Question

我在代码sprint5问题中实现nCr MODm时遇到问题。链接问题是...... https://www.hackerrank.com/contests/codesprint5/challenges/matrix-tracing。我学到的是我可以将mudular算法的规则应用于阶乘计算和逆因子计算，也可以计算pow（a，b）MODm。但我不知道我错过了什么导致了错误的答案。这是我目前的代码。

#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
#include <map>
#include<math.h>
using namespace std;
const int md = 1000000007;
const int co = 2000020;
unsigned long long int ft[co];

long long int fact(unsigned long long int n)
{   
   return ft[n];
}

void fct(){
    ft[1]=1;
    for(unsigned long long int i = 2;i<=2000020;i++){
        ft[i]=(i*ft[i-1]) % md;
        }
    }

long long int pow(long long int x, long long int n, long long int mod){
    long long int result=1; 
    while(n>0){
        if(n%2 ==1){
            result = (result*x) % mod;
        }
        n= n>>1;
        x= (x*x)% mod;  
    }
    return result;
}

int main() {
    /* Enter your code here. Read input from STDIN. Print output to STDOUT */  
    unsigned long long int m , n;
    long long result;
    int T;
    fct();
    cin>>T;
    while(T--){
        cin>>m>>n; 
        unsigned long long int mod = md-2;
         result = (fact(m+n-2) * pow( ( fact(m-1) * fact(n-1) ) , mod, md )) % md ;
        cout<<result<<endl;
    }
    return 0;
}

Answer 1

最后我的代码中出现了错误。

...错误

我应该使用常量变量md和co作为无符号long long int而不是int
第二个错误是在pow(a,b) % md中计算pow() .....的算法函数，我应该先进行x % md进一步处理因为x的传递概率可能大于md。

目前的工作代码是.....

#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
#include <map>
#include<math.h>
using namespace std;
const unsigned long long int md = 1000000007; 
const unsigned long long int co = 2000020;
unsigned long long int ft[co];

unsigned long long int fact(unsigned long long int n)
{   
    return ft[n];
}

void fct(){
    ft[0]=1;
    for(unsigned long long int i = 1;i<=2000020;i++){
        ft[i]=(i*ft[i-1]) % md;
    }
}

unsigned long long int pow(unsigned long long int x, unsigned long long int n, unsigned long long int mod){
    unsigned long long int result=1; 
    x = x % md;
    while(n>0){
        if(n%2 ==1){
            result = (result*x) % md;
        }
        n= n>>1;
        x= (x*x)% md;   
    }
    return result;
}

int main() {
    /* Enter your code here. Read input from STDIN. Print output to STDOUT */  
    unsigned long long int m , n;
    unsigned long long int result;
    int T;
    fct();
    cin>>T;
    while(T--){
        cin>>m>>n; 
        unsigned long long int mod = md-2;   
        result = (fact(m+n-2) * pow( ( fact(m-1) * fact(n-1) ) , mod, md )) % md ;
        cout<<result<<endl; 
    }

    return 0;
}

为非常大的数字实现nCr和逆因子（MODm）

1 个答案: