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[pat (basic level) practice] - [simple mathematics] 1062 simplest fraction
2022-07-06 00:57:00 【IronmanJay】
List of articles
One 【 questions 】
- Class B
Two 【 Title number 】
- 1062 Simplest fraction (20 branch )
3、 ... and 【 Title Description 】
- A fraction is usually written as the division of two integers : N / M N/M N/M, among M M M Not for 0. The simplest fraction is a fraction representation in which the numerator and denominator have no common divisor .
- Now let's give two unequal positive fractions N 1 / M 1 N_1 /M_1 N1/M1 and N 2 / M 2 N_2 /M_2 N2/M2 , You are required to list them in descending order. The denominator between them is K K K The simplest fraction of .
Four 【 Title Example 】
Input format :
Enter and press... In one line N / M N/M N/M The format gives two positive fractions , Followed by a positive integer denominator K K K, Separated by spaces . The title guarantees that all integers given do not exceed 1000.Output format :
Press in a line N / M N/M N/M The format lists the denominator between two given scores K K K All the simplest fractions of , In order from small to large , In the meantime 1 Space separation . There must be no extra space at the beginning and end of the line . The title is guaranteed to have at least 1 Outputs .sample input :
7/18 13/20 12sample output :
5/12 7/12
5、 ... and 【 Their thinking 】
- The idea of this question is quite normal , The general idea is to convert two fractions into decimals , Traverse all the scores between two numbers , You need to ensure that this score is between two numbers , And it is the simplest fraction ( As long as the numerator and denominator have no common divisor, it is the simplest fraction ), Because we should ensure that the denominator is given K K K, So from 1 So let's start walking through K K K, Look for every possible score , Output only when conditions are met . But there are a few things to note , As shown below :
①: The result of division needs to be used d o u b l e double double type , Because there must be scores
②: Note that the two inputs of the topic are not necessarily in order , Need to compare the size , Convenient, the back is quite
③: Pay attention to the spaces , There is no space in front of the first output , There is a space in front of the rest of the output
6、 ... and 【 The final score 】
- 20 branch
7、 ... and 【 Code implementation 】
#include<stdio.h>
#include<stdbool.h>
bool HasCommonDivisor(int i,int k)
{
for(int j = 2;j<=i;j++)
{
if(i % j == 0 && k % j == 0)
{
return true;
}
}
return false;
}
int main()
{
int n1,m1,n2,m2,k;
scanf("%d/%d %d/%d %d",&n1,&m1,&n2,&m2,&k);
double d1 = (double)n1 / m1;
double d2 = (double)n2 / m2;
bool flag = true;
if(d1 > d2)
{
double temp = d2;
d2 = d1;
d1 = temp;
}
for(int i = 1;i<k;i++)
{
if(!HasCommonDivisor(i,k))
{
double d = (double)i / k;
if(d > d1 && d < d2)
{
if(flag == true)
{
printf("%d/%d",i,k);
flag = false;
}
else
{
printf(" %d/%d",i,k);
}
}
}
}
return 0;
}
8、 ... and 【 Submit results 】
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