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Find the Mobile Number formed using first digits of arrays of absolute differences of consecutive numbers

Last Updated : 12 Jan, 2022

Given a String ph[], the task is to find a new number for the user, based on following conditions:

The new number will also start from the same digit as of original number.
The digits of the new number will be the first digits of a series of arrays of absolute differences of the consecutive elements.

Examples:

Input: ph = “9827218706”
Output: 9154301011
Explanation:
Input: ph =”9647253846″
Output: 9310100011

Approach: Consider the following steps to solve this problem:

Convert every character from the string into integer and store it into the array ph1[] using list comprehension.
Declare an empty string ph2.
Convert first element of array ph1[ ] into a string and add it to ph2.
Using List comprehension create an array by storing the absolute difference of consecutive elements.
Assign this array to ph1.
Repeat step 3-5, ten times as the phone number have ten digits.

Below is the implementation of the above approach.

Python3

# Function to find lucky phone number

def phone(ph, n):

# Converting char to int and storing into array.

ph1 = [int(i) for i in ph]

# Empty string to store lucky number.

ph2 = ""

# Loop for performing action

# and adding digit to ph2.

for _ in range(n):

# Convert first element into

# string and adding to ph2.

ph2 += str(ph1[0])

# Creating new ph1 by subtracting

# consecutive element.

ph1 = [abs(ph1[j]-ph1[j + 1]) \

for j in range(len(ph1)-1)]

# Return lucky number ph2

return ph2

# Original number

ph = "9827218706"

# Calling phone function.

num = phone(ph, len(ph))

# Print the lucky number

print(num)

Output

9154301011

Time Complexity: O(N*N)
Auxiliary Space: O(N)

Efficient Approach: In this approach, no extra space is required for storing elements in the array. First, declare an empty string ph2 in which lucky number will be stored, now create a for loop in which the first character of the string will be added to ph2 and again another for loop to find the absolute difference of consecutive element. Now the string of absolute difference will be assigned to ph1 which is the original number and the same steps will be followed. Follow the steps below to solve the problem:

Initialize a string variable ph2[] as an empty string.
Iterate over the range [0, N) using the variable i and perform the following tasks:
- Add ph[0] to the variable ph2[].
- Initialize a string variable S[] as an empty string.
- Iterate over the range [0, N-1) using the variable j and perform the following tasks:
  - Add the value of str(abs(int(ph[j])-int(ph[j+1]))) to the variable S[].
- Set the value of ph as S[].
After performing the above steps, print the value of ph2[] as the answer.

Below is the implementation of the above approach.

Python3

# Function to find lucky number.

def phone(ph, n):

# ph2 is empty string to store lucky number.

ph2 = ""

# For loop for finding lucky number

for i in range(len(ph)):

# Add first element of ph to ph2

ph2 += ph[0]

# S for storing the difference

S = ""

# Loop to calculate the absolute difference

for j in range(len(ph)-1):

x = abs(int(ph[j])-int(ph[j + 1]))

S += str(x)

# Assigning S to ph.

ph = S

# Return the lucky number

return ph2

# Original number

ph = "9827218706"

# Call phone function

num = phone(ph, len(ph))

# Printing lucky number

print(num)

Output

9154301011

Time Complexity: O(N*N)
Auxiliary Space: O(N)

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Find the Mobile Number formed using first digits of arrays of absolute differenc...

Find the Mobile Number formed using first digits of arrays of absolute differences of consecutive numbers

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