正文
F - 等式（1/x + 1/y = 1/n）
小程序：扫一扫查出行【扫一扫了解最新限行尾号】
复制小程序
链接：https://www.nowcoder.com/acm/contest/90/F
来源：牛客网
题目描述给定n，求1/x + 1/y = 1/n （x<=y）的解数。（x、y、n均为正整数）
输入描述:
在第一行输入一个正整数T。接下来有T行，每行输入一个正整数n，请求出符合该方程要求的解数。（1<=n<=1e9）
输出描述:
输出符合该方程要求的解数。
示例1输入31201801011000000000
输出15181
思路：
给定n，求1/x + 1/y = 1/n （x<=y）的解数。（x、y、n均为正整数）
输入描述:
在第一行输入一个正整数T。接下来有T行，每行输入一个正整数n，请求出符合该方程要求的解数。（1<=n<=1e9）
输出描述:
输出符合该方程要求的解数。
示例1
输入31201801011000000000
31201801011000000000
输出15181
15181
1/x + 1/y = 1/n
-> yn + xn - xy = 0
-> yn + xn - xy -n^2 +n^2 = 0
-> n^2 = (n - x) * ( n - y)
即：求n^2的约数组合数，n^2的质因数与n的质因数相同，个数为n的两倍
代码：#include <algorithm>#include <bitset>#include <cmath>#include <cstdio>#include <cstdlib>#include <cstring>#include <iostream>#include <map>#include <queue>#include <set>#include <stack>#include <string>#include <vector>using namespace std;#define is_lower(c) (c >= 'a' && c <= 'z')#define is_upper(c) (c >= 'A' && c <= 'Z')#define is_alpha(c) (is_lower(c) || is_upper(c))#define is_digit(c) (c >= '0' && c <= '9')#define min(a, b) ((a) < (b) ? (a) : (b))#define max(a, b) ((a) > (b) ? (a) : (b))#define PI acos(-1)#define IO \ ios::sync_with_stdio(); \ cin.tie(); \ cout.tie();#define For(i, a, b) for (int i = a; i <= b; i++)typedef long long ll;typedef unsigned long long ull;typedef pair<int, int> pii;typedef pair<ll, ll> pll;typedef vector<int> vi;const ll inf = 0x3f3f3f3f;;const ll inf_ll = (ll)1e18;const ll maxn = 100005LL;const ll mod = 2012LL; + ;int main() { int T,n; cin>>T; while(T--) { cin>>n; ]={}; ; ; i * i <= n; i++) { ) { ) { ans[len]++; n /= i; } len++; } } ) ans[len]++; ll res = ; ; i <= len ; i++) res *= ans[i] * + ; res = (res + ) / ; cout << res << endl; }}
#include <algorithm>#include <bitset>#include <cmath>#include <cstdio>#include <cstdlib>#include <cstring>#include <iostream>#include <map>#include <queue>#include <set>#include <stack>#include <string>#include <vector>using namespace std;#define is_lower(c) (c >= 'a' && c <= 'z')#define is_upper(c) (c >= 'A' && c <= 'Z')#define is_alpha(c) (is_lower(c) || is_upper(c))#define is_digit(c) (c >= '0' && c <= '9')#define min(a, b) ((a) < (b) ? (a) : (b))#define max(a, b) ((a) > (b) ? (a) : (b))#define PI acos(-1)#define IO \ ios::sync_with_stdio(); \ cin.tie(); \ cout.tie();#define For(i, a, b) for (int i = a; i <= b; i++)typedef long long ll;typedef unsigned long long ull;typedef pair<int, int> pii;typedef pair<ll, ll> pll;typedef vector<int> vi;const ll inf = 0x3f3f3f3f;;const ll inf_ll = (ll)1e18;const ll maxn = 100005LL;const ll mod = 2012LL; + ;int main() { int T,n; cin>>T; while(T--) { cin>>n; ]={}; ; ; i * i <= n; i++) { ) { ) { ans[len]++; n /= i; } len++; } } ) ans[len]++; ll res = ; ; i <= len ; i++) res *= ans[i] * + ; res = (res + ) / ; cout << res << endl; }}
