Strange Numbers

The idea here is to perform a breadth-first search over all the numbers from 1 to ‘N’ inclusive with 0, 1, 6, 8, and 9 as their digits. Initially, we will insert all the numbers between 1 to ‘N’  inclusive having a single - digit with 0 or 1 or 6 or 8 or 9 as their digit into a queue. We will gradually increase the length(i.e., number of digits) of the numbers present in the queue and insert it into the queue if the number lies between 1 to ‘N’ inclusive. Refer to the below diagram for a clear understanding.

For all the numbers present in the queue, we will check if the current number is a strange number.

Algorithm:

• Declare an integer, say ‘cntStrange’ to count the total number of strange numbers in a given range, and initialize it with 0.
• Declare an integer, say ‘currNumber’, to keep track of the current number during our BFS traversal.
• Declare a queue of integers.
• Run a loop for ‘digit’ in [0, 1, 6, 8, 9]:
  • If ‘digit’ lies between 1 and ‘N’ inclusive
    • Insert ‘digit’ into the queue
• Run a loop until the queue is not empty:
  • Store the front of the queue in ‘currNumber’ and remove it from the queue.
  • Call the ‘isStrangeNumber’ function to check if ‘currNumber’ is a strange number or not.
  • If ‘currNumber’ is a strange number:
    • Increment ‘cntStrange’ i.e., do cntStrange = cntStrange + 1.
  • Append digits 0, 1, 6, 8, and 9 to ‘currNumber’
  • Run a loop for ‘digit’ in [0, 1, 6, 8, 9]:
    • Declare an integer, say ‘appendedNumber’
    • Update ‘appendedNumber’ as ‘appendedNumber’ = currNumber * 10 + digit
    • If ‘appendedNumber’ lies between 1 and ‘N’, inclusive
      • Insert ‘appendedNumber’ into the queue.
• Return ‘cntStrange’.

Description of ‘isStrangeNumber’ function

This function is used to check whether the current number is a strange number or not.

This function will take one parameter:

• currNumber: An integer denoting the current number.

bool isStrangeNumber(currNumber):

• Declare a variable ‘rotatedNumber’ to store the value of ‘currNumber’ after rotating 180 degrees.
• Declare a variable ‘dummy’ and initialize it with ‘currNumber’.
• Run a loop while ‘dummy’ is greater than 0.
  • Declare a variable ‘currDigit’ and initialize it with the rightmost digit of ‘dummy’, i.e., do currDigit = dummy % 10.
  • Remove the rightmost digit of ‘dummy’, i.e., do dummy = dummy / 10
  • If ‘currDigit’ is 6, then make it 9, or if the ‘currDigit is 9, make it 6, i.e., rotate the ‘currDigit’ by 180 degrees.
  • Append the ‘currDigit’ to ‘rotatedNumber’ i.e. do rotatedNumber = rotatedNumber * 10 + currDigit.
• If ‘currNumber’ is not equal to ‘rotatedNumber’ then return true,  as the current number follows properties of a strange number.
• Else return false, as the current number does not follow properties of a strange number as after rotating, the number must be different.

The idea here is to perform a depth-first search over all the numbers from 1 to ‘N’ inclusive with 0, 1, 6, 8, and 9 as their digits. Initially, we will start the depth-first search from all the numbers between 1 to ‘N’ inclusive having a single - digit with 0 or 1 or 6 or 8 or 9 as their first digit. We will gradually increase the length(i.e., number of digits) of the numbers and recursively do a depth-first search if the number lies between 1 to ‘N’ inclusive. For every number that we encounter during the depth-first search, we will check if it is a strange number or not. If it is a strange number, then we will increment our answer.

Algorithm:

• Declare an integer, say ‘cntStrange’ to count the total number of strange numbers in a given range.
• Call the ‘depthFirstSearch’ function with ‘N’ and 0 as arguments and store its returned value into ‘cntStrange’
• Return ‘cntStrange’

Description of ‘isStrangeNumber’ function

This function is used to check whether the current number is a strange number or not.

This function will take one parameter:

• currNumber: An integer denoting the current number.

bool isStrangeNumber(currNumber):

• Declare a variable ‘rotatedNumber’ to store the value of ‘currNumber’ after rotating 180 degrees.
• Declare a variable ‘dummy’ and initialize it with ‘currNumber’.
• Run a loop while ‘dummy’ is greater than 0.
  • Declare a variable ‘currDigit’ and initialize it with the rightmost digit of ‘dummy’, i.e., do currDigit = dummy % 10.
  • Remove the rightmost digit of ‘dummy’, i.e., do dummy = dummy / 10
  • If ‘currDigit’ is 6, then make it 9, or if the ‘currDigit is 9, make it 6, i.e., rotate the ‘currDigit’ by 180 degrees.
  • Append the ‘currDigit’ to ‘rotatedNumber’ i.e. do rotatedNumber = rotatedNumber * 10 + currDigit.
• If ‘currNumber’ is not equal to ‘rotatedNumber’ then return true,  as the current number follows properties of a strange number.
• Else return false, as the current number does not follow properties of a strange number as after rotating, the number must be different.

Description of ‘depthFirstSearch’ function

This function will take two parameters:

• N: An integer given in the problem.
• currNumber: An integer denoting the current number in depth-first search.

int depthFirstSearch(N, currNumber):

• Declare a variable ‘answer’ to count the total number of strange numbers in a given range and initialize it with 0.
• Call the ‘isStrangeNumber’ function to check if ‘currNumber’ is a strange number or not.
• If ‘currNumber’ is a strange number:
  • Increment ‘answer’ i.e., do answer = answer + 1.
• Append digits 0, 1, 6, 8, and 9 to ‘currNumber’
• Run a loop for ‘digit’ in [0, 1, 6, 8, 9]:
  • Declare an integer, say ‘appendedNumber’
  • Make appendedNumber = currNumber * 10 + digit
  • If ‘appendedNumber’ lies between 1 and ‘N’, inclusive
    • Declare an integer, say ‘currAnswer’
    • Call the ‘depthFirstSearch’ function with ‘N’ and ‘appendedNumber’ as arguments and store its returned value into ‘currAnswer’
    • Add ‘currAnswer’ to the ‘answer’ i.e. do answer = answer + currAnswer
• Return ‘answer’