SILAMBARASAN A

Posted on Mar 31

RECURSION SUMS

#beginners #tutorial #algorithms #python

1. PRINT 1 to 5

PYTHON CODE:

def fact(i):
    if i<=5:
        print(i)
        i+=1
        fact(i)
fact(1)

🔁 Simple Flow

fact(1)
→ print 1
→ fact(2)

fact(2)
→ print 2
→ fact(3)

fact(3)
→ print 3
→ fact(4)

fact(4)
→ print 4
→ fact(5)

fact(5)
→ print 5
→ fact(6)

fact(6)
→ stop ❌`

🧾 Output

1
2
3
4
5

2. ODD NUMBERS PRINT: 1 3 5 7

PYHTON CODE :

def fact(i):
if i<=15:
if i%2!=0:
print(i)
i+=1
fact(i)
fact(1)

🔁 Simple Flow
fact(1)
→ 1 is odd → print 1
→ call fact(2)

fact(2)
→ not odd ❌
→ call fact(3)

fact(3)
→ print 3
→ call fact(4)

fact(4)
→ skip
→ call fact(5)

...

👉 continues same until 15

fact(15)
→ print 15
→ call fact(16)

fact(16)
→ stop ❌

🧾 Output
1 3 5 7 9 11 13 15

3. FACTORIAL :

Factorial meaning:

5! = 5 × 4 × 3 × 2 × 1 = 120

PYHTON CODE :
def factorial(n):
if n == 0 or n == 1:
return 1
return n * factorial(n - 1)
print(factorial(5))

🔁 Simple Flow
factorial(5)
→ 5 * factorial(4)

factorial(4)
→ 4 * factorial(3)

factorial(3)
→ 3 * factorial(2)

factorial(2)
→ 2 * factorial(1)

factorial(1)
→ return 1 ✅ (stop)

🔙 Backward Calculation

factorial(2) = 2 * 1 = 2
factorial(3) = 3 * 2 = 6
factorial(4) = 4 * 6 = 24
factorial(5) = 5 * 24 = 120

🧾 Output

120

4. SUM OF N NUMBERS

✅ What this code does

👉 Finds sum of first n numbers

5 → 1 + 2 + 3 + 4 + 5 = 15

PYHTON CODE :

python def SUM(n): if n == 1: return 1 return n + SUM(n - 1) print(SUM(5))

🔁 Simple Flow

SUM(5)
→ 5 + SUM(4)

SUM(4)
→ 4 + SUM(3)

SUM(3)
→ 3 + SUM(2)

SUM(2)
→ 2 + SUM(1)

SUM(1)
→ return 1 ✅ (stop)

🔙 Backward Calculation

SUM(2) = 2 + 1 = 3
SUM(3) = 3 + 3 = 6
SUM(4) = 4 + 6 = 10
SUM(5) = 5 + 10 = 15

🧾 Output
15

5. COUNT DIVISORS

✅ What this code does

👉 Counts how many numbers divide num (except 1 and itself)

For 100:
👉 Divisors = 2, 4, 5, 10, 20, 25, 50
👉 Count = 7

PYHTON CODE :

python def count_divisors(num, div=2, count=0): if div > num // 2: return count if num % div == 0: count += 1 return count_divisors(num, div + 1, count) print(count_divisors(100))

🔍 How it Works

For num = 100:

Start div = 2
If divisible → increase count
Call function again with div + 1
Stops when div > 50

6. prime check

PYHTON CODE :

`python

def is_prime(num, div=2):
if div > num // 2:
return True
if num % div == 0:
return False
return is_prime(num, div + 1)
num = int(input("enter a number: "))
if num > 1 and is_prime(num):
print("This number is Prime")
else:
print("This number is not Prime")
`

🔁 How It Works (Simple)