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"Python3 implementation of the above approach"
"def maxPresum ( a , b ) : NEW_LINE"
"Stores the maximum prefix sum of the array A [ ]"
"X = max ( a [ 0 ] , 0 ) NEW_LINE"
"Traverse the array A [ ]"
"for i in range ( 1 , len ( a ) ) : NEW_LINE INDENT a [ i ] += a [ i - 1 ] NEW_LINE X = max ( X , a [ i ] ) NEW_LINE DEDENT"
"Stores the maximum prefix sum of the array B [ ]"
"Y = max ( b [ 0 ] , 0 ) NEW_LINE"
"Traverse the array B [ ]"
"for i in range ( 1 , len ( b ) ) : NEW_LINE INDENT b [ i ] += b [ i - 1 ] NEW_LINE Y = max ( Y , b [ i ] ) NEW_LINE DEDENT return X + Y NEW_LINE"
"Driver code"
"A = [ 2 , - 1 , 4 , - 5 ] NEW_LINE B = [ 4 , - 3 , 12 , 4 , - 3 ] NEW_LINE print ( maxPresum ( A , B ) ) NEW_LINE"
"Python3 program for the above approach"
"import math NEW_LINE"
"Function to check if N can be represented as sum of two perfect cubes or not"
"def sumOfTwoCubes ( n ) : NEW_LINE INDENT lo = 1 NEW_LINE hi = round ( math . pow ( n , 1 / 3 ) ) NEW_LINE while ( lo <= hi ) : NEW_LINE INDENT curr = ( lo * lo * lo + hi * hi * hi ) NEW_LINE if ( curr == n ) : NEW_LINE DEDENT DEDENT"
"If it is same return true ;"
"return True NEW_LINE if ( curr < n ) : NEW_LINE"
"If the curr smaller than n increment the lo"
"lo += 1 NEW_LINE else : NEW_LINE"
"If the curr is greater than curr decrement the hi"
"hi -= 1 NEW_LINE return False NEW_LINE"
"Driver Code"
"N = 28 NEW_LINE"
"Function call to check if N can be represented as sum of two perfect cubes or not"
"if ( sumOfTwoCubes ( N ) ) : NEW_LINE INDENT print ( " True " ) NEW_LINE DEDENT else : NEW_LINE INDENT print ( " False " ) NEW_LINE DEDENT"
"Python3 program for the above approach"
"sieve = [ 1 ] * ( 1000000 + 1 ) NEW_LINE"
"Function to generate all prime numbers upto 10 ^ 6"
"def sieveOfPrimes ( ) : NEW_LINE"
"Initialize sieve [ ] as 1"
"global sieve NEW_LINE N = 1000000 NEW_LINE"
"Iterate over the range [ 2 , N ]"
"for i in range ( 2 , N + 1 ) : NEW_LINE INDENT if i * i > N : NEW_LINE INDENT break NEW_LINE DEDENT DEDENT"
"If current element is non - prime"
"if ( sieve [ i ] == 0 ) : NEW_LINE INDENT continue NEW_LINE DEDENT"
"Make all multiples of i as 0"
"for j in range ( i * i , N + 1 , i ) : NEW_LINE INDENT sieve [ j ] = 0 NEW_LINE DEDENT"
"Function to construct an array A [ ] satisfying the given conditions"
"def getArray ( arr , N ) : NEW_LINE INDENT global sieve NEW_LINE DEDENT"
"Stores the resultant array"
"A = [ 0 ] * N NEW_LINE"
"Stores all prime numbers"
"v = [ ] NEW_LINE"
"Sieve of Erastosthenes"
"sieveOfPrimes ( ) NEW_LINE for i in range ( 2 , int ( 1e5 ) + 1 ) : NEW_LINE"
"Append the integer i if it is a prime"
"if ( sieve [ i ] ) : NEW_LINE INDENT v . append ( i ) NEW_LINE DEDENT"
"Indicates current position in list of prime numbers"
"j = 0 NEW_LINE"
"Traverse the array arr [ ]"
"for i in range ( N ) : NEW_LINE INDENT ind = arr [ i ] NEW_LINE DEDENT"
"If already filled with another prime number"
"if ( A [ i ] != 0 ) : NEW_LINE INDENT continue NEW_LINE DEDENT"
"If A [ i ] is not filled but A [ ind ] is filled"
"elif ( A [ ind ] != 0 ) : NEW_LINE"
"Store A [ i ] = A [ ind ]"
"A [ i ] = A [ ind ] NEW_LINE"
"If none of them were filled"
"else : NEW_LINE"
"To make sure A [ i ] does not affect other values , store next prime number"
"prime = v [ j ] NEW_LINE A [ i ] = prime NEW_LINE A [ ind ] = A [ i ] NEW_LINE j += 1 NEW_LINE"
"Print the resultant array"
"for i in range ( N ) : NEW_LINE INDENT print ( A [ i ] , end = " ▁ " ) NEW_LINE DEDENT"
"Driver Code"
"if __name__ == ' _ _ main _ _ ' : NEW_LINE INDENT arr = [ 4 , 1 , 2 , 3 , 4 ] NEW_LINE N = len ( arr ) NEW_LINE DEDENT"
"Function Call"
"getArray ( arr , N ) NEW_LINE"
"Function to find Nth number in base 9"
"def findNthNumber ( N ) : NEW_LINE"
"Stores the Nth number"
"result = 0 NEW_LINE p = 1 NEW_LINE"
"Iterate while N is greater than 0"
"while ( N > 0 ) : NEW_LINE"
"Update result"
"result += ( p * ( N % 9 ) ) NEW_LINE"
"Divide N by 9"
"N = N // 9 NEW_LINE"
"Multiply p by 10"
"p = p * 10 NEW_LINE"
"Return result"
"return result NEW_LINE"
"Driver Code"
"if __name__ == ' _ _ main _ _ ' : NEW_LINE INDENT N = 9 NEW_LINE print ( findNthNumber ( N ) ) NEW_LINE DEDENT"
"Python3 implementation of the approach"
"import math NEW_LINE"
"Function to check if the integer A is a rotation of the integer B"
"def check ( A , B ) : NEW_LINE INDENT if ( A == B ) : NEW_LINE INDENT return 1 NEW_LINE DEDENT DEDENT"
"Stores the count of digits in A"
"dig1 = math . floor ( math . log10 ( A ) + 1 ) NEW_LINE"
"Stores the count of digits in B"
"dig2 = math . floor ( math . log10 ( B ) + 1 ) NEW_LINE"
"If dig1 not equal to dig2"
"if ( dig1 != dig2 ) : NEW_LINE INDENT return 0 NEW_LINE DEDENT temp = A NEW_LINE while ( True ) : NEW_LINE"
"Stores position of first digit"
"power = pow ( 10 , dig1 - 1 ) NEW_LINE"
"Stores the first digit"
"firstdigit = A // power NEW_LINE"
"Rotate the digits of the integer"
"A = A - firstdigit * power NEW_LINE A = A * 10 + firstdigit NEW_LINE"
"If A is equal to B"
"if ( A == B ) : NEW_LINE INDENT return 1 NEW_LINE DEDENT"
"If A is equal to the initial value of integer A"
"if ( A == temp ) : NEW_LINE INDENT return 0 NEW_LINE DEDENT"
"Driver code"
"A , B = 967 , 679 NEW_LINE if ( check ( A , B ) ) : NEW_LINE INDENT print ( " Yes " ) NEW_LINE DEDENT else : NEW_LINE INDENT print ( " No " ) NEW_LINE DEDENT"
"Function to count the number of unique quadruples from an array that satisfies the given condition"
"def sameProductQuadruples ( nums , N ) : NEW_LINE"
"Hashmap to store the product of pairs"
"umap = { } ; NEW_LINE"
"Store the count of required quadruples"
"res = 0 ; NEW_LINE"
"Traverse the array arr [ ] and generate all possible pairs"
"for i in range ( N ) : NEW_LINE INDENT for j in range ( i + 1 , N ) : NEW_LINE DEDENT"
"Store their product"
"prod = nums [ i ] * nums [ j ] ; NEW_LINE if prod in umap : NEW_LINE"
"Pair ( a , b ) can be used to generate 8 unique permutations with another pair ( c , d )"
"res += 8 * umap [ prod ] ; NEW_LINE"
"Increment umap [ prod ] by 1"
"umap [ prod ] += 1 ; NEW_LINE else : NEW_LINE umap [ prod ] = 1 NEW_LINE"
"Print the result"
"print ( res ) ; NEW_LINE"
"Driver Code"
"if __name__ == " _ _ main _ _ " : NEW_LINE INDENT arr = [ 2 , 3 , 4 , 6 ] ; NEW_LINE N = len ( arr ) ; NEW_LINE sameProductQuadruples ( arr , N ) ; NEW_LINE DEDENT"
"Python3 implementation of the above Approach"
"MOD = 1000000007 NEW_LINE"
"Iterative Function to calculate ( x ^ y ) % p in O ( log y )"
"def power ( x , y , p = MOD ) : NEW_LINE"
"Initialize Result"
"res = 1 NEW_LINE"
"Update x if x >= MOD to avoid multiplication overflow"
"x = x % p NEW_LINE while ( y > 0 ) : NEW_LINE"
"If y is odd , multiply x with result"
"if ( y & 1 ) : NEW_LINE INDENT res = ( res * x ) % p NEW_LINE DEDENT"
"y = y / 2"
"y = y >> 1 NEW_LINE"
"Change x to x ^ 2"
"x = ( x * x ) % p NEW_LINE return res NEW_LINE"
"Utility function to find the Total Number of Ways"
"def totalWays ( N , M ) : NEW_LINE"
"Number of Even Indexed Boxes"
"X = N // 2 NEW_LINE"
"Number of partitions of Even Indexed Boxes"
"S = ( X * ( X + 1 ) ) % MOD NEW_LINE"
"Number of ways to distribute objects"
"print ( power ( S , M , MOD ) ) NEW_LINE"
"Driver Code"
"if __name__ == ' _ _ main _ _ ' : NEW_LINE"
"N = number of boxes M = number of distinct objects"
"N , M = 5 , 2 NEW_LINE"
"Function call to get Total Number of Ways"
"totalWays ( N , M ) NEW_LINE"
"Function to check if the graph constructed from given array contains a cycle or not"
"def isCycleExists ( arr , N ) : NEW_LINE INDENT valley = 0 NEW_LINE DEDENT"
"Traverse the array"
"for i in range ( 1 , N ) : NEW_LINE"
"If arr [ i ] is less than arr [ i - 1 ] and arr [ i ]"
"if ( arr [ i ] < arr [ i - 1 ] and arr [ i ] < arr [ i + 1 ] ) : NEW_LINE INDENT print ( " Yes " ) NEW_LINE return NEW_LINE DEDENT print ( " No " ) NEW_LINE"
"Driver Code"
"if __name__ == ' _ _ main _ _ ' : NEW_LINE"
"Given array"
"arr = [ 1 , 3 , 2 , 4 , 5 ] NEW_LINE"
"Size of the array"
"N = len ( arr ) NEW_LINE isCycleExists ( arr , N ) NEW_LINE"
"Function to maximize the first array element"
"def getMax ( arr , N , K ) : NEW_LINE"
"Traverse the array"
"for i in range ( 1 , N , 1 ) : NEW_LINE"
"Initialize cur_val to a [ i ]"
"cur_val = arr [ i ] NEW_LINE"
"If all operations are not over yet"
"while ( K >= i ) : NEW_LINE"
"If current value is greater than zero"
"if ( cur_val > 0 ) : NEW_LINE"
"Incrementing first element of array by 1"
"arr [ 0 ] = arr [ 0 ] + 1 NEW_LINE"
"Decrementing current value of array by 1"
"cur_val = cur_val - 1 NEW_LINE"
"Decrementing number of operations by i"
"K = K - i NEW_LINE"
"If current value is zero , then break"
"else : NEW_LINE INDENT break NEW_LINE DEDENT"
"Print first array element"
"print ( arr [ 0 ] ) NEW_LINE"
"Driver Code"
"if __name__ == ' _ _ main _ _ ' : NEW_LINE"
"Given array"
"arr = [ 1 , 0 , 3 , 2 ] NEW_LINE"
"Size of the array"
"N = len ( arr ) NEW_LINE"
"Given K"
"K = 5 NEW_LINE"
"Prints the maximum possible value of the first array element"
"getMax ( arr , N , K ) NEW_LINE"
"Python3 program of the above approach"
"import sys NEW_LINE"
"Function to find the gcd of the two numbers"
"def gcd ( a , b ) : NEW_LINE INDENT if a == 0 : NEW_LINE INDENT return b NEW_LINE DEDENT return gcd ( b % a , a ) NEW_LINE DEDENT"
"Function to find distinct elements in the array by repeatidely inserting the absolute difference of all possible pairs"
"def DistinctValues ( arr , N ) : NEW_LINE"
End of preview (truncated to 100 rows)