HDU 1452 Happy 2004 (unique decomposition theorem)

Topic Links: Transmission Door

Test instructions

To 2004^x all the approximate and.

Analysis:

By the unique decomposition theorem

X=p1^a1*p2^a2*...*pn^an

Then its approximate sum = (P1^0+P1^1^...+P1^A1) *...* (PN^0+PN^1^...+PN)

The code is as follows:

#include <iostream> #include <cstring> #include <algorithm> #include <cstdio>using namespace std;const int mod = 29;int quick_mod (int a,int b) {    int ans = 1;    while (b) {        if (b&1) ans=ans*a%mod;        b>>=1;        A=a*a%mod;    }    return ans;} int fac[10],cnt;int num[10];void init () {    int n = 2004;    CNT = 0;    memset (num,0,sizeof (num));    for (int i=2;i*i<=n;i++) {        if (n%i==0) {            fac[cnt]=i;            while (n%i==0) n/=i,num[cnt]++;            cnt++;        }    }    if (n>1) fac[cnt]=n,num[cnt++]=1;} int main () {    int n;    while (~SCANF ("%d", &n) &&n) {        init ();        int ans = 1;        for (int i=0;i<cnt;i++) {            num[i]*=n;            int INV = Quick_mod (fac[i]-1,mod-2);            Ans=ans* ((Quick_mod (fac[i],num[i]+1) -1+mod) *inv%mod)%mod;        }        printf ("%d\n", ans);    }    return 0;}

HDU 1452 Happy 2004 (unique decomposition theorem)