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Traversing the string
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for i in range ( len ( num ) ) : NEW_LINE INDENT if ( i % 2 == 0 ) : NEW_LINE INDENT proOdd = proOdd * int ( num [ i ] ) NEW_LINE DEDENT else : NEW_LINE INDENT proEven = proEven * int ( num [ i ] ) NEW_LINE DEDENT DEDENT if ( proOdd == proEven ) : NEW_LINE INDENT print ( " Yes " ) NEW_LINE DEDENT else : NEW_LINE INDENT print ( " No " ) NEW_LINE DEDENT
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Driver code
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if __name__ == " _ _ main _ _ " : NEW_LINE INDENT n = 4324 NEW_LINE getResult ( n ) NEW_LINE DEDENT
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Function to return the sum of digits of x
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def sumOfDigits ( x ) : NEW_LINE INDENT sum = 0 NEW_LINE while x != 0 : NEW_LINE INDENT sum += x % 10 NEW_LINE x = x // 10 NEW_LINE DEDENT return sum NEW_LINE DEDENT
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Function to return the count of required numbers
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def countNumbers ( l , r ) : NEW_LINE INDENT count = 0 NEW_LINE for i in range ( l , r + 1 ) : NEW_LINE DEDENT
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If i is divisible by 2 and sum of digits of i is divisible by 3
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if i % 2 == 0 and sumOfDigits ( i ) % 3 == 0 : NEW_LINE INDENT count += 1 NEW_LINE DEDENT
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Return the required count
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return count NEW_LINE
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Driver code
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l = 1000 ; r = 6000 NEW_LINE print ( countNumbers ( l , r ) ) NEW_LINE
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Function to find the sum of minimum of all subarrays
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def findMinSum ( arr , n ) : NEW_LINE INDENT sum = 0 NEW_LINE for i in range ( 0 , n ) : NEW_LINE INDENT sum += arr [ i ] * ( n - i ) NEW_LINE DEDENT return sum NEW_LINE DEDENT
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Driver code
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arr = [ 3 , 5 , 7 , 8 ] NEW_LINE n = len ( arr ) NEW_LINE print ( findMinSum ( arr , n ) ) NEW_LINE
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Function to return the max length of the sub - array that have the maximum average ( average value of the elements )
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def maxLenSubArr ( a , n ) : NEW_LINE INDENT cm , Max = 1 , 0 NEW_LINE DEDENT
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Finding the maximum value
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for i in range ( 0 , n ) : NEW_LINE INDENT if a [ i ] > Max : NEW_LINE INDENT Max = a [ i ] NEW_LINE DEDENT DEDENT i = 0 NEW_LINE while i < n - 1 : NEW_LINE INDENT count = 1 NEW_LINE DEDENT
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If consecutive maximum found
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if a [ i ] == a [ i + 1 ] and a [ i ] == Max : NEW_LINE
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Find the max length of consecutive max
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for j in range ( i + 1 , n ) : NEW_LINE INDENT if a [ j ] == Max : NEW_LINE INDENT count += 1 NEW_LINE i += 1 NEW_LINE DEDENT else : NEW_LINE INDENT break NEW_LINE DEDENT DEDENT if count > cm : NEW_LINE INDENT cm = count NEW_LINE DEDENT else : NEW_LINE i += 1 NEW_LINE i += 1 NEW_LINE return cm NEW_LINE
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Driver code
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if __name__ == " _ _ main _ _ " : NEW_LINE INDENT arr = [ 6 , 1 , 6 , 6 , 0 ] NEW_LINE n = len ( arr ) NEW_LINE print ( maxLenSubArr ( arr , n ) ) NEW_LINE DEDENT
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Function to return the minimized sum
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def minSum ( arr , n , x ) : NEW_LINE INDENT Sum = 0 NEW_LINE DEDENT
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To store the largest element from the array which is divisible by x
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largestDivisible , minimum = - 1 , arr [ 0 ] NEW_LINE for i in range ( 0 , n ) : NEW_LINE
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Sum of array elements before performing any operation
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Sum += arr [ i ] NEW_LINE
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If current element is divisible by x and it is maximum so far
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if ( arr [ i ] % x == 0 and largestDivisible < arr [ i ] ) : NEW_LINE INDENT largestDivisible = arr [ i ] NEW_LINE DEDENT
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Update the minimum element
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if arr [ i ] < minimum : NEW_LINE INDENT minimum = arr [ i ] NEW_LINE DEDENT
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If no element can be reduced then there 's no point in performing the operation as we will end up increasing the sum when an element is multiplied by x
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if largestDivisible == - 1 : NEW_LINE INDENT return Sum NEW_LINE DEDENT
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Subtract the chosen elements from the sum and then add their updated values
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sumAfterOperation = ( Sum - minimum - largestDivisible + ( x * minimum ) + ( largestDivisible // x ) ) NEW_LINE
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Return the minimized sum
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return min ( Sum , sumAfterOperation ) NEW_LINE
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Driver code
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if __name__ == " _ _ main _ _ " : NEW_LINE INDENT arr = [ 5 , 5 , 5 , 5 , 6 ] NEW_LINE n = len ( arr ) NEW_LINE x = 3 NEW_LINE print ( minSum ( arr , n , x ) ) NEW_LINE DEDENT
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Function to return the maximum bitwise AND possible among all the possible pairs
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def maxAND ( L , R ) : NEW_LINE
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If there is only a single value in the range [ L , R ]
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if ( L == R ) : NEW_LINE INDENT return L ; NEW_LINE DEDENT
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If there are only two values in the range [ L , R ]
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elif ( ( R - L ) == 1 ) : NEW_LINE INDENT return ( R & L ) ; NEW_LINE DEDENT else : NEW_LINE INDENT if ( ( ( R - 1 ) & R ) > ( ( R - 2 ) & ( R - 1 ) ) ) : NEW_LINE INDENT return ( ( R - 1 ) & R ) ; NEW_LINE DEDENT else : NEW_LINE INDENT return ( ( R - 2 ) & ( R - 1 ) ) ; NEW_LINE DEDENT DEDENT
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Driver code
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L = 1 ; NEW_LINE R = 632 ; NEW_LINE print ( maxAND ( L , R ) ) ; NEW_LINE
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Function to check whether the number is a special prime or not
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def checkSpecialPrime ( sieve , num ) : NEW_LINE
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While number is not equal to zero
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while ( num ) : NEW_LINE
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If the number is not prime return false .
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if ( sieve [ num ] == False ) : NEW_LINE INDENT return False NEW_LINE DEDENT
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Else remove the last digit by dividing the number by 10.
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num = int ( num / 10 ) NEW_LINE
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If the number has become zero then the number is special prime , hence return true
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return True NEW_LINE
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Function to find the Smallest Special Prime which is greater than or equal to a given number
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def findSpecialPrime ( N ) : NEW_LINE INDENT sieve = [ True for i in range ( N * 10 + 1 ) ] NEW_LINE sieve [ 0 ] = False NEW_LINE sieve [ 1 ] = False NEW_LINE DEDENT
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sieve for finding the Primes
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for i in range ( 2 , N * 10 + 1 ) : NEW_LINE INDENT if ( sieve [ i ] ) : NEW_LINE INDENT for j in range ( i * i , N * 10 + 1 , i ) : NEW_LINE INDENT sieve [ j ] = False NEW_LINE DEDENT DEDENT DEDENT
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There is always an answer possible
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while ( True ) : NEW_LINE
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Checking if the number is a special prime or not
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if ( checkSpecialPrime ( sieve , N ) ) : NEW_LINE
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If yes print the number and break the loop .
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print ( N ) NEW_LINE break NEW_LINE
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Else increment the number .
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else : NEW_LINE INDENT N += 1 NEW_LINE DEDENT
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Driver code
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if __name__ == ' _ _ main _ _ ' : NEW_LINE INDENT N = 379 NEW_LINE findSpecialPrime ( N ) NEW_LINE N = 100 NEW_LINE findSpecialPrime ( N ) NEW_LINE DEDENT
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Python3 implementation of the approach
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import sys NEW_LINE
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Function to return the minimum number of moves required to make n divisible by 25
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def minMoves ( n ) : NEW_LINE
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Convert number into string
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s = str ( n ) ; NEW_LINE
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To store required answer
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ans = sys . maxsize ; NEW_LINE
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Length of the string
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len1 = len ( s ) ; NEW_LINE
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To check all possible pairs
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for i in range ( len1 ) : NEW_LINE INDENT for j in range ( len1 ) : NEW_LINE INDENT if ( i == j ) : NEW_LINE INDENT continue ; NEW_LINE DEDENT DEDENT DEDENT
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Make a duplicate string
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t = s ; NEW_LINE cur = 0 ; NEW_LINE
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Number of swaps required to place ith digit in last position
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list1 = list ( t ) ; NEW_LINE for k in range ( i , len1 - 1 ) : NEW_LINE INDENT e = list1 [ k ] ; NEW_LINE list1 [ k ] = list1 [ k + 1 ] ; NEW_LINE list1 [ k + 1 ] = e ; NEW_LINE cur += 1 ; NEW_LINE DEDENT t = ' ' . join ( list1 ) ; NEW_LINE
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Number of swaps required to place jth digit in 2 nd last position
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list1 = list ( t ) ; NEW_LINE for k in range ( j - ( j > i ) , len1 - 2 ) : NEW_LINE INDENT e = list1 [ k ] ; NEW_LINE list1 [ k ] = list1 [ k + 1 ] ; NEW_LINE list1 [ k + 1 ] = e ; NEW_LINE cur += 1 ; NEW_LINE DEDENT t = ' ' . join ( list1 ) ; NEW_LINE
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Find first non zero digit
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pos = - 1 ; NEW_LINE for k in range ( len1 ) : NEW_LINE INDENT if ( t [ k ] != '0' ) : NEW_LINE INDENT pos = k ; NEW_LINE break ; NEW_LINE DEDENT DEDENT
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Place first non zero digit in the first position
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for k in range ( pos , 0 , - 1 ) : NEW_LINE INDENT e = list1 [ k ] ; NEW_LINE list1 [ k ] = list1 [ k + 1 ] ; NEW_LINE list1 [ k + 1 ] = e ; NEW_LINE cur += 1 ; NEW_LINE DEDENT t = ' ' . join ( list1 ) ; NEW_LINE
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Convert string to number
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nn = int ( t ) ; NEW_LINE
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If this number is divisible by 25 then cur is one of the possible answer
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if ( nn % 25 == 0 ) : NEW_LINE INDENT ans = min ( ans , cur ) ; NEW_LINE DEDENT
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If not possible
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if ( ans == sys . maxsize ) : NEW_LINE INDENT return - 1 ; NEW_LINE DEDENT return ans ; NEW_LINE
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Driver code
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n = 509201 ; NEW_LINE print ( minMoves ( n ) ) ; NEW_LINE
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Function to return the required number
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def getMaxNum ( a , b , c ) : NEW_LINE
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If b % c = 0 then b is the required number
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if ( b % c == 0 ) : NEW_LINE INDENT return b NEW_LINE DEDENT
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Else get the maximum multiple of c smaller than b
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x = ( ( b // c ) * c ) NEW_LINE if ( x >= a and x <= b ) : NEW_LINE INDENT return x NEW_LINE DEDENT else : NEW_LINE INDENT return - 1 NEW_LINE DEDENT
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Driver code
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a , b , c = 2 , 10 , 3 NEW_LINE print ( getMaxNum ( a , b , c ) ) NEW_LINE
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Function to return the number of pairs ( x , y ) such that x < y
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def getPairs ( a ) : NEW_LINE
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Length of the array
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n = len ( a ) NEW_LINE
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Calculate the number of valid pairs
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count = ( n * ( n - 1 ) ) // 2 NEW_LINE
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Return the count of valid pairs
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return count NEW_LINE
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Driver code
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a = [ 2 , 4 , 3 , 1 ] NEW_LINE print ( getPairs ( a ) ) NEW_LINE
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Function to return the count of total positions the Bishop can visit in a single move
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def countSquares ( row , column ) : NEW_LINE
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Count top left squares
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topLeft = min ( row , column ) - 1 NEW_LINE
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Count bottom right squares
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bottomRight = 8 - max ( row , column ) NEW_LINE
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Count top right squares
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topRight = min ( row , 9 - column ) - 1 NEW_LINE
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Count bottom left squares
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bottomLeft = 8 - max ( row , 9 - column ) NEW_LINE
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Return total count
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return ( topLeft + topRight + bottomRight + bottomLeft ) NEW_LINE
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Bishop 's Position
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row = 4 NEW_LINE column = 4 NEW_LINE print ( countSquares ( row , column ) ) NEW_LINE
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Function that return true if the Bishop can take down the pawn
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def canTakeDown ( bishopX , bishopY , pawnX , pawnY ) : NEW_LINE
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If pawn is at angle 45 or 225 degree from bishop 's Position
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if ( pawnX - bishopX == pawnY - bishopY ) : NEW_LINE INDENT return True NEW_LINE DEDENT
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If pawn is at angle 135 or 315 degree from bishop 's Position
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elif ( - pawnX + bishopX == pawnY - bishopY ) : NEW_LINE INDENT return True NEW_LINE DEDENT else : NEW_LINE INDENT return False NEW_LINE DEDENT
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Bishop 's Position
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bishopX = 5 NEW_LINE bishopY = 5 NEW_LINE
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Pawn 's Position
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pawnX = 1 NEW_LINE pawnY = 1 NEW_LINE if ( canTakeDown ( bishopX , bishopY , pawnX , pawnY ) ) : NEW_LINE INDENT print ( " Yes " ) NEW_LINE DEDENT else : NEW_LINE INDENT print ( " No " ) NEW_LINE DEDENT
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Python3 program to find maximum number moves possible
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N = 1000005 NEW_LINE
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To store number of prime factors of each number
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primeFactors = [ 0 ] * N ; NEW_LINE
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Function to find number of prime factors of each number
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def findPrimeFactors ( ) : NEW_LINE INDENT for i in range ( 2 , N ) : NEW_LINE DEDENT
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if i is a prime number
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if ( primeFactors [ i ] == 0 ) : NEW_LINE INDENT for j in range ( i , N , i ) : NEW_LINE DEDENT
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increase value by one from it 's preveious multiple
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primeFactors [ j ] = primeFactors [ j // i ] + 1 ; NEW_LINE
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make prefix sum this will be helpful for multiple test cases
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for i in range ( 1 , N ) : NEW_LINE INDENT primeFactors [ i ] += primeFactors [ i - 1 ] ; NEW_LINE DEDENT
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Driver Code
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if __name__ == " _ _ main _ _ " : NEW_LINE
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Generate primeFactors array
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findPrimeFactors ( ) ; NEW_LINE a = 6 ; b = 3 ; NEW_LINE
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required answer
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print ( primeFactors [ a ] - primeFactors [ b ] ) ; NEW_LINE
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Python 3 implementation of the above approach
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from math import floor , pow NEW_LINE import sys NEW_LINE
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Function to return digit sum
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def digitSum ( n ) : NEW_LINE INDENT ans = 0 ; NEW_LINE while ( n ) : NEW_LINE INDENT ans += n % 10 ; NEW_LINE n = int ( n / 10 ) ; NEW_LINE DEDENT return ans NEW_LINE DEDENT
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Function to find out the smallest integer
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def findInt ( n , m ) : NEW_LINE INDENT minDigit = floor ( m / 9 ) NEW_LINE DEDENT
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Start of the iterator ( Smallest multiple of n )
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start = ( int ( pow ( 10 , minDigit ) ) - int ( pow ( 10 , minDigit ) ) % n ) NEW_LINE while ( start < sys . maxsize ) : NEW_LINE INDENT if ( digitSum ( start ) == m ) : NEW_LINE INDENT return start NEW_LINE DEDENT else : NEW_LINE INDENT start += n NEW_LINE DEDENT DEDENT return - 1 NEW_LINE
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Driver code
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if __name__ == ' _ _ main _ _ ' : NEW_LINE INDENT n = 13 NEW_LINE m = 32 NEW_LINE print ( findInt ( n , m ) ) NEW_LINE DEDENT
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Python 3 implementation of the above approach
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from math import sqrt NEW_LINE
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Function to find the smallest divisor
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def smallestDivisor ( n ) : NEW_LINE INDENT mx = int ( sqrt ( n ) ) NEW_LINE for i in range ( 2 , mx + 1 , 1 ) : NEW_LINE INDENT if ( n % i == 0 ) : NEW_LINE INDENT return i NEW_LINE DEDENT DEDENT return n NEW_LINE DEDENT
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Function to find the maximum sum
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def maxSum ( n ) : NEW_LINE INDENT res = n NEW_LINE while ( n > 1 ) : NEW_LINE INDENT divi = smallestDivisor ( n ) NEW_LINE n = int ( n / divi ) NEW_LINE res += n NEW_LINE DEDENT return res NEW_LINE DEDENT
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Driver Code
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if __name__ == ' _ _ main _ _ ' : NEW_LINE INDENT n = 34 NEW_LINE print ( maxSum ( n ) ) NEW_LINE DEDENT
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Function that returns true if all the elements of the array can be made equal with the given operation
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def isPossible ( n , k , arr ) : NEW_LINE
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To store the sum of the array elements and the maximum element from the array
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sum = arr [ 0 ] NEW_LINE maxVal = arr [ 0 ] ; NEW_LINE for i in range ( 1 , n ) : NEW_LINE INDENT sum += arr [ i ] NEW_LINE maxVal = max ( maxVal , arr [ i ] ) NEW_LINE DEDENT if ( int ( maxVal ) > int ( ( sum + k ) / n ) ) : NEW_LINE INDENT return False NEW_LINE DEDENT return True NEW_LINE
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Driver code
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if __name__ == ' _ _ main _ _ ' : NEW_LINE INDENT k = 8 NEW_LINE arr = [ 1 , 2 , 3 , 4 ] NEW_LINE n = len ( arr ) NEW_LINE if ( isPossible ( n , k , arr ) ) : NEW_LINE INDENT print ( " Yes " ) NEW_LINE DEDENT else : NEW_LINE INDENT print ( " No " ) NEW_LINE DEDENT DEDENT
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Python3 implementation of the approach
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from math import * NEW_LINE
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Function to return the maximum value of ( x + y + z ) such that ( ax + by + cz = n )
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def maxResult ( n , a , b , c ) : NEW_LINE INDENT maxVal = 0 NEW_LINE DEDENT
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i represents possible values of a * x
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for i in range ( 0 , n + 1 , a ) : NEW_LINE
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j represents possible values of b * y
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for j in range ( 0 , n - i + 1 , b ) : NEW_LINE INDENT z = ( n - ( i + j ) ) / c NEW_LINE DEDENT
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