: • If a>b then • { • compare a & c: • If a>c Then Display a is the largest number. • Otherwise( if c>a) Then Display c is the largest number. • } • Otherwise(if b>a) then • { • compare b & c: • If b>c Then Display b is the largest number. • Otherwise(if c>a) Then Display c is the greatest number. • } • Step 5: Stop
- 5. Flowchart: largest among three different numbers
- 6. • Write an algorithm to find all roots of a quadratic equation ax2 +bx+c=0. • Step 1: Start • Step 2: Declare variables a, b, c, D, r1, r2, real and imaginary; • Step 3: read a,b,c • Step 4: Calculate discriminant as: D←b2 -4ac • Step 5: Test discriminant and perform as: • Step5.1: If D≥0 then do- r1←(-b+√D)/2a , r2←(-b- √D)/2a ;then Display r1 and r2 as roots. • Step5.2:Otherwise(Else) Calculate real part and imaginary part as: • real←b/2a, imaginary ←√(-D)/2a and Display real +j(imaginary) and real -j(imaginary) as roots • Step 6: Stop
- 7. Flowchart: roots of a quadratic equation ax2 +bx+c=0
- 8. • Write an algorithm to find the factorial of a number entered by user. • Step 1: Start • Step 2: Declare variables n,factorial and i. • Step 3: Initialize variables as factorial←1 and i←1 • Step 4: Read(i/p) value of n whose factorial is to be calculated • Step 5: Repeat the steps while i is smaller than n+1 • 5.1: multiply factorial by i and again store result in factorial as: factorial←factorial*i • 5.2: increase i by 1 as:i←i+1 • Step 6: Display last value stored in factorial • Step 7: Stop
- 9. Flow chart: factorial of a number
- 10. • Write an algorithm to find the factorial of a number entered by user. • Step 1: Start • Step 2: Declare variables n,factorial and i. • Step 3: Initialize variables as factorial←1 and i←n • Step 4: Read(i/p) value of n whose factorial is to be calculated • Step 5: Repeat the steps while i is not equal to 0 • 5.1: multiply factorial by i and again store result in factorial as: factorial←factorial*i • 5.2: decrease i by 1 as:i←i-1 • Step 6: Display last value stored in factorial • Step 7: Stop
- 11. • Write an algorithm to check whether a number entered by user is prime or not. • Step 1: Start • Step 2: Declare variables n,i,flag. • Step 3: Initialize variables: flag←1 & i←2 • Step 4: Read n from user to be tested as prime or not. • Step 5: Repeat the steps while i<(n/2) • 5.1 If remainder of n%i equals 0 • then flag←0 & Go to step 6 • 5.2 otherwise increment i as:i←i+1 • Step 6: If flag=0 then write n is not prime • otherwise write n is prime • Step 7: Stop
- 12. Flow chart: To test whether a number is prime or not.
- 13. Write an algorithm to find the Fibonacci series till term=1000. Step 1: Start Step 2: Declare variables first_term,second_term and temp. Step 3: Initialize variables first_term=0 & second_term=1 Step 4: Display first_term and second_term Step 5: Repeat the steps while second_term<=1000 5.1: temp=second_term 5.2: second_term=second_term+first_term 5.3: first_term=temp 5.4: Display second_term Step 6: Stop
- 14. Flow-Chart Fibonacci series till term=1000.
- 15. Write an algorithm to find sum of the digits of a number (ex: num=452;sum of digits=4+5+2=>11) Step 1: start Step 2: declare variables num, sum,rem Step 3: initialize sum=0 & i/p value of num Step 4: Repeat steps while num is greater than 0 or not equal to 0 Step 4.1: To extract digit of unit place:divide num by 10 and save its remainder in rem as: rem=num%10 Step 4.2: To remove digit of unit place our no. Is changed(it has 1 digit less):divide num by 10 and save its quotient in num again as: num=num/10 Step 4.3: add rem with sum and again save it in sum as: sum=sum+rem Step 5: display sum Step 6: stop
- 16. Flow-Chart: sum of the digits of a number