51nod 1116 K进制下的大数 暴力/数论

题目链接:

http://www.51nod.com/onlineJudge/questionCode.html#!problemId=1116

题意:

题解:

代码:

暴力：

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define MS(a) memset(a,0,sizeof(a))
#define MP make_pair
#define PB push_back
const int INF = 0x3f3f3f3f;
const ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
inline ll read(){
    ll x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
//////////////////////////////////////////////////////////////////////////
const int maxn = 1e5+10;

string str;
int len;

bool check(int k){
    ll sum=0;
    for(int i=0; i<len; i++){
        if(str[i]>='A') sum =  sum*k + (str[i]-'A'+10);
        else sum = sum*k + (str[i]-'0');
        sum %= (k-1);
    }
    return sum%(k-1) == 0;
}

int main(){
    cin >> str;
    int mx=-1;
    len=str.size();
    for(int i=0; i<len; i++)
        mx = max(mx,str[i]-'A'+10);

    int k,f=0;
    for(k=mx+1; k<=36; k++){
        if(check(k)) {f=1; break;}
    }

    if(f) cout << k << endl;
    else cout << "No Solution" << endl;


    return 0;
}

数学：

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define MS(a) memset(a,0,sizeof(a))
#define MP make_pair
#define PB push_back
const int INF = 0x3f3f3f3f;
const ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
inline ll read(){
    ll x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
//////////////////////////////////////////////////////////////////////////
const int maxn = 1e5+10;

string str;
ll sum;

int main(){
    cin >> str;
    int mx=-1,len = str.size();
    for(int i=0; i<len; i++){
        if(str[i]>='A') mx=max(mx,str[i]-'A'+10),sum += str[i]-'A'+10;
        else mx=max(mx,str[i]-'0'),sum += str[i]-'0';
    }

    int f = 0,ans;
    for(int i=mx; i<36; i++){
        if(sum % i == 0){
            f = 1;
            ans = i+1;
            break;
        }
    }

    if(f) cout << ans << endl;
    else cout << "No Solution" << endl;

    return 0;
}