LightOj 1005 (Rooks)

#lightoj #cp #problem_solving #recursion #combinatorics

Idea 1

  • Put a rook in row 1 , so there are c ways (c columns) to do that c * solve(r-1,c-1,k-1)
  • and don’t put a rook in row 1 , so there are r-1 rows solve(r-1,c,k)
  • So , ans = c * solve(r-1,c-1,k-1) + solve(r-1,c,k)

Idea 2

  • take k row from n row = nCk
  • take k col from n col = nCk
  • how many ways k rook arrange among themselves = k!

ans = nCk * nCk * k!

comb[n][k] = comb[n-1][k] + comb[n-1][k-1]

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 /*Which of the favors of your Lord will you deny ?*/

#include<bits/stdc++.h>
using namespace std;

#define LL long long
#define PII pair<int,int>
#define LPII pair<LL, pair<int,int> >
#define MP make_pair
#define F first
#define S second
#define LINF LLONG_MAX


LL shomadhan(LL r,LL c,LL k)
{
    if(k > r || k > c)
        return 0;
    else if(k==(LL)0)
        return 1;
    else if(r==(LL)1)
        return c;
    else return c*shomadhan(r-1,c-1,k-1)+shomadhan(r-1,c,k);


}

int main()
{
    //freopen("LightOj1099.txt","w",stdout);

    int tc;
    scanf("%d",&tc);

    for(int i=1; i<=tc; i++)
    {
        LL n,k;
        scanf("%lld %lld",&n,&k);

        LL ans=shomadhan(n,n,k);

        printf("Case %d: %lld\n",i,ans);
    }

    return 0;
}