poj 2891 Strange Way to Express Integers
2013-12-02 12:02
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线性同余方程模板。求x满足,x%ai = ri。
#include<algorithm>
#include<iostream>
#include<cstring>
#include<vector>
#include<cstdio>
#include<cmath>
#include<map>
#define LL long long
#define REP(i, n) for(int i = 0; i < n; i ++)
#define CLR(a, b) memset(a, b, sizeof(a))
using namespace std;
void Ex_gcd(LL a, LL b, LL& d, LL& x, LL& y)
{
if(!b) {d = a; x = 1; y = 0;}
else {Ex_gcd(b, a % b, d, y, x); y -= x * (a / b); }
}
int main()
{
int n;
LL a1, r1, a2, r2, ans, a, b, c, d, x, y;
while(scanf("%d", &n) != EOF)
{
bool flag = true;
scanf("%I64d%I64d", &a1, &r1);
for(int i = 1; i < n; i ++)
{
scanf("%I64d%I64d", &a2, &r2);
if(!flag) continue;
a = a1, b = a2, c = r2 - r1;
Ex_gcd(a, b, d, x, y);
if(c % d != 0) flag = false;
int t = b / d;
x = (x * (c / d) % t + t) % t;
r1 = a1 * x + r1;
a1 = a1 * (a2 / d);
}
if(!flag) puts("-1");
else printf("%I64d\n", r1);
}
}
#include<algorithm>
#include<iostream>
#include<cstring>
#include<vector>
#include<cstdio>
#include<cmath>
#include<map>
#define LL long long
#define REP(i, n) for(int i = 0; i < n; i ++)
#define CLR(a, b) memset(a, b, sizeof(a))
using namespace std;
void Ex_gcd(LL a, LL b, LL& d, LL& x, LL& y)
{
if(!b) {d = a; x = 1; y = 0;}
else {Ex_gcd(b, a % b, d, y, x); y -= x * (a / b); }
}
int main()
{
int n;
LL a1, r1, a2, r2, ans, a, b, c, d, x, y;
while(scanf("%d", &n) != EOF)
{
bool flag = true;
scanf("%I64d%I64d", &a1, &r1);
for(int i = 1; i < n; i ++)
{
scanf("%I64d%I64d", &a2, &r2);
if(!flag) continue;
a = a1, b = a2, c = r2 - r1;
Ex_gcd(a, b, d, x, y);
if(c % d != 0) flag = false;
int t = b / d;
x = (x * (c / d) % t + t) % t;
r1 = a1 * x + r1;
a1 = a1 * (a2 / d);
}
if(!flag) puts("-1");
else printf("%I64d\n", r1);
}
}
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