【HDOJ】4345 Permutation

即求P1^n1+P2^n2 + ... + Pk^nk <= n，其中Pk为素数的所有可能组合。
思路是DP。1~1000的素数就不到200个。
dp[i][j]表示上式和不超过且当前最小素数为P[j]的所有可能情况。注意dp[i][0]+1即为所求。

 /* 4345 */
 #include <iostream>
 #include <sstream>
 #include <string>
 #include <map>
 #include <queue>
 #include <set>
 #include <stack>
 #include <vector>
 #include <deque>
 #include <algorithm>
 #include <cstdio>
 #include <cmath>
 #include <ctime>
 #include <cstring>
 #include <climits>
 #include <cctype>
 #include <cassert>
 #include <functional>
 #include <iterator>
 #include <iomanip>
 using namespace std;
 //#pragma comment(linker,"/STACK:102400000,1024000")

 #define sti                set<int>
 #define stpii            set<pair<int, int> >
 #define mpii            map<int,int>
 #define vi                vector<int>
 #define pii                pair<int,int>
 #define vpii            vector<pair<int,int> >
 #define rep(i, a, n)     for (int i=a;i<n;++i)
 #define per(i, a, n)     for (int i=n-1;i>=a;--i)
 #define clr                clear
 #define pb                 push_back
 #define mp                 make_pair
 #define fir                first
 #define sec                second
 #define all(x)             (x).begin(),(x).end()
 #define SZ(x)             ((int)(x).size())
 #define lson            l, mid, rt<<1
 #define rson            mid+1, r, rt<<1|1

 const int maxn = ;
 bool isPrime[maxn];
 int P[maxn], pn = ;
 __int64 dp[maxn][];
 __int64 ans[maxn];

 void init() {
     memset(isPrime, true, sizeof(isPrime));
     rep(i, , maxn) {
         if (isPrime[i]) {
             P[pn++] = i;
             for (int j=i*i; j<maxn; j+=i)
                 isPrime[j] = false;
         }
     }

     #ifndef ONLINE_JUDGE
         printf("pn = %d\n", pn);
     #endif
     ans[] = ;
     rep(i, , ) {
         rep(j, , pn) {
             if (P[j] > i)
                 break;
             for (int k=P[j]; k<=i; k*=P[j]) {
                 dp[i][j] += dp[i-k][j+] + ;
             }
         }
         per(j, , )
             dp[i][j] += dp[i][j+];
         ans[i] = dp[i][] + ;
     }

     #ifndef ONLINE_JUDGE
         rep(i, , )
             printf("%d: %I64d\n", i, ans[i]);
     #endif
 }

 int main() {
     ios::sync_with_stdio(false);
     #ifndef ONLINE_JUDGE
         freopen("data.in", "r", stdin);
         freopen("data.out", "w", stdout);
     #endif

     int n;

     init();

     while (scanf("%d", &n)!=EOF)
         printf("%I64d\n", ans[n]);

     #ifndef ONLINE_JUDGE
         printf("time = %d.\n", (int)clock());
     #endif

     return ;
 }