给定两个值“ m”和“ n”,算术级数的第五项为零。任务是找到此AP的第m项和第n项的比率。
例子:
Input: m = 10, n = 20
Output: 1/3
Input: m = 10, n = 15
Output: 1/2
方法: Acc。声明中,第五项为零。现在通过示例了解概念。由于A5 = a + 4 * d = 0。
现在,我们必须找到m =第10个项与n =第20个项的比率。
A[10]
= A + 9 * d
= A5 + 5 * d
= 0 + 5 * d
= 5 * d
Similarly, A[20]
= A + 19 * d
= A5 + 15 * d
= 0 + 15 * d
= 15 * d
Now, we have to find ratio, so Ans= A[10] / A[20]
以下是所需的实现:
C++
// C++ implementation of above approach
#include
#define ll long long int
using namespace std;
// Function to find the ratio
void findRatio(ll m, ll n)
{
ll Am = m - 5, An = n - 5;
// divide numerator by gcd to get
// smallest fractional value
ll numerator = Am / (__gcd(Am, An));
// divide denominator by gcd to get
// smallest fractional value
ll denominator = An / (__gcd(Am, An));
cout << numerator << "/" << denominator << endl;
}
// Driver code
int main()
{
// let d=1 as d doesn't affect ratio
ll m = 10, n = 20;
findRatio(m, n);
return 0;
}
Java
// java implementation of above approach
public class GFG {
// Function to calculate the GCD
static int GCD(int a, int b) {
if (b==0) return a;
return GCD(b,a%b);
}
// Function to find the ratio
static void findRatio(int m,int n)
{
int Am = m - 5, An = n - 5 ;
// divide numerator by GCD to get
// smallest fractional value
int numerator = Am / GCD(Am, An) ;
// divide denominator by GCD to get
// smallest fractional value
int denominator = An / GCD(Am, An) ;
System.out.println(numerator + "/" + denominator);
}
// Driver code
public static void main (String args[]){
// let d=1 as d doesn't affect ratio
int m = 10, n = 20;
findRatio(m, n);
}
// This code is contributed by ANKITRAI1
}
Python3
# Python3 implementation of above approach
# Function to find the ratio
from fractions import gcd
def findRatio(m,n):
Am = m - 5
An = n - 5
# divide numerator by gcd to get
# smallest fractional value
numerator=Am//(gcd(Am,An))
# divide denominator by gcd to get
#smallest fractional value
denominator = An // (gcd(Am, An))
print(numerator,'/',denominator)
# Driver code
# let d=1 as d doesn't affect ratio
if __name__=='__main__':
m = 10
n = 20
findRatio(m, n)
# this code is contributed by sahilshelangia
C#
// C# implementation of above approach
using System;
public class GFG {
// Function to calculate the GCD
static int GCD(int a, int b) {
if (b==0) return a;
return GCD(b,a%b);
}
// Function to find the ratio
static void findRatio(int m,int n)
{
int Am = m - 5, An = n - 5 ;
// divide numerator by GCD to get
// smallest fractional value
int numerator = Am / GCD(Am, An) ;
// divide denominator by GCD to get
// smallest fractional value
int denominator = An / GCD(Am, An) ;
Console.Write(numerator + "/" + denominator);
}
// Driver code
public static void Main (){
// let d=1 as d doesn't affect ratio
int m = 10, n = 20;
findRatio(m, n);
}
}
PHP
Javascript
输出:
1/3