Programa para somar duas frações
Experimente no GfG Practice 
Saída
Dadas duas matrizes inteiras um[] e b[] contendo dois inteiros, cada um representando o numerador e o denominador de uma fração, respectivamente. A tarefa é encontrar a soma das duas frações e retornar o numerador e o denominador do resultado.
Exemplos:
Entrada : uma = [1 2] b = [3 2]
Saída : [2 1]
Explicação: 1/2 + 3/2 = 2/1Entrada : uma = [1 3] b = [3 9]
Saída : [2 3]
Explicação: 1/3 + 3/9 = 2/3Entrada : uma = [1 5] b = [3 15]
Saída : [2 5]
Explicação: 1/5 + 3/15 = 2/5
Algoritmo para adicionar duas frações
- Encontre um denominador comum encontrando o LCM (Mínimo Múltiplo Comum) dos dois denominadores.
- Alterar o frações ter o mesmo denominador e adicionar os dois termos.
- Reduza a fração final obtida em sua forma mais simples dividindo o numerador e o denominador pelo seu maior fator comum.
#include using namespace std ; // Function to find gcd of a and b int gcd ( int n1 int n2 ) { if ( n1 == 0 ) return n2 ; return gcd ( n2 % n1 n1 ); } //Function to add two fractions vector < int > addFraction ( vector < int > a vector < int > b ) { vector < int > ans ; // Finding gcd of den1 and den2 int den = gcd ( a [ 1 ] b [ 1 ]); // Denominator of final fraction obtained // finding LCM of den1 and den2 // LCM * GCD = a * b den = ( a [ 1 ] * b [ 1 ]) / den ; // Changing the fractions to have same denominator // Numerator of the final fraction obtained int num = ( a [ 0 ]) * ( den / a [ 1 ]) + ( b [ 0 ]) * ( den / b [ 1 ]); // finding the common factor of numerator and denominator int common_factor = gcd ( num den ); // Converting the result into simpler // fraction by dividing them with common factor den = den / common_factor ; num = num / common_factor ; ans . push_back ( num ); ans . push_back ( den ); return ans ; } int main () { vector < int > a = { 1 2 }; vector < int > b = { 3 2 }; vector < int > ans = addFraction ( a b ); cout < < ans [ 0 ] < < ' ' < < ans [ 1 ]; return 0 ; }
C #include // Function to find gcd of a and b int gcd ( int n1 int n2 ) { if ( n1 == 0 ) return n2 ; return gcd ( n2 % n1 n1 ); } // Function to add two fractions void addFraction ( int a [] int b [] int result []) { // Finding gcd of den1 and den2 int den = gcd ( a [ 1 ] b [ 1 ]); // Denominator of final fraction obtained // finding LCM of den1 and den2 // LCM * GCD = a * b den = ( a [ 1 ] * b [ 1 ]) / den ; // Changing the fractions to have same denominator // Numerator of the final fraction obtained int num = ( a [ 0 ]) * ( den / a [ 1 ]) + ( b [ 0 ]) * ( den / b [ 1 ]); // finding the common factor of numerator and denominator int common_factor = gcd ( num den ); // Converting the result into simpler // fraction by dividing them with common factor den = den / common_factor ; num = num / common_factor ; result [ 0 ] = num ; result [ 1 ] = den ; } int main () { int a [] = { 1 2 };; int b [] = { 3 2 };; int ans [ 2 ]; addFraction ( a b ans ); printf ( '%d %d' ans [ 0 ] ans [ 1 ]); return 0 ; }
Java import java.util.ArrayList ; import java.util.List ; public class Main { // Function to find gcd of a and b public static int gcd ( int n1 int n2 ) { if ( n1 == 0 ) return n2 ; return gcd ( n2 % n1 n1 ); } // Function to add two fractions public static List < Integer > addFraction ( List < Integer > a List < Integer > b ) { List < Integer > ans = new ArrayList <> (); // Finding gcd of den1 and den2 int den = gcd ( a . get ( 1 ) b . get ( 1 )); // Denominator of final fraction obtained // finding LCM of den1 and den2 // LCM * GCD = a * b den = ( a . get ( 1 ) * b . get ( 1 )) / den ; // Changing the fractions to have same denominator // Numerator of the final fraction obtained int num = ( a . get ( 0 )) * ( den / a . get ( 1 )) + ( b . get ( 0 )) * ( den / b . get ( 1 )); // finding the common factor of numerator and denominator int common_factor = gcd ( num den ); // Converting the result into simpler // fraction by dividing them with common factor den = den / common_factor ; num = num / common_factor ; ans . add ( num ); ans . add ( den ); return ans ; } public static void main ( String [] args ) { List < Integer > a = new ArrayList <> (); a . add ( 1 ); a . add ( 2 ); List < Integer > b = new ArrayList <> (); b . add ( 3 ); b . add ( 2 ); List < Integer > ans = addFraction ( a b ); System . out . println ( ans . get ( 0 ) + ' ' + ans . get ( 1 )); } }
Python from math import gcd # Function to add two fractions def addFraction ( a b ): # Finding gcd of den1 and den2 den = gcd ( a [ 1 ] b [ 1 ]) # Denominator of final fraction obtained # finding LCM of den1 and den2 # LCM * GCD = a * b den = ( a [ 1 ] * b [ 1 ]) // den # Changing the fractions to have same denominator # Numerator of the final fraction obtained num = ( a [ 0 ]) * ( den // a [ 1 ]) + ( b [ 0 ]) * ( den // b [ 1 ]) # finding the common factor of numerator and denominator common_factor = gcd ( num den ) # Converting the result into simpler # fraction by dividing them with common factor den //= common_factor num //= common_factor return [ num den ] if __name__ == '__main__' : a = [ 1 2 ] b = [ 3 2 ] ans = addFraction ( a b ) print ( f ' { ans [ 0 ] } { ans [ 1 ] } ' )
C# // Function to find gcd of a and b int gcd ( int n1 int n2 ) { if ( n1 == 0 ) return n2 ; return gcd ( n2 % n1 n1 ); } // Function to add two fractions List < int > addFraction ( List < int > a List < int > b ) { List < int > ans = new List < int > (); // Finding gcd of den1 and den2 int den = gcd ( a [ 1 ] b [ 1 ]); // Denominator of final fraction obtained // finding LCM of den1 and den2 // LCM * GCD = a * b den = ( a [ 1 ] * b [ 1 ]) / den ; // Changing the fractions to have same denominator // Numerator of the final fraction obtained int num = ( a [ 0 ]) * ( den / a [ 1 ]) + ( b [ 0 ]) * ( den / b [ 1 ]); // finding the common factor of numerator and denominator int common_factor = gcd ( num den ); // Converting the result into simpler // fraction by dividing them with common factor den = den / common_factor ; num = num / common_factor ; ans . Add ( num ); ans . Add ( den ); return ans ; } public static void Main () { List < int > a = new List < int > { 1 2 }; List < int > b = new List < int > { 3 2 }; List < int > ans = addFraction ( a b ); Console . WriteLine ( ans [ 0 ] + ' ' + ans [ 1 ]); }
JavaScript // Function to find gcd of a and b function gcd ( n1 n2 ) { if ( n1 === 0 ) return n2 ; return gcd ( n2 % n1 n1 ); } // Function to add two fractions function addFraction ( a b ) { let ans = []; // Finding gcd of den1 and den2 let den = gcd ( a [ 1 ] b [ 1 ]); // Denominator of final fraction obtained // finding LCM of den1 and den2 // LCM * GCD = a * b den = ( a [ 1 ] * b [ 1 ]) / den ; // Changing the fractions to have same denominator // Numerator of the final fraction obtained let num = ( a [ 0 ]) * ( den / a [ 1 ]) + ( b [ 0 ]) * ( den / b [ 1 ]); // finding the common factor of numerator and denominator let common_factor = gcd ( num den ); // Converting the result into simpler // fraction by dividing them with common factor den = den / common_factor ; num = num / common_factor ; ans . push ( num ); ans . push ( den ); return ans ; } let a = [ 1 2 ]; let b = [ 3 2 ]; let ans = addFraction ( a b ); console . log ( ans [ 0 ] + ' ' + ans [ 1 ]);
Saída
2 1
Complexidade de tempo : O(log(min(a b))
Espaço Auxiliar : O(1)
