题目链接:hdu 5453 Dividing This Product
分块打表,按照1e7的长度,先用程序打出一张 ans[300][50] 的表。然后对于每组数据,最多在用素数筛选法求一遍1e7即可。
还有一个用记忆化搜索的在线做法,复杂度为 o(n0.75) ,但是因为用了map维护dp,所以TLE了。连接
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
const int prime[303] = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999};
const int ans[303][52] = 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const int part = 1e7;
const int maxn = 5 * 1e8;
const int maxm = 3 * 1e4;
int N, M, C, P[maxm], vis[part+5];
void init () { C = 0; memset(vis, 0, sizeof(vis)); for (int i = 2; i * i <= maxn; i++) { if (vis[i]) continue; P[C++] = i; for (int j = i + i; j * j <= maxn; j += i) vis[j] = 1; }
}
int main () { init(); int cas, bw = 1; scanf("%d", &cas); for (int kcas = 1; kcas <= cas; kcas++) { scanf("%d%d", &N, &M); int u = 0; while (prime[u] < M) u++; int ret = ans[u][N/part]; int s = N / part * part; bw++; for (int i = 0; i < C; i++) { int l = s / P[i] * P[i]; while (l < s || l <= P[i]) l += P[i]; for (int j = l; j <= N; j += P[i]) vis[j-s] = bw; }
for (int i = max(2, s); i <= N; i++)
if (vis[i-s] != bw && i != M)
ret = 1LL * ret * i % M;
printf("Case #%d: %d\n", kcas, ret);
}
return 0;
}
#include <cstdio>
#include <cstring>
#include <cmath>
#include <vector>
#include <map>
#include <algorithm>
using namespace std;
const int maxn = 5 * 1e8;
const int maxm = 3 * 1e4;
typedef pair<int,int> pii;
int N, M, C, P[maxm];
bool vis[maxm];
map<int, pii> dp[maxm];
void init () {
C = 0;
P[C++] = 1;
memset(vis, false, sizeof(vis));
for (int i = 2; i * i <= maxn; i++) {
if (vis[i]) continue;
P[C++] = i;
for (int j = i + i; j * j <= maxn; j += i)
vis[j] = true;
}
}
int pow_mod(int x, int n) {
int ret = 1;
while (n) {
if (n&1) ret = ret * x % M;
x = x * x % M;
n >>= 1;
}
return ret;
}
int fac(int n) {
int t = n / M, k = n % M, ret = 1;
for (int i = 1; i < M; i++)
ret = ret * i % M;
ret = pow_mod(ret, t);
for (int i = 1; i <= k; i++)
ret = ret * i % M;
return ret;
}
int solve (int i, int v) {
if (dp[i].count(v)) return dp[i][v].first;
if (P[i] * P[i] > v || P[i] == M) {
int tmp = solve(i-1, v);
dp[i][v] = dp[i-1][v];
return tmp;
}
if (i == 0) {
int tmp = fac(v);
dp[i][v] = make_pair(tmp, v - v / M);
return tmp;
}
int ret = solve(i-1, v) * solve(i-1, P[i-1]) % M;
int div = solve(i-1, v / P[i]);
int c = dp[i-1][v/P[i]].second - dp[i-1][P[i-1]].second;
int pri = P[i] == M ? 1 : pow_mod(P[i], c);
ret = ret * pow_mod(div * pri % M, M-2) % M;
dp[i][v] = make_pair(ret, dp[i-1][v].second - c);
return ret;
}
int main () {
init();
int cas;
scanf("%d", &cas);
for (int kcas = 1; kcas <= cas; kcas++) {
scanf("%d%d", &N, &M);
int m = sqrt(N), n = 0;
while (P[n] < m && n < C - 1) n++;
for (int i = 0; i <= n; i++) dp[i].clear();
printf("Case #%d: %d\n", kcas, solve(n, N));
}
return 0;
}