UVa 10692 - Huge Mod (數論 + 歐拉定理擴展)

題意

計算abcdmodm

思路

用歐拉公式即可，不過要保證符合b>=ϕ(m) 的前提！網上很多代碼都是錯的。可以試下這組數據：1000 3 12 1 1。
就連uHunt上的標程都是錯的。。

寫了個Check函數每次判斷是不是符合條件。

代碼

#include <stack>
#include <cstdio>
#include <list>
#include <cassert>
#include <set>
#include <fstream>
#include <iostream>
#include <string>
#include <sstream>
#include <vector>
#include <queue>
#include <functional>
#include <cstring>
#include <algorithm>
#include <cctype>
#pragma comment(linker, "/STACK:102400000,102400000")
#include <string>
#include <map>
#include <cmath>
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/hash_policy.hpp>
//using namespace std;
//using namespace __gnu_pbds;
#define LL long long
#define ULL unsigned long long
#define SZ(x) (int)x.size()
#define Lowbit(x) ((x) & (-x))
#define MP(a, b) make_pair(a, b)
#define MS(p, num) memset(p, num, sizeof(p))
#define PB push_back
#define X first
#define Y second
#define ROP freopen("input.txt", "r", stdin);
#define MID(a, b) (a + ((b - a) >> 1))
#define LC rt << 1, l, mid
#define RC rt << 1|1, mid + 1, r
#define LRT rt << 1
#define RRT rt << 1|1
#define FOR(i, a, b) for (int i=(a); (i) < (b); (i)++)
#define FOOR(i, a, b) for (int i = (a); (i)<=(b); (i)++)
#define TRAVERSAL(u, i) for (int i = head[u]; i != -1; i = edge[i].nxt)
const double PI = acos(-1.0);
const int INF = 0x3f3f3f3f;
const double eps = 1e-8;
const int MAXN = 10000+10;
const int MOD = 100000007;
const int dir[][2] = { {-1, 0}, {1, 0}, {0, -1}, {0, 1} };
const int seed = 131;
int cases = 0;
typedef std::pair<int, int> pii;

int phi[MAXN], m, n;
char str[1000];
int num[20];

int pow_mod(LL a, LL n, LL m)
{
    int ret = 1;
    while (n)
    {
        if (n & 1) ret = ret * a % m;
        a = a * a % m;
        n >>= 1;
    }
    return ret;
}

void get_phi_table()
{
    for (int i = 2; i < MAXN; i++) if (!phi[i])
        for (int j = i; j < MAXN; j += i)
        {
            if (!phi[j]) phi[j] = j;
            phi[j] = phi[j] / i * (i-1);
        }
}

int Check(int u, int target)
{
    if (u == n-1) return num[u];
    int ret = Check(u+1, target);
    if (ret >= target) return target;
    int tmp = 1;
    for (int i = 0; i < ret; i++)
    {
        tmp = tmp * num[u];
        if (tmp >= target) return target;
    }
    return tmp;
}

int simple_pow(int u)
{
    if (u == n-1) return num[u];
    return pow_mod(num[u], simple_pow(u+1), INF);
}

int dfs(int u, int mod)
{
    if (mod == 1) return 0;
    if (u == n-1) return num[u] % mod;
    int ans = dfs(u+1, phi[mod]);
    if (Check(u+1, phi[mod]) >= phi[mod]) return pow_mod(num[u], ans + phi[mod], mod);
    else return pow_mod(num[u], simple_pow(u+1), mod);
}

int main()
{
    //ROP;
    get_phi_table();
    while (gets(str), str[0] != '#')
    {
        char *p = strtok(str, " ");
        sscanf(p, "%d", &m);
        p = strtok(NULL, " ");
        sscanf(p, "%d", &n);
        for (int i = 0; i < n; i++)
        {
            p = strtok(NULL, " ");
            sscanf(p, "%d", &num[i]);
        }
        printf("Case #%d: %d\n", ++cases, dfs(0, m));
    }
    return 0;
}