BZOJ4591[SHOI2015] super-energy particle cannon • change

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Author: User

BZOJ4591[SHOI2015] super-energy particle cannon • change

Test instructions

(Sigma (I,0,k) C (n,i))%2333. n,k≤1018


According to the Lucas theorem (I will not), C (n,k)%2333=c (n/2333,k/2333) *c (n%2333,k%2333), it is possible to do some simplification (eliminate the mold)

(Sigma (I,0,k) C (n,i))=sigma (i,0,k) C (n/2333,i/2333) *c (n%2333,i%2333)

=Sigma (i,0,k/2333-1) C (n/2333,i)* (Sigma (j,0,2332) C (n%2333,j)) +C (n/2333,k/2333)*sigma (i,0,k% 2333) C (n%2333,i)

Start by handing out I,j≤2333 's c[i][j] and Sm[i][j] (for Sigma (K,0,J) c[i][k]), then the upper orange part can be seen as a simplified part of the red part, recursively solved until the N,k range ≤2333 return sm[n][k] , and the blue part of the upper formula can be solved recursively by Lucas theorem to N,k range ≤2333return C[n][k].


1#include <cstdio>2#include <cstring>3#include <algorithm>4 #defineInc (I,J,K) for (int i=j;i<=k;i++)5 #definell Long Long6 #defineMAXN 23347 #defineMoD 23338 using namespacestd;9 Ten inline ll read () { One     CharCh=getchar (); ll f=1, x=0; A      while(ch<'0'|| Ch>'9'){if(ch=='-') f=-1; Ch=GetChar ();} -      while(ch>='0'&&ch<='9') x=x*Ten+ch-'0', ch=GetChar (); -     returnf*x; the } -ll N,K,C[MAXN][MAXN],SM[MAXN][MAXN];intT; - voidCalc () { -c[0][0]=sm[0][0]=1; Inc (I,1, MoD) sm[0][i]=1; +Inc (I,1, MoD) { -d[n][0]=sm[i][0]=1; +Inc (J,1, i) c[i][j]= (c[i-1][j-1]+c[i-1][J])%MoD; AInc (J,1, MoD) sm[i][j]= (sm[i][j-1]+C[I][J])%MoD; at     } - } - ll Solvec (ll n,ll k) { -     if(N<=mod&&k<=mod)returnC[N][K];Else returnSolvec (N/mod,k/mod) *c[n%mod][k%mod]%MoD; - } - ll Solvesm (ll n,ll k) { in     if(K<mod)returnSolvec (N/mod,k/mod) *sm[n%mod][k%mod]%MoD; -     return(Solvesm (n/mod,k/mod-1) *sm[n%mod][mod-1]%mod+solvec (n/mod,k/mod) *sm[n%mod][k%mod]%mod)%MoD; to } + intMain () { -t=read (); Calc (); theInc (I,1, t) {n=read (); K=read (); printf ("%lld\n", Solvesm (n,k)%mod);} *     return 0; $}


Bzoj4591[shoi2015] super-capable particle cannon/change

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