That’s quite a comprehensive list of programming problems! Here’s a structured breakdown for clarity, grouped by category:

Problems on Arrays

  1. Basic Operations

    • Find the smallest number in an array
    • Find the largest number in an array
    • Second smallest and second largest elements in an array
    • Reverse a given array
    • Count frequency of each element in an array
    • Calculate the sum of the elements of the array
    • Average of all elements in an array
    • Find the median of the given array

  2. Rearrangement and Rotation

    • Rearrange array in increasing-decreasing order
    • Rotate the array by K elements (Block Swap Algorithm)
    • Remove duplicates from a sorted array
    • Remove duplicates from an unsorted array
    • Rotation of elements of array (left and right)
    • Finding circular rotation of an array by K positions


  3. Search and Rank

    • Search an element in an array
    • Replace each element of the array by its rank
    • Sort elements of an array by frequency
    • Sort an array according to the order defined by another array
    • Check if an array is a subset of another array


  4. Special Problems

    • Find all repeating elements in an array
    • Find all non-repeating elements in an array
    • Find all symmetric pairs in an array
    • Maximum product subarray in an array
    • Finding equilibrium index of an array

Problems on Numbers

  1. Number Properties

    • Check if a number is palindrome
    • Find all palindrome numbers in a given range
    • Check if a number is prime
    • Prime numbers in a given range
    • Check if a number is Armstrong
    • Check if a number is a perfect number
    • Check if a number is even or odd
    • Check if a number is positive or negative


  2. Series and Sums

    • Sum of first N natural numbers
    • Sum of an AP series
    • Sum of a GP series
    • Sum of numbers in a given range


  3. Comparisons and Operations

    • Greatest of two numbers
    • Greatest of three numbers
    • Leap year or not
    • Reverse digits of a number
    • Maximum and minimum digit in a number
    • Factorial of a number
    • Power of a number
    • Factors of a given number
    • Print all prime factors of a given number
    • GCD and LCM of two numbers


  4. Special Numbers

    • Check if a number is a strong number
    • Check if a number is automorphic
    • Check if a number is Harshad
    • Check if a number is abundant


  5. Other

    • Permutations of N people occupying R seats
    • Program to add two fractions
    • Replace all 0s with 1s in a number
    • Check if a number can be expressed as a sum of two primes
    • Calculate the area of a circle
    • Find roots of a quadratic equation

Problems on Number Systems

  1. Conversions

    • Binary to Decimal
    • Binary to Octal
    • Decimal to Binary
    • Decimal to Octal
    • Octal to Binary
    • Octal to Decimal


  2. Extras

    • Convert digits/numbers to words

Problems on Sorting

  1. Algorithms
    • Bubble Sort
    • Selection Sort
    • Insertion Sort
    • Quick Sort
    • Merge Sort

Problems on Strings

  1. Basic Operations

    • Check if a string is a palindrome
    • Reverse a string
    • Count number of vowels, consonants, spaces
    • Remove all vowels from a string
    • Remove spaces from a string
    • Remove characters except alphabets


  2. Frequency and Characters

    • Frequency of characters
    • Find non-repeating characters
    • Maximum occurring character
    • Remove duplicates
    • Print all duplicates


  3. Manipulations

    • Capitalize first and last character of each word
    • Change every letter to the next lexicographic alphabet
    • Change case of each character
    • Concatenate two strings


  4. Search and Substrings

    • Find a substring and its starting position
    • Find a word with the highest number of repeated letters


  5. Miscellaneous

    • Reverse words in a string
    • Sort characters in a string
    • Count words in a string
    • Check if two strings are anagrams
    • Handle wildcards in string matches
    • Remove characters of one string from another
01. Problems on Arrays - Basic Operations 
				
					# 1. Find the smallest number in an array
def find_smallest(arr):
    return min(arr)

# 2. Find the largest number in an array
def find_largest(arr):
    return max(arr)

# 3. Second smallest and second largest elements in an array
def find_second_smallest_largest(arr):
    unique_sorted = sorted(set(arr))
    if len(unique_sorted) < 2:
        return None, None  # Not enough elements
    return unique_sorted[1], unique_sorted[-2]

# 4. Reverse a given array
def reverse_array(arr):
    return arr[::-1]

# 5. Count frequency of each element in an array
from collections import Counter
def count_frequency(arr):
    return dict(Counter(arr))

# 6. Calculate the sum of the elements of the array
def calculate_sum(arr):
    return sum(arr)

# 7. Average of all elements in an array
def calculate_average(arr):
    return sum(arr) / len(arr) if arr else 0

# 8. Find the median of the given array
def find_median(arr):
    arr_sorted = sorted(arr)
    n = len(arr_sorted)
    mid = n // 2
    if n % 2 == 0:
        return (arr_sorted[mid - 1] + arr_sorted[mid]) / 2
    else:
        return arr_sorted[mid]

# Example usage
array = [7, 2, 9, 1, 4, 6, 2]

print("Smallest:", find_smallest(array))
print("Largest:", find_largest(array))
second_smallest, second_largest = find_second_smallest_largest(array)
print("Second Smallest:", second_smallest)
print("Second Largest:", second_largest)
print("Reversed Array:", reverse_array(array))
print("Frequency Count:", count_frequency(array))
print("Sum of Elements:", calculate_sum(array))
print("Average of Elements:", calculate_average(array))
print("Median:", find_median(array))

				
			
				
					# 1. Rearrange array in increasing-decreasing order
def rearrange_increasing_decreasing(arr):
    arr.sort()
    mid = len(arr) // 2
    return arr[:mid] + arr[mid:][::-1]

# 2. Rotate the array by K elements (Block Swap Algorithm)
def rotate_array(arr, k):
    def swap_blocks(arr, start, end, d):
        for i in range(d):
            arr[start + i], arr[end + i] = arr[end + i], arr[start + i]

    n = len(arr)
    k %= n
    if k == 0:
        return arr
    i, j = k, n - k
    while i != j:
        if i < j:
            swap_blocks(arr, k - i, k + j - i, i)
            j -= i
        else:
            swap_blocks(arr, k - i, k, j)
            i -= j
    swap_blocks(arr, k - i, k, i)
    return arr

# 3. Remove duplicates from a sorted array
def remove_duplicates_sorted(arr):
    return list(dict.fromkeys(arr))

# 4. Remove duplicates from an unsorted array
def remove_duplicates_unsorted(arr):
    return list(dict.fromkeys(arr))

# 5. Rotation of elements of array (left and right)
def rotate_left(arr, k):
    k %= len(arr)
    return arr[k:] + arr[:k]

def rotate_right(arr, k):
    k %= len(arr)
    return arr[-k:] + arr[:-k]

# 6. Finding circular rotation of an array by K positions
def circular_rotation(arr, k):
    return rotate_left(arr, k)

# Example usage
if __name__ == "__main__":
    array = [7, 2, 9, 1, 4, 6, 2]
    print("Original Array:", array)

    # 1. Rearrange in increasing-decreasing order
    print("Rearranged (Increasing-Decreasing):", rearrange_increasing_decreasing(array))

    # 2. Rotate array by K elements
    print("Rotated Array by 2 (Block Swap):", rotate_array(array.copy(), 2))

    # 3. Remove duplicates from sorted array
    print("Remove Duplicates (Sorted):", remove_duplicates_sorted(sorted(array)))

    # 4. Remove duplicates from unsorted array
    print("Remove Duplicates (Unsorted):", remove_duplicates_unsorted(array))

    # 5. Rotation of elements (left and right)
    print("Left Rotation by 2:", rotate_left(array, 2))
    print("Right Rotation by 2:", rotate_right(array, 2))

    # 6. Circular rotation by K positions
    print("Circular Rotation by 3:", circular_rotation(array, 3))

DSA Practice Sheet

*Company wise details for Questions coming soon.
Note – This Sheet is only meant for Prime & Super Students.

Coding Practice Sheet

*Company wise details for Questions coming soon.
Note – This Sheet is only meant for Prime & Super Students.

  • Sum of Natural Numbers
  • Count Digits
  • Palindrome Number
  • Factorial of a Number
  • Trailing Zeros in Factorial
  • GCD or HCF of Two Numbers
  • LCM of Two Numbers
  • Check for Prime
  • Prime Factorization
  • All Divisors of a Number
  • Sieve of Eratosthenes
  • Computing Power

  • Iterative Power (Binary Exponentiation)

  • List (Dynamic Sized Array) Introduction
  • Working of List in Python
  • Average or Mean of a List
  • Separate Even and Odd
  • Get Smaller Elements
  • Slicing (List, Tuple, and String)
  • Comprehensions in Python
  • Largest Element in a List
  • Second Largest Element in a List
  • Check if a List is Sorted
  • Reverse a List in Python
  • Remove Duplicates
  • Left Rotate a List by One

20 Basic Numerical Problems and It’s Solution — Python Basics

1. Find the Sum of the First N Natural Numbers

Given a Natural Number of N, we need to find the sum of all the natural numbers until the value of N. We can use different methods to write the Python code and one of the most effective method is using For Loop.

Code:


range = int(input("Enter the ranges: "))
add = 0
for  i in range(range+1):
     add = add + i

print(f”The sum of the first {ranges} numbers is {add}“)

2. Check Whether a Number is Abundant Number or not

A number in which the sum of it’s divisors is greater than the number is known as Abundant Number

Let’s take number 12 as an example

Sum of it’s divisors = 1+2+3+4+6 = 16 which is greater than 12. Hence, It is an abundant number

Code:

num = int(input("Enter the number : "))
add = 0 
for i in range(1, num):
    if (num%i==0):
        add = add + i

if (num<add):
print(f’{num} is an abundant number’)
else:
print(“It is not an abundant number”)

3. Check Whether a Number is Automorphic Number or Not

A Number is known as an Automorphic Number if the last digits of it’s square is same as the number itself

Let’s take number 76 as an example

76² = 5776

The last two digit of the square , 76 is equal to the number itself

Code:

num = int(input("Enter a number : "))
length = len(str(num))
sqr = str(num ** 2)
print(sqr)

new = int(sqr[(length):])
print(new)

if (new == num):
print(“It is an Automorphic Number”)
else:
print(“It is not an Automorphic Number”)

 

4. Print N number of Automorphic numbers in a given range

A Range N will be given and we need to print all the automorphic numbers up to that range. To Know more about Automorphic Number, Refer To Question 4.

Code :

range = int(input('Enter the given range : '))

for i in range(1, range):
sqr = i**2
mod = 10 ** len(str(i))
if (sqr%mod == i):
print(i)

 

5. Print Harshad Numbers in nth range

A number that is divisible by sum of it’s own digits is know an Harshad Number.

Example: 12 , 1+ 2 = 3 , 12 is divisible by 3

Code:

range = int(input("Enter the range : "))

for i in range(1, range):
add = 0 #Use Flag Equations in Outer Loop
for j in str(i):
add = add + int(j)
if (i %add == 0):
print(i)

6. Print the Armstrong Numbers in Nth Range

An number is an Armstrong number if the sum of its own digits, each raised to the power of n, is equal to the number itself.

Example:
153 = 1³ + 5³ + 3³ = 153

1634 = 1⁴ + 6⁴ + 3⁴ + 4⁴ = 1634

Code :

range = int(input("Enter the range : "))

for i in range(1, range):
add = 0
length = len(str(i))
temp = i
while (temp != 0):
reminder = temp % 10
add = add + (reminder**length)
temp = temp // 10

if (i==add):
print(i)

7. Check Whether a Number is Palindrome or Not

A number when reversed, equates to the same number is known as Palindrome Number

121 reversed is 121 itself

Code:


num = int(input("Enter a number: "))

temp = num
new = 0
while (temp!=0):
reminder = temp % 10
new = (new * 10) + reminder
temp = temp // 10

print(new)

if (num == new):
print(“The Number is Palindrome”)
else:
print(“The Number is not a palindrome”)

8. Print the Reverse of a Number

Code:

num = int(input("Enter a number: "))

temp = num
new = 0
while (temp!=0):
reminder = temp % 10
new = (new * 10) + reminder
temp = temp // 10

print(new)

9. Find the Sum of the digits of a number

Each digit of a number is taken and added to get the required result

Code:


num = int(input("Enter a number : "))

# Let us Do This By using modulus

add = 0

while (num!=0):
reminder = num % 10
add = add + reminder
num = num // 10

print(add)

10. Greatest Of Three Numbers

Code:

n1, n2, n3 = map(int, input("Enter Three Numbers : ").split())

if (n1>=n2) and (n1>=n3):
print(f’{n1} is the greatest’)
elif (n2>=n1) and (n2>=n3):
print(f’{n2} is the greatest’)
elif (n3>=n1) and (n3>=n2):
print(f’{n3} is the greatest’)
else:
print(“They are all Equal”)

11. Print Abundant Numbers in The range N

Numbers upto the range N is checked whether it is an abundant number or not. For more reference , Check Problem Number 3

Code:

# A number that is smaller than the sum of all its factors except the number itself is known as an abundant number

num = int(input(“Enter the number : “))
add = 0
for i in range(1, num):
if (num%i==0):
add = add + i

if (num<add):
print(f’{num} is an abundant number’)
else:
print(“It is not an abundant number”)

11. Check whether a Year is Leap Year or Not.

Conditions for a Leap Year :

  1. The year should be perfectly divisible by 400.
  2. The year divisible by 4 but not by 100.

Code

year = int(input("Enter a Year  :"))

if (year%4==0 and year%100 !=0) or (year%400 == 0):
print(“Leap Year”)
else:
print(“No Leap Year”)

12. Checking Whether a number is prime or not

Prime Number is a number which is divisible by 1 and the number itself

Code


num = int(input("Enter a number : "))

flag = 0
if (num>1):
for i in range(2, num):
if (num%i==0):
flag = 1
break;
if flag == 1:
print(“Composite Number”)
else:
print(“Prime Number”)

else:
print(“Neither Prime Nor Composite”)

13.Print the Prime Numbers in a Given Range

Code

range = int(input("Enter the range you want: "))

for i in range(2, range):
flag = 0 #Used To Assume a number is prime , on every new outerloop , the value is resetted to 0
for j in range(2, i):
if (i%j==0):
flag = 1
break;
if (flag ==0):
print(i)

14. Find the Factorial of a Number

Example:

Factorial of 5 = 5*4*3*2*1 = 120

Code:

num = int(input("Enter a number : "))

product = 1

for i in range(1,num+1):
product = product * i

print(f”The Factorial of the number is {product}“)

15. Find the Power Of a Number using Iteration (Most Basic)

Code:

num, power = map(int, input("Enter the num and the power : ").split())

#print(num ** power)

# Using Simple Iteration

output = 1
for i in range(power):
output = output * num

print(output)

16. Check whether a number is Perfect Number or Not

A perfect number is a number whose sum of it’s divisors is equal to the number itself.

For example, 28

Sum of it’s divisors = 1 + 14 + 2 + 4 + 7 = 28 which is equal to the number itself

Code:

num = int(input("Enter a number : "))
add = 0

for i in range(1, num):
if num % i == 0:
add = add + i

if (num == add):
print(“Perfect Number”)
else:
print(“Not Perfect Number”)

Visualization

17. Find the Prime Factors of a Given Number:

Factors of a Number which is only divisible by 1 and the number itself is known as Prime Factors

Code:


n = int(input("Enter the number : "))
arr = []
for i in range(2, n):
    if n % i == 0:
        arr.append(i)
print(arr)
sol = []

for j in arr:
flag = 0
for k in range(2, j):
if j % k == 0:
flag = 1
break
if flag == 0:
sol.append(j)

print(“The Prime Factors of the number are: “)
for m in sol:
print(m, end=‘ ‘)

18. Find whether a number is perfect square or not

Examples of Perfect Number : 4, 9, 16, 25 etc

Code

import math 
num = int(input("Enter the number : "))
result1 = int(math.sqrt(num))
if float(result1) == math.sqrt(num):
    print("Yes")
else:
    print("No")

19. Check Whether Two Numbers forms a friendly pair or not

  1. Read Two Numbers
  2. Find The Factors of Both The Numbers
  3. Divide the sum of the factors with the number for each of these numbers
  4. If the resultant of the above step for each numbers are same, then both of these numbers are said to be friendly pairs.

Code

num1, num2 = map(int, input("Enter the two numbers : ").split())

sum1 = 0
sum2 = 0
for i in range(1, num1+1):
if num1 % i == 0:
sum1 = sum1 + i

for j in range(1, num2+1):
if num2 % j == 0:
sum2 = sum2 + j

result1 = sum1 / num1

if (result1==result2):
print(f”{num1} and {num2} are friendly pairs”)
else:
print(“They are not friendly pairs”)

20. Check Whether or Not the Number is a Strong Number

A Number whose sum of the factorials of it’s digits is equal to the number itself is known as Strong Number

For Example :

145;

1!+4!+5! = 145; Hence it is a strong number.

Code

n = int(input("Enter a number : "))

digits = []
for i in str(n):
digits.append(int(i))
add = 0
for i in digits:
product = 1
for j in range(1, i+1):
product = product * j
add = add + product
print(add)
if (n==add):
print(“It is a strong number”)
else:
print(“It is not a strong number”)

Conclusion

These are some of the most important and basic numerical questions which are being repeatedly asked in various tests.

There are many other methods to solve the same question, explore them too. Try to solve the questions without looking at the given code and check whether you are getting the desired output.