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binomialcoff.cpp
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binomialcoff.cpp
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#include<iostream>
#include<stdio.h>
#include<stdlib.h>
using namespace std;
static int c[50][50];
int min(int a,int b){return a<b?a:b;}
int bincoff(int n,int k)
{
if(k==0 || k==n)
return 1;
else return bincoff(n-1,k-1)+bincoff(n-1,k);
}
int bincoff1(int n,int k)
{
if(c[n][k]==0)
{
if(k==0 || k==n)
c[n][k]=1;
else
c[n][k]=bincoff1(n-1,k)+bincoff1(n-1,k-1);
}
return c[n][k];
}
int bincoffdp(int n,int k)
{
int c[50][50],i,j;
for(i=0;i<=n;i++)
c[i][0]=c[i][i]=1;
for(i=1;i<=n;i++)
{
for(j=1;j<=min(i,k);j++)
{
c[i][j]=c[i-1][j-1]+c[i-1][j];
}
}
return c[n][k];
}
int bincoffdp1(int n,int k)
{
int c[50]={0},i,j;
c[0]=1;
for(i=1;i<=n;i++)
{
for(j=min(i,k);j>0;j--)
{
c[j]=c[j]+c[j-1];
}
}
return c[k];
}
int binomialCoeff(int n, int k)
{
int* C = (int*)calloc(k+1, sizeof(int));
int i, j, res;
C[0] = 1;
for(i = 1; i <= n; i++)
{
for(j = min(i, k); j > 0; j--)
C[j] = C[j] + C[j-1];
}
res = C[k]; // Store the result before freeing memory
free(C); // free dynamically allocated memory to avoid memory leak
return res;
}
int main()
{
int t,n,k;
cin>>t;
while(t--)
{
cin>>n>>k;
cout<<binomialCoeff(n,k)<<" "<<bincoff1(n,k)<<" "<<bincoffdp1(n,k)<<"\n";
}
return 0;
}