Given a number N, the task is to check if the all sub-numbers of this number have distinct digit product.
- An N digit number has N*(N+1)/2 sub-numbers. For example, all possible sub-numbers of 975 are 9, 7, 5, 97, 75, 975.
- Digit product of a number is product of its digits.
Input : N = 324 Output : YES Sub-numbers of 324 are 3, 2, 4, 32, 24 and 324 and digit products are 3, 2, 4, 6, 8 and 24 respectively. All the digit products are different. Input : N = 323 Output : NO Sub-numbers of 323 are 3, 2, 3, 32, 23 and 323 and digit products are 3, 2, 3, 6, 6 and 18 respectively. Digit products 3 and 6 have occurred twice.
- Make a digit array i.e., an array with its elements as digits of given number N.
- Now finding sub-numbers of N is similar to finding all possible subarrays of the digit array.
- Maintain a list of digit products of these subarrays.
- If any digit product has appeared more than once, print NO.
- Else print YES.
Below is the implementation of the above approach :
# Python3 program to check if all
# sub-numbers have distinct Digit product
# Function to calculate product of
# digits between given indexes
def digitProduct(digits, start, end):
pro = 1
for i in range(start, end + 1):
pro *= digits[i]
# Function to check if all sub-numbers
# have distinct Digit product
s = str(N)
# Length of number N
length = len(s)
# Digit array
digits = [None] * length
# set to maintain digit products
products = set()
for i in range(0, length):
digits[i] = int(s[i])
# Finding all possible subarrays
for i in range(0, length):
for j in range(i, length):
val = digitProduct(digits, i, j)
if val in products:
# Driver Code
if __name__ == “__main__”:
N = 324
if isDistinct(N) == True:
# This code is contributed
# by Rituraj Jain
- Check whether a number can be expressed as a product of single digit numbers
- Integers from the range that are composed of a single distinct digit
- Product of N with its largest odd digit
- Digit - Product - Sequence
- Check if frequency of each digit is less than the digit
- Product of non-repeating (distinct) elements in an Array
- Find two distinct prime numbers with given product
- Distinct Prime Factors of Array Product
- First digit in product of an array of numbers
- Maximum number with same digit factorial product
- Largest palindrome which is product of two n-digit numbers
- Last digit of Product of two Large or Small numbers (a * b)
- Maximum of sum and product of digits until number is reduced to a single digit
- Check if all array elements are distinct
- Check whether a number has exactly three distinct factors or not
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