Codeforces Round #384 (Div. 2) C. Vladik and fractions(构造题)
Description
Vladik and Chloe decided to determine who of them is better at math. Vladik claimed that for any positive integer n he can represent fraction as a sum of three distinct positive fractions in form
.
Help Vladik with that, i.e for a given n find three distinct positive integers x, y and z such that . Because Chloe can't check Vladik's answer if the numbers are large, he asks you to print numbers not exceeding 109.
If there is no such answer, print -1.
Input
The single line contains single integer n (1 ≤ n ≤ 104).
Output
If the answer exists, print 3 distinct numbers x, y and z (1 ≤ x, y, z ≤ 109, x ≠ y, x ≠ z, y ≠ z). Otherwise print -1.
If there are multiple answers, print any of them.
Sample Input
3 7
Sample Output
2 7 42 7 8 56
思路
题意:
给出一个数 n ,问是否存在三个不同的整数 x ,y ,z 满足。
题解:
,因此,我们可以让1/z = 1 / n,剩下的为 1/x + 1/y = 1/n,通过恒等变换可以知道 1/x = ny / (y - n),可以发现,y = n + 1时候,x 必然为整数,因此x = n + n * n,y = n + 1,z = n。需要注意的是,当 n = 1时,x = 2,y = 2,不符合题意。
#include<bits/stdc++.h> using namespace std; int main() { int n; scanf("%d",&n); if (n == 1) printf("-1\n"); else printf("%d %d %d\n",n*n + n,n + 1,n); return 0; }
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