Find all the possible remainders when N is divided by all positive integers from 1 to N + 1 | Python3 implementation of the approach ; Function to find all the distinct remainders when n is divided by all the elements from the range [ 1 , n + 1 ] ; Set will be used to store the remainders in order to eliminate duplicates ; Find the remainders ; Print the contents of the set ; Driver code
from math import ceil , floor , sqrt NEW_LINE def findRemainders ( n ) : NEW_LINE INDENT vc = dict ( ) NEW_LINE for i in range ( 1 , ceil ( sqrt ( n ) ) + 1 ) : NEW_LINE INDENT vc [ n // i ] = 1 NEW_LINE DEDENT for i in range ( n // ceil ( sqrt ( n ) ) - 1 , - 1 , - 1 ) : NEW_LINE INDENT vc [ i ] = 1 NEW_LINE DEDENT for it in sorted ( vc ) : NEW_LINE INDENT print ( it , end = " ▁ " ) NEW_LINE DEDENT DEDENT n = 5 NEW_LINE findRemainders ( n ) NEW_LINE