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HDU3579 线性同余方程（模板 余数不一定互质）

2024-09-07 00:11:35   219人阅读

Hello Kiki
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 258 Accepted Submission(s): 111
 
Problem Description
One day I was shopping in the supermarket. There was a cashier counting coins seriously when a little kid running and singing \\\\\\\"门前大桥下游过一群鸭，快来快来 数一数，二四六七八\\\\\\\". And then the cashier put the counted coins back morosely and count again...
Hello Kiki is such a lovely girl that she loves doing counting in a different way. For example, when she is counting X coins, she count them N times. Each time she divide the coins into several same sized groups and write down the group size Mi and the number of the remaining coins Ai on her note.
One day Kiki\\\\\\\‘s father found her note and he wanted to know how much coins Kiki was counting.
 
Input
The first line is T indicating the number of test cases.
Each case contains N on the first line, Mi(1 <= i <= N) on the second line, and corresponding Ai(1 <= i <= N) on the third line.
All numbers in the input and output are integers.
1 <= T <= 100, 1 <= N <= 6, 1 <= Mi <= 50, 0 <= Ai < Mi
 
Output

            For each case output the least positive integer X which Kiki was counting in the sample output format. If there is no solution then output -1.
 
Sample Input
2
2
14 57
5 56
5
19 54 40 24 80
11 2 36 20 76
 
Sample Output
Case 1: 341
Case 2: 5996
 
Author
digiter (Special Thanks echo)
 
Source
2010 ACM-ICPC Multi-University Training Contest（14）——Host by BJTU
 

题意：

求同于方程。上模板。

代码：

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
const int maxn=100005;
const int inf=0x7fffffff;
typedef long long ll;
void ex_gcd(ll a,ll b,ll &d,ll &x,ll &y)//扩展欧几里得
{
    if(!b) {d=a;x=1;y=0;}
    else{
        ex_gcd(b,a%b,d,y,x);
        y-=x*(a/b);
    }
}
ll ex_crt(ll *m,ll *r,int n)
{
    ll M=m[1],R=r[1],x,y,d;
    for(int i=2;i<=n;i++){
        ex_gcd(M,m[i],d,x,y);
        if((r[i]-R)%d) return -1;
        x=(r[i]-R)/d*x%(m[i]/d);
        R+=x*M;
        M=M/d*m[i];
        R%=M;
    }
    return R>0?R:R+M;
}
int main()
{
    int t,n;
    scanf("%d",&t);
    for(int cas=1;cas<=t;cas++){
        scanf("%d",&n);
        ll m[maxn],r[maxn];//m除数，r余数
        for(int i=1;i<=n;i++) scanf("%lld",&m[i]);
        for(int i=1;i<=n;i++) scanf("%lld",&r[i]);
        printf("Case %d: %I64d\n",cas,ex_crt(m,r,n));
    }
    return 0;
}

 

HDU3579 线性同余方程（模板 余数不一定互质）


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