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Function to find two numbers whose sum is N and do not contain any digit as k | def findAandB ( n , k ) : NEW_LINE INDENT flag = 0 NEW_LINE DEDENT |
Check every number i and ( n - i ) | for i in range ( 1 , n ) : NEW_LINE |
Check if i and n - i doesn 't contain k in them print i and n-i | if str ( i ) . count ( chr ( k + 48 ) ) == 0 and str ( n - i ) . count ( chr ( k + 48 ) ) == 0 : NEW_LINE INDENT print ( i , n - i ) NEW_LINE flag = 1 NEW_LINE break NEW_LINE DEDENT |
check if flag is 0 then print - 1 | if ( flag == 0 ) : NEW_LINE INDENT print ( - 1 ) NEW_LINE DEDENT |
Driver Code | if __name__ == ' _ _ main _ _ ' : NEW_LINE |
Given N and K | N = 100 NEW_LINE K = 0 NEW_LINE |
Function Call | findAandB ( N , K ) NEW_LINE |
Function to find the value of P * Q ^ - 1 mod 998244353 | def calculate ( p , q ) : NEW_LINE INDENT mod = 998244353 NEW_LINE expo = 0 NEW_LINE expo = mod - 2 NEW_LINE DEDENT |
Loop to find the value until the expo is not zero | while ( expo ) : NEW_LINE |
Multiply p with q if expo is odd | if ( expo & 1 ) : NEW_LINE INDENT p = ( p * q ) % mod NEW_LINE DEDENT q = ( q * q ) % mod NEW_LINE |
Reduce the value of expo by 2 | expo >>= 1 NEW_LINE return p NEW_LINE |
Driver code | if __name__ == ' _ _ main _ _ ' : NEW_LINE INDENT p = 1 NEW_LINE q = 4 NEW_LINE DEDENT |
Function call | print ( calculate ( p , q ) ) NEW_LINE |
Function that print two numbers with the sum X and maximum possible LCM | def maxLCMWithGivenSum ( X ) : NEW_LINE |
If X is odd | if X % 2 != 0 : NEW_LINE INDENT A = X / 2 NEW_LINE B = X / 2 + 1 NEW_LINE DEDENT |
If X is even | else : NEW_LINE |
If floor ( X / 2 ) is even | if ( X / 2 ) % 2 == 0 : NEW_LINE INDENT A = X / 2 - 1 NEW_LINE B = X / 2 + 1 NEW_LINE DEDENT |
If floor ( X / 2 ) is odd | else : NEW_LINE INDENT A = X / 2 - 2 NEW_LINE B = X / 2 + 2 NEW_LINE DEDENT |
Print the result | print ( int ( A ) , int ( B ) , end = " ▁ " ) NEW_LINE |
Driver Code | if __name__ == ' _ _ main _ _ ' : NEW_LINE |
Given Number | X = 30 NEW_LINE |
Function call | maxLCMWithGivenSum ( X ) NEW_LINE |
Function to find the longest subarray with sum is not divisible by k | def MaxSubarrayLength ( arr , n , k ) : NEW_LINE |
left is the index of the leftmost element that is not divisible by k | left = - 1 NEW_LINE |
sum of the array | sum = 0 NEW_LINE for i in range ( n ) : NEW_LINE |
Find the element that is not multiple of k | if ( ( arr [ i ] % k ) != 0 ) : NEW_LINE |
left = - 1 means we are finding the leftmost element that is not divisible by k | if ( left == - 1 ) : NEW_LINE INDENT left = i NEW_LINE DEDENT |
Updating the rightmost element | right = i NEW_LINE |
Update the sum of the array up to the index i | sum += arr [ i ] NEW_LINE |
Check if the sum of the array is not divisible by k , then return the size of array | if ( ( sum % k ) != 0 ) : NEW_LINE INDENT return n NEW_LINE DEDENT |
All elements of array are divisible by k , then no such subarray possible so return - 1 | elif ( left == - 1 ) : NEW_LINE INDENT return - 1 NEW_LINE DEDENT else : NEW_LINE |
length of prefix elements that can be removed | prefix_length = left + 1 NEW_LINE |
length of suffix elements that can be removed | suffix_length = n - right NEW_LINE |
Return the length of subarray after removing the elements which have lesser number of elements | return n - min ( prefix_length , suffix_length ) NEW_LINE |
Driver Code | if __name__ == " _ _ main _ _ " : NEW_LINE INDENT arr = [ 6 , 3 , 12 , 15 ] NEW_LINE n = len ( arr ) NEW_LINE K = 3 NEW_LINE print ( MaxSubarrayLength ( arr , n , K ) ) NEW_LINE DEDENT |
Python3 implementation to find minimum steps to convert X to Y by repeated division and multiplication | def solve ( X , Y ) : NEW_LINE |
Check if X is greater than Y then swap the elements | if ( X > Y ) : NEW_LINE INDENT temp = X NEW_LINE X = Y NEW_LINE Y = temp NEW_LINE DEDENT |
Check if X equals Y | if ( X == Y ) : NEW_LINE INDENT print ( 0 ) NEW_LINE DEDENT elif ( Y % X == 0 ) : NEW_LINE INDENT print ( 1 ) NEW_LINE DEDENT else : NEW_LINE INDENT print ( 2 ) NEW_LINE DEDENT |
Driver code | X = 8 NEW_LINE Y = 13 NEW_LINE solve ( X , Y ) NEW_LINE |
Python3 program for the above approach | from collections import defaultdict NEW_LINE |
Function to count the quadruples | def countQuadraples ( N ) : NEW_LINE |
Counter variable | cnt = 0 NEW_LINE |
Map to store the sum of pair ( a ^ 2 + b ^ 2 ) | m = defaultdict ( int ) NEW_LINE |
Iterate till N | for a in range ( 1 , N + 1 ) : NEW_LINE INDENT for b in range ( 1 , N + 1 ) : NEW_LINE DEDENT |
Calculate a ^ 2 + b ^ 2 | x = a * a + b * b NEW_LINE |
Increment the value in map | m [ x ] += 1 NEW_LINE for c in range ( 1 , N + 1 ) : NEW_LINE for d in range ( 1 , N + 1 ) : NEW_LINE x = c * c + d * d NEW_LINE |
Check if this sum was also in a ^ 2 + b ^ 2 | if x in m : NEW_LINE INDENT cnt += m [ x ] NEW_LINE DEDENT |
Return the count | return cnt NEW_LINE |
Driver Code | if __name__ == " _ _ main _ _ " : NEW_LINE |
Given N | N = 2 NEW_LINE |
Function Call | print ( countQuadraples ( N ) ) NEW_LINE |
function to find the number of pairs satisfying the given cond . | def count_pairs ( a , b , N ) : NEW_LINE |
count variable to store the count of possible pairs | count = 0 ; NEW_LINE |
Nested loop to find out the possible pairs | for i in range ( 0 , N - 1 ) : NEW_LINE INDENT for j in range ( i + 1 , N ) : NEW_LINE DEDENT |
Check if the given condition is satisfied or not . If yes then increment the count . | if ( ( a [ i ] + a [ j ] ) > ( b [ i ] + b [ j ] ) ) : NEW_LINE INDENT count += 1 ; NEW_LINE DEDENT |
Return the count value | return count ; NEW_LINE |
Size of the arrays | N = 5 ; NEW_LINE |
Initialise the arrays | a = [ 1 , 2 , 3 , 4 , 5 ] ; NEW_LINE b = [ 2 , 5 , 6 , 1 , 9 ] ; NEW_LINE |
Python3 program of the above approach | from bisect import bisect_left NEW_LINE |
Function to find the number of pairs . | def numberOfPairs ( a , b , n ) : NEW_LINE |
Array c [ ] where c [ i ] = a [ i ] - b [ i ] | c = [ 0 for i in range ( n ) ] NEW_LINE for i in range ( n ) : NEW_LINE INDENT c [ i ] = a [ i ] - b [ i ] NEW_LINE DEDENT |
Sort the array c | c = sorted ( c ) NEW_LINE |
Initialise answer as 0 | answer = 0 NEW_LINE |
Iterate from index 0 to n - 1 | for i in range ( 1 , n ) : NEW_LINE |
If c [ i ] <= 0 then in the sorted array c [ i ] + c [ pos ] can never greater than 0 where pos < i | if ( c [ i ] <= 0 ) : NEW_LINE INDENT continue NEW_LINE DEDENT |
Find the minimum index such that c [ i ] + c [ j ] > 0 which is equivalent to c [ j ] >= - c [ i ] + 1 | pos = bisect_left ( c , - c [ i ] + 1 ) NEW_LINE |
Add ( i - pos ) to answer | answer += ( i - pos ) NEW_LINE |
Return the answer | return answer NEW_LINE |
Driver code | if __name__ == ' _ _ main _ _ ' : NEW_LINE |
Number of elements in a and b | n = 5 NEW_LINE |
Array a | a = [ 1 , 2 , 3 , 4 , 5 ] NEW_LINE |
Array b | b = [ 2 , 5 , 6 , 1 , 9 ] NEW_LINE print ( numberOfPairs ( a , b , n ) ) NEW_LINE |
Function to find the K - value for every index in the array | def print_h_index ( arr , N ) : NEW_LINE |
Multiset to store the array in the form of red - black tree | ms = [ ] NEW_LINE |
Iterating over the array | for i in range ( N ) : NEW_LINE |
Inserting the current value in the multiset | ms . append ( arr [ i ] ) NEW_LINE ms . sort ( ) NEW_LINE |
Condition to check if the smallest value in the set is less than it 's size | if ( ms [ 0 ] < len ( ms ) ) : NEW_LINE |
Erase the smallest value | ms . pop ( 0 ) NEW_LINE |
h - index value will be the size of the multiset | print ( len ( ms ) , end = ' ▁ ' ) NEW_LINE |
Driver Code | if __name__ == ' _ _ main _ _ ' : NEW_LINE |
Array | arr = [ 9 , 10 , 7 , 5 , 0 , 10 , 2 , 0 ] NEW_LINE |
Size of the array | N = len ( arr ) NEW_LINE |
Function call | print_h_index ( arr , N ) NEW_LINE |
Function to find count of prime | def findPrimes ( arr , n ) : NEW_LINE |
Find maximum value in the array | max_val = max ( arr ) NEW_LINE |
Find and store all prime numbers up to max_val using Sieve Create a boolean array " prime [ 0 . . n ] " . A value in prime [ i ] will finally be false if i is Not a prime , else true . | prime = [ True for i in range ( max_val + 1 ) ] NEW_LINE |
Remaining part of SIEVE | prime [ 0 ] = False NEW_LINE prime [ 1 ] = False NEW_LINE p = 2 NEW_LINE while ( p * p <= max_val ) : NEW_LINE |
If prime [ p ] is not changed , then it is a prime | if ( prime [ p ] == True ) : NEW_LINE |
Update all multiples of p | for i in range ( p * 2 , max_val + 1 , p ) : NEW_LINE INDENT prime [ i ] = False NEW_LINE DEDENT p += 1 NEW_LINE return prime ; NEW_LINE |
Function to print Non - repeating primes | def nonRepeatingPrimes ( arr , n ) : NEW_LINE |
Precompute primes using Sieve | prime = findPrimes ( arr , n ) ; NEW_LINE |
Create HashMap to store frequency of prime numbers | mp = dict ( ) NEW_LINE |
Traverse through array elements and Count frequencies of all primes | for i in range ( n ) : NEW_LINE INDENT if ( prime [ arr [ i ] ] ) : NEW_LINE INDENT if ( arr [ i ] in mp ) : NEW_LINE INDENT mp [ arr [ i ] ] += 1 NEW_LINE DEDENT else : NEW_LINE INDENT mp [ arr [ i ] ] = 1 NEW_LINE DEDENT DEDENT DEDENT |
Traverse through map and print non repeating primes | for entry in mp . keys ( ) : NEW_LINE INDENT if ( mp [ entry ] == 1 ) : NEW_LINE INDENT print ( entry ) ; NEW_LINE DEDENT DEDENT |
Driver code | if __name__ == ' _ _ main _ _ ' : NEW_LINE INDENT arr = [ 2 , 3 , 4 , 6 , 7 , 9 , 7 , 23 , 21 , 3 ] NEW_LINE n = len ( arr ) NEW_LINE nonRepeatingPrimes ( arr , n ) ; NEW_LINE DEDENT |
Function to generate prefix product array | def prefixProduct ( a , n ) : NEW_LINE |
Update the array with the product of prefixes | for i in range ( 1 , n ) : NEW_LINE INDENT a [ i ] = a [ i ] * a [ i - 1 ] ; NEW_LINE DEDENT |
Print the array | for j in range ( 0 , n ) : NEW_LINE INDENT print ( a [ j ] , end = " , ▁ " ) ; NEW_LINE DEDENT return 0 ; NEW_LINE |
Driver Code | arr = [ 2 , 4 , 6 , 5 , 10 ] ; NEW_LINE N = len ( arr ) ; NEW_LINE prefixProduct ( arr , N ) ; NEW_LINE |
Function to find the number of ways to distribute N items among 3 people | def countWays ( N ) : NEW_LINE |