UVA - 1649 Binomial coefficients (组合数+二分)

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 typedef long long ll;
 4 typedef double db;
 5 const ll N=2000+10,inf=0x3f3f3f3f3f3f3f3f;
 6 const ll up[]= {0,0,44721361,181714,12449,2608};
 7 ll m,C[N][N];
 8 struct D {
 9     ll n,k;
10     bool operator<(const D& b)const {return n!=b.n?n<b.n:k<b.k;}
11 };
12 set<D> ans;
13 ll c(ll n,ll k) {
14     ll ret=1;
15     for(ll i=1; i<=k; ++i)ret=ret*(n-i+1)/i;
16     return ret;
17 }
18 ll bi(ll l,ll r,ll k) {
19     while(l<=r) {
20         ll mid=(l+r)>>1;
21         ll t=c(mid,k);
22         if(t==m)return mid;
23         t<m?l=mid+1:r=mid-1;
24     }
25     return -1;
26 }
27 int main() {
28     C[0][0]=1;
29     for(ll i=1; i<N; ++i)
30         for(ll j=0; j<=i; ++j)
31             C[i][j]=j==0||j==i?1:min(inf,C[i-1][j]+C[i-1][j-1]);
32     ll T;
33     for(scanf("%lld",&T); T--;) {
34         ans.clear();
35         scanf("%lld",&m);
36         for(ll i=1; i<N; ++i) {
37             ll j=lower_bound(C[i],C[i]+i/2+1,m)-C[i];
38             if(C[i][j]==m)ans.insert({i,j}),ans.insert({i,i-j});
39         }
40         ans.insert({m,1}),ans.insert({m,m-1});
41         for(ll i=2; i<=5; ++i) {
42             ll j=bi(i,up[i],i);
43             if(j!=-1)ans.insert({j,i}),ans.insert({j,j-i});
44         }
45         printf("%lld\n",ans.size());
46         ll f=1;
47         for(D x:ans) {
48             f?f--:printf(" ");
49             printf("(%lld,%lld)",x.n,x.k);
50         }
51         puts("");
52     }
53     return 0;
54 }