【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 = 1005;
bool isPrime[maxn];
int P[maxn], pn = 0;
__int64 dp[maxn][205];
__int64 ans[maxn];

void init() {
    memset(isPrime, true, sizeof(isPrime));
    rep(i, 2, 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
", pn);
    #endif
    ans[1] = 1;
    rep(i, 2, 1001) {
        rep(j, 0, pn) {
            if (P[j] > i)
                break;
            for (int k=P[j]; k<=i; k*=P[j]) {
                dp[i][j] += dp[i-k][j+1] + 1;
            }
        }
        per(j, 0, 200)
            dp[i][j] += dp[i][j+1];
        ans[i] = dp[i][0] + 1;
    }
    
    #ifndef ONLINE_JUDGE
        rep(i, 1, 1001)
            printf("%d: %I64d
", 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
", ans[n]);
    
    #ifndef ONLINE_JUDGE
        printf("time = %d.
", (int)clock());
    #endif
    
    return 0;
}