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Function to check if N is a pentadecagon number | def isPentadecagon ( N ) : NEW_LINE INDENT n = ( 11 + sqrt ( 104 * N + 121 ) ) / 26 ; NEW_LINE DEDENT |
Condition to check if the number is a pentadecagon number | return ( n - int ( n ) == 0 ) ; NEW_LINE |
Driver Code | if __name__ == " _ _ main _ _ " : NEW_LINE |
Given number | N = 15 ; NEW_LINE |
Function call | if ( isPentadecagon ( N ) ) : NEW_LINE INDENT print ( " Yes " ) ; NEW_LINE DEDENT else : NEW_LINE INDENT print ( " No " ) ; NEW_LINE DEDENT |
Python3 program for the above approach | import math NEW_LINE |
Function to check if N is a Tetradecagonal Number | def istetradecagonal ( N ) : NEW_LINE INDENT n = ( 10 + math . sqrt ( 96 * N + 100 ) ) / 24 NEW_LINE DEDENT |
Condition to check if the number is a tetradecagonal number | if ( n - int ( n ) ) == 0 : NEW_LINE INDENT return True NEW_LINE DEDENT return False NEW_LINE |
Given Number | N = 11 NEW_LINE |
Function call | if ( istetradecagonal ( N ) ) : NEW_LINE INDENT print ( " Yes " ) NEW_LINE DEDENT else : NEW_LINE INDENT print ( " No " ) NEW_LINE DEDENT |
Function to calculate the N - th Icosagonal number | def Icosagonal_num ( n ) : NEW_LINE |
Formula to calculate nth Icosagonal number & return it | return ( 18 * n * n - 16 * n ) // 2 NEW_LINE |
Function to find the sum of the first N Icosagonal numbers | def sum_Icosagonal_num ( n ) : NEW_LINE |
Variable to store the sum | summ = 0 NEW_LINE |
Loop to iterate through the first N values and find the sum of first N Icosagonal numbers | for i in range ( 1 , n + 1 ) : NEW_LINE |
function to get the Icosagonal_num | summ += Icosagonal_num ( i ) NEW_LINE return summ NEW_LINE |
Driver Code | if __name__ == ' _ _ main _ _ ' : NEW_LINE INDENT n = 5 NEW_LINE DEDENT |
Display the sum of first N Icosagonal number | print ( sum_Icosagonal_num ( n ) ) NEW_LINE |
Function to find the Centered_Pentagonal number | def Centered_Pentagonal_num ( n ) : NEW_LINE |
Formula to calculate nth Centered_Pentagonal number & return it into main function . | return ( 5 * n * n - 5 * n + 2 ) // 2 NEW_LINE |
Function to find the sum of the first N Centered_Pentagonal numbers | def sum_Centered_Pentagonal_num ( n ) : NEW_LINE |
To get the sum | summ = 0 NEW_LINE for i in range ( 1 , n + 1 ) : NEW_LINE |
Function to get the Centered_Pentagonal_num | summ += Centered_Pentagonal_num ( i ) NEW_LINE return summ NEW_LINE |
Driver Code | if __name__ == ' _ _ main _ _ ' : NEW_LINE INDENT n = 5 NEW_LINE DEDENT |
display first Nth Centered_Pentagonal number | print ( sum_Centered_Pentagonal_num ( n ) ) NEW_LINE |
Function to calculate the N - th Centered tridecagonal number | def Centered_tridecagonal_num ( n ) : NEW_LINE |
Formula to calculate Nth Centered tridecagonal number & return it | return ( 13 * n * ( n - 1 ) + 2 ) // 2 NEW_LINE |
Function to find the sum of the first N Centered tridecagonal numbers | def sum_Centered_tridecagonal_num ( n ) : NEW_LINE |
Variable to store the sum | summ = 0 NEW_LINE |
Loop to iterate and find the sum of first N Centered tridecagonal numbers | for i in range ( 1 , n + 1 ) : NEW_LINE INDENT summ += Centered_tridecagonal_num ( i ) NEW_LINE DEDENT return summ NEW_LINE |
Driver Code | if __name__ == ' _ _ main _ _ ' : NEW_LINE INDENT n = 5 NEW_LINE print ( sum_Centered_tridecagonal_num ( n ) ) NEW_LINE DEDENT |
Python3 program to check if N is a concentric hexagonal number | import math NEW_LINE |
Function to check if the number is a concentric hexagonal number | def isConcentrichexagonal ( N ) : NEW_LINE INDENT n = math . sqrt ( ( 2 * N ) / 3 ) NEW_LINE DEDENT |
Condition to check if the number is a concentric hexagonal number | return ( n - int ( n ) ) == 0 NEW_LINE |
Driver code | N = 6 NEW_LINE |
Function call | if isConcentrichexagonal ( N ) : NEW_LINE INDENT print ( " Yes " ) NEW_LINE DEDENT else : NEW_LINE INDENT print ( " No " ) NEW_LINE DEDENT |
A utility function that find the Prime Numbers till N | def computePrime ( N ) : NEW_LINE |
Resize the Prime Number | Prime = [ True ] * ( N + 1 ) NEW_LINE Prime [ 0 ] = False NEW_LINE Prime [ 1 ] = False NEW_LINE |
Loop till sqrt ( N ) to find prime numbers and make their multiple false in the bool array Prime | i = 2 NEW_LINE while i * i <= N : NEW_LINE INDENT if ( Prime [ i ] ) : NEW_LINE INDENT for j in range ( i * i , N , i ) : NEW_LINE INDENT Prime [ j ] = False NEW_LINE DEDENT DEDENT i += 1 NEW_LINE DEDENT return Prime NEW_LINE |
Function that returns the count of SPP ( Sexy Prime Pair ) Pairs | def countSexyPairs ( arr , n ) : NEW_LINE |
Find the maximum element in the given array arr [ ] | maxE = max ( arr ) NEW_LINE |
Function to calculate the prime numbers till N | Prime = computePrime ( maxE ) NEW_LINE |
To store the count of pairs | count = 0 NEW_LINE |
To store the frequency of element in the array arr [ ] | freq = [ 0 ] * ( maxE + 6 ) NEW_LINE for i in range ( n ) : NEW_LINE INDENT freq [ arr [ i ] ] += 1 NEW_LINE DEDENT |
Sort before traversing the array | arr . sort ( ) NEW_LINE |
Traverse the array and find the pairs with SPP ( Sexy Prime Pair ) s | for i in range ( n ) : NEW_LINE |
If current element is Prime , then check for ( current element + 6 ) | if ( Prime [ arr [ i ] ] ) : NEW_LINE INDENT if ( ( arr [ i ] + 6 ) <= ( maxE ) and freq [ arr [ i ] + 6 ] > 0 and Prime [ arr [ i ] + 6 ] ) : NEW_LINE INDENT count += 1 NEW_LINE DEDENT DEDENT |
Return the count of pairs | return count NEW_LINE |
Driver code | if __name__ == " _ _ main _ _ " : NEW_LINE INDENT arr = [ 6 , 7 , 5 , 11 , 13 ] NEW_LINE n = len ( arr ) NEW_LINE DEDENT |
Function call to find SPP ( Sexy Prime Pair ) s pair | print ( countSexyPairs ( arr , n ) ) NEW_LINE |
Function to find the number of ways | def countWays ( N ) : NEW_LINE |
Check if number is less than 2 | if ( N <= 2 ) : NEW_LINE INDENT print ( " - 1" ) NEW_LINE DEDENT else : NEW_LINE |
Calculate the sum | ans = ( N - 1 ) * ( N - 2 ) / 2 NEW_LINE print ( ans ) NEW_LINE |
Driver code | if __name__ == ' _ _ main _ _ ' : NEW_LINE INDENT N = 5 NEW_LINE countWays ( N ) NEW_LINE DEDENT |
Python3 implementation to check that a integer is a power of two | import math NEW_LINE |
Function to check if the number is a power of two | def isPowerOfTwo ( n ) : NEW_LINE INDENT return ( math . ceil ( math . log ( n ) // math . log ( 2 ) ) == math . floor ( math . log ( n ) // math . log ( 2 ) ) ) ; NEW_LINE DEDENT |
Driver code | if __name__ == ' _ _ main _ _ ' : NEW_LINE INDENT N = 8 NEW_LINE if isPowerOfTwo ( N ) : NEW_LINE INDENT print ( ' Yes ' ) NEW_LINE DEDENT else : NEW_LINE INDENT print ( ' No ' ) NEW_LINE DEDENT DEDENT |
Function to count the pairs | def count_pairs ( x ) : NEW_LINE |
Initializing answer with 1 | ans = 1 ; NEW_LINE |
Iterating through bits of x | while ( x > 0 ) : NEW_LINE |
Check if bit is 1 | if ( x % 2 == 1 ) : NEW_LINE |
Multiplying ans by 3 if bit is 1 | ans = ans * 3 ; NEW_LINE x = x // 2 ; NEW_LINE return ans ; NEW_LINE |
Driver code | if __name__ == ' _ _ main _ _ ' : NEW_LINE INDENT X = 6 ; NEW_LINE print ( count_pairs ( X ) ) ; NEW_LINE DEDENT |
Python3 implementation for above approach | import sys NEW_LINE |
Function to find the Kth not divisible by N | def kthNonDivisible ( N , K ) : NEW_LINE |
Lowest possible value | L = 1 NEW_LINE |
Highest possible value | H = sys . maxsize NEW_LINE |
To store the Kth non divisible number of N | ans = 0 NEW_LINE |
Using binary search | while ( L <= H ) : NEW_LINE |
Calculating mid value | mid = ( L + H ) // 2 NEW_LINE |
Sol would have the value by subtracting all multiples of n till mid | sol = mid - mid // N NEW_LINE |
Check if sol is greater than k | if ( sol > K ) : NEW_LINE |
H should be reduced to find minimum possible value | H = mid - 1 NEW_LINE |
Check if sol is less than k then L will be mid + 1 | elif ( sol < K ) : NEW_LINE L = mid + 1 NEW_LINE |
Check if sol is equal to k | else : NEW_LINE |
ans will be mid | ans = mid NEW_LINE |
H would be reduced to find any more possible value | H = mid - 1 NEW_LINE |
Print the answer | print ( ans ) NEW_LINE |
Driver Code | N = 3 NEW_LINE K = 7 NEW_LINE |
Function call | kthNonDivisible ( N , K ) NEW_LINE |
Function to print the required pair | def printPair ( n ) : NEW_LINE |
Print the pair | print ( "1" , end = " ▁ " ) NEW_LINE print ( n - 1 ) NEW_LINE |
Driver code | n = 14 NEW_LINE printPair ( n ) NEW_LINE |
Function to check number is autobiographical | def isAutoBiographyNum ( number ) : NEW_LINE INDENT count = 0 ; NEW_LINE DEDENT |
Convert integer to string | NUM = str ( number ) ; NEW_LINE size = len ( NUM ) ; NEW_LINE |
Iterate for every digit to check for their total count | for i in range ( size ) : NEW_LINE INDENT position = ord ( NUM [ i ] ) - ord ( '0' ) ; NEW_LINE count = 0 ; NEW_LINE DEDENT |
Check occurrence of every number and count them | for j in range ( size ) : NEW_LINE INDENT digit = ord ( NUM [ j ] ) - ord ( '0' ) ; NEW_LINE if ( digit == i ) : NEW_LINE INDENT count += 1 ; NEW_LINE DEDENT DEDENT |
Check if any position mismatches with total count them return with false else continue with loop | if ( position != count ) : NEW_LINE INDENT return False ; NEW_LINE DEDENT return True ; NEW_LINE |
Function to return the length of the largest subarray whose every element is a autobiographical number | def checkArray ( arr , n ) : NEW_LINE INDENT current_length = 0 ; NEW_LINE max_length = 0 ; NEW_LINE DEDENT |
Utility function which checks every element of array for autobiographical number | for i in range ( n ) : NEW_LINE |
Check if element arr [ i ] is an autobiographical number | if ( isAutoBiographyNum ( arr [ i ] ) ) : NEW_LINE |
Increment the current length | current_length += 1 ; NEW_LINE else : NEW_LINE current_length = 0 ; NEW_LINE |
Update max_length value | max_length = max ( max_length , current_length ) ; NEW_LINE |
Return the final result | return max_length ; NEW_LINE |
Driver code | if __name__ == " _ _ main _ _ " : NEW_LINE INDENT arr = [ 21200 , 1 , 1303 , 1210 , 2020 ] ; NEW_LINE n = len ( arr ) ; NEW_LINE print ( checkArray ( arr , n ) ) ; NEW_LINE DEDENT |
Python3 implementation of nodes at prime height in the given tree | MAX = 100000 NEW_LINE graph = [ [ ] for i in range ( MAX + 1 ) ] NEW_LINE |
To store Prime Numbers | Prime = [ True for i in range ( MAX + 1 ) ] NEW_LINE |
To store height of each node | height = [ 0 for i in range ( MAX + 1 ) ] NEW_LINE |
Function to find the prime numbers till 10 ^ 5 | def SieveOfEratosthenes ( ) : NEW_LINE INDENT Prime [ 0 ] = Prime [ 1 ] = False NEW_LINE i = 2 NEW_LINE while i * i <= MAX : NEW_LINE DEDENT |
Traverse all multiple of i and make it false | if ( Prime [ i ] ) : NEW_LINE INDENT for j in range ( 2 * i , MAX , i ) : NEW_LINE INDENT Prime [ j ] = False NEW_LINE DEDENT DEDENT i += 1 NEW_LINE |
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