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Hi i have problem in implementing nCr MODm in code sprint5 problem. Link to the problem is ...... https://www.hackerrank.com/contests/codesprint5/challenges/matrix-tracing. what I learned yet is I can apply rules of mudular arithmatic to factorial computation and inverse factorial computation and also to computing pow(a,b) MODm.But I don't know what I am missing which is leading to wrong answer. Here is my current code .

#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;
}
Tushar
  • 61
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  • Your `fact` function returns in the first line, so most of it won't be executed. – interjay Jan 22 '14 at 09:40
  • nope it is just fct() function which just precomputes factorials which will be needed in future. – Tushar Jan 22 '14 at 09:41
  • Then why is all the code in `fact` there? If it's not meant to be executed, remove it from the question. – interjay Jan 22 '14 at 09:42
  • Actually fact function grab values from ft[] array which is already computed by fct(). – Tushar Jan 22 '14 at 09:42
  • That is because I tried both things computing when needed and then replaced with precomputing ....which worked faster – Tushar Jan 22 '14 at 09:44
  • I was hoping if you could help me out figuring if I did something wrong in implementing the thing – Tushar Jan 22 '14 at 09:50

1 Answers1

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Finally I got the errors in my code.

errors....

  1. I should use constant variables md and co as unsigned long long int instead of only int
  2. Second error is in algorithm for computing pow(a,b) % md ..... in pow() function, I should first do x % md before processing further because there is probability that x can be passed greater than md .

current working code is.....

#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;
}
Tushar
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