【HDOJ】4373 Mysterious For

1. 题目描述
有两种不同类型的循环，并给出一个由1、2组成的序列，表示嵌套的循环类型。
问这样组着的循环一共需要多少次循环？并将结果模364875103。

2.基本思路
显然，每当遇到一个类型1的序列，即可以判定12...2的嵌套循环共多少次，而1类型的循环次数为常亮。
因此，将原序列从1分开，并将每个子序列的循环次数相乘即为总的循环次数。
1     共循环n次 = C[n][1]
12   共循环n*(n+1)/2次 = C[n+1][2]
122 共循环n*(n+1)*(n+2)/6次 = C[n+2][3]
12..2 |2|=m 共循环n*(n+1)*(n+2)/6次 = C[n+m-1][m]
由Lucas定理可知，假设p为素数，有

比较悲剧的是364875103是个合数，将它拆解为两个素数并使用LUCAS后，
我们可以知道ans=a1(mod p1), ans=a2(mod p2), 且p1, p2互素，求ans = ? (mod p1*p2)。
使用中国剩余定理。
使用欧拉定理求逆。

3. 代码

/* 4373 */
#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
#define LL                __int64

const int maxn = 25;
const int mod1 = 97;
const int mod2 = 3761599;
const int mod = 364875103;
LL fact1[mod1+15];
LL fact2[mod2+15];
LL e1, e2;
int pos[maxn];
int n, m, k;

LL Pow(LL base, LL n, LL mod) {
    LL ret = 1;
    
    base %= mod;
    while (n) {
        if (n & 1)
            ret = ret * base % mod;
        base = base * base % mod;
        n >>= 1;
    }
    
    return ret;
}

void init() {
    fact1[0] = fact2[0] = 1;
    rep(i, 1, mod1)
        fact1[i] = fact1[i-1] * i % mod1;
    rep(i, 1, mod2)
        fact2[i] = fact2[i-1] * i % mod2;
    e1 = mod2 * Pow(mod2, mod1-2, mod1);
    e2 = mod1 * Pow(mod1, mod2-2, mod2);
    
    #ifndef ONLINE_JUDGE
        printf("e1 = %I64d, e2 = %I64d\n", e1, e2);
    #endif
}

LL C(LL n, LL m, LL mod, LL *fact) {
    if (n < m)    return 0;
    return fact[n] * Pow(fact[m]*fact[n-m], mod-2, mod) % mod;
}

LL Lucas(LL n, LL m, LL mod, LL *fact) {
    if (m == 0)    return 1;
    return C(n%mod, m%mod, mod, fact) * Lucas(n/mod, m/mod, mod, fact);
}

void solve() {
    LL ans = 1, tmp;
    LL a1, a2;
    
    rep(i, 0, k) {
        m = pos[i+1]-pos[i];
        a1 = Lucas(n+m-1, m, mod1, fact1);
        a2 = Lucas(n+m-1, m, mod2, fact2);
        tmp = (a1*e1 + a2*e2) % mod;
        #ifndef ONLINE_JUDGE
            printf("a1 = %I64d, a2=%I64d, tmp=%I64d\n", a1, a2, tmp);
        #endif
        ans = ans * tmp % mod;
    }
    
    printf("%I64d\n", ans);
}

int main() {
    ios::sync_with_stdio(false);
    #ifndef ONLINE_JUDGE
        freopen("data.in", "r", stdin);
        freopen("data.out", "w", stdout);
    #endif
    
    int t;
    
    init();
    scanf("%d", &t);
    rep(tt, 1, t+1) {
        scanf("%d%d%d", &n, &m, &k);
        rep(i, 0, k)
            scanf("%d", &pos[i]);
        pos[k] = m;
        printf("Case #%d: ", tt);
        solve();
    }
    
    #ifndef ONLINE_JUDGE
        printf("time = %d.\n", (int)clock());
    #endif
    
    return 0;
}

4. 数据生成器

from copy import deepcopy
from random import randint, shuffle
import shutil
import string


def GenDataIn():
    with open("data.in", "w") as fout:
        t = 20
        bound = 10**5
        fout.write("%d\n" % (t))
        for tt in xrange(t):
            n = randint(20, bound)
            m = randint(20, bound)
            k = randint(1, 15)
            fout.write("%d %d\n%d " % (n, m, k))
            L = [0]
            st = set()
            for i in xrange(1, k):
                while True:
                    x = randint(1, m)
                    if x not in st:
                        break
                L.append(x)
                st.add(x)
            L = sorted(L)
            fout.write(" ".join(map(str, L)) + "\n")
            
            
def MovDataIn():
    desFileName = "F:\eclipse_prj\workspace\hdoj\data.in"
    shutil.copyfile("data.in", desFileName)

    
if __name__ == "__main__":
    GenDataIn()
    MovDataIn()