hdu 5453 Dividing This Product(分块打表)

题目链接：hdu 5453 Dividing This Product

解题思路

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

代码

• AC代码

#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] = {{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0},{1,1,1,2,1,2,2,2,1,1,2,1,2,1,1,1,1,2,2,1,1,1,2,2,2,1,1,1,1,2,1,1,2,1,2,2,2,1,1,1,1,1,2,2,1,1,1,1,1,2,1,0},{1,4,3,2,3,4,1,2,2,4,4,3,1,2,4,4,2,4,2,1,2,2,2,1,1,4,2,1,3,2,2,3,3,3,1,1,4,2,4,1,1,1,1,2,3,2,4,3,2,3,4,0},{1,1,3,3,4,6,4,6,4,1,1,2,4,2,4,5,1,3,4,2,4,2,5,6,4,2,1,4,3,2,3,2,5,5,6,6,5,6,6,6,1,1,1,1,6,1,4,3,6,1,2,0},{1,7,6,2,5,4,6,7,5,9,3,1,9,6,5,3,6,10,2,9,10,2,2,7,2,7,10,3,9,8,8,6,9,8,4,7,6,7,4,4,8,6,8,4,4,3,4,3,2,1,10,0},{1,10,4,1,1,12,9,3,11,4,7,5,2,9,2,4,5,4,8,3,9,12,6,5,2,3,4,4,3,6,7,8,6,8,7,3,2,6,5,4,12,8,3,12,7,10,9,7,1,6,8,0},{1,15,5,15,14,1,9,2,4,14,9,4,3,5,11,16,4,4,9,3,16,4,2,13,15,8,8,2,2,5,15,11,5,12,10,3,6,4,1,6,16,6,6,14,12,15,11,9,12,9,4,0},{1,10,10,3,13,4,8,6,11,14,12,15,15,14,10,16,15,2,12,2,2,10,18,10,2,14,5,3,17,10,13,10,18,5,3,18,1,4,6,4,8,8,11,14,9,1,17,16,10,13,17,0},{1,16,19,6,3,2,1,16,3,22,11,14,5,12,13,13,17,3,5,1,6,9,6,13,19,22,10,18,9,6,13,1,22,8,7,3,17,11,18,13,16,16,19,11,9,8,19,14,2,8,6,0},{1,19,16,17,12,27,14,27,28,16,18,23,16,26,13,27,12,1,6,6,21,21,8,4,11,17,15,8,19,8,13,5,6,19,7,15,11,13,11,14,3,11,14,25,8,2,4,11,21,26,15,0},{1,30,4,19,23,8,21,8,28,25,25,27,25,27,12,16,18,25,30,8,22,22,11,18,25,30,19,29,14,7,24,25,20,3,14,20,20,27,16,19,22,23,12,1,27,21,5,30,1,12,1,0},{1,7,22,6,23,32,13,23,1,9,32,9,16,23,28,32,11,10,23,36,1,26,2,27,32,10,19,22,23,18,5,17,21,34,5,32,26,28,18,14,35,2,22,6,10,11,20,17,36,8,22,0},{1,38,15,2,11,13,10,19,36,20,33,9,18,35,22,29,2,39,9,6,5,16,22,17,17,37,25,23,22,15,9,3,1,35,11,16,8,32,22,37,33,35,1,11,24,36,22,32,35,22,35,0},{1,33,5,41,22,42,23,40,39,6,9,14,34,5,37,33,36,12,21,26,41,31,9,2,39,7,16,39,39,3,41,9,24,41,42,14,8,19,24,21,38,15,29,18,40,23,37,42,39,10,3,0},{1,41,13,25,30,10,17,25,38,5,18,13,13,44,6,33,43,42,17,11,22,37,46,32,34,5,5,35,15,23,11,41,21,41,28,21,5,31,34,17,21,19,25,23,29,17,37,24,11,14,12,0},{1,33,44,35,44,26,36,26,50,20,20,27,30,39,16,15,32,46,23,21,4,18,45,24,28,43,11,15,37,51,43,22,5,23,4,22,11,52,39,28,2,51,38,51,26,20,44,32,22,51,51,0},{1,34,8,25,46,39,37,37,45,13,50,15,2,34,34,40,43,3,9,7,19,12,9,48,25,46,50,9,29,48,12,8,47,14,47,2,44,11,8,12,15,56,32,16,43,17,49,19,12,39,41,0},{1,41,17,30,57,32,58,54,53,37,48,7,27,4,36,22,36,23,41,31,26,30,52,25,32,6,37,45,29,9,43,40,19,19,8,29,50,11,6,38,19,34,33,26,30,17,18,3,58,40,55,0},{1,29,31,14,5,35,56,10,2,40,58,39,55,50,9,63,7,17,50,30,18,29,22,40,64,14,17,58,13,55,42,44,7,53,26,23,43,57,27,10,15,29,21,62,38,36,18,36,8,1,60,0},{1,31,45,55,52,70,9,16,41,30,14,2,45,68,38,9,3,59,24,43,22,38,1,39,32,36,61,42,40,17,26,52,11,57,27,10,27,69,14,50,64,7,10,55,1,12,39,44,47,27,49,0},{1,16,13,65,43,48,69,66,15,1,18,13,55,70,61,39,59,59,22,40,23,46,48,39,70,33,28,71,36,12,55,41,58,9,72,3,6,56,15,28,7,26,47,63,18,4,47,63,38,51,26,0},{1,76,34,15,2,1,50,55,22,72,71,11,12,75,27,61,74,63,35,23,46,16,23,76,68,40,59,30,67,45,24,14,17,42,28,58,32,30,1,23,58,5,73,54,25,69,22,40,24,68,23,0},{1,71,24,79,63,78,21,47,41,2,76,6,15,65,36,42,25,70,72,80,25,75,55,35,4,79,39,26,23,81,35,70,71,76,53,47,23,4,1,11,8,72,62,48,26,62,41,36,68,69,78,0},{1,82,9,5,11,64,8,83,36,55,51,47,83,5,14,29,40,35,79,84,85,6,20,69,73,7,6,72,34,52,12,87,53,42,66,21,78,51,7,53,23,69,48,62,69,51,61,37,12,47,79,0},{1,38,30,23,51,5,23,46,15,20,25,4,67,60,63,62,60,40,50,14,48,64,21,73,2,95,34,64,22,30,16,39,91,45,14,7,53,64,25,75,58,55,33,59,81,17,26,81,69,67,70,0},{1,97,67,71,4,20,37,33,75,11,31,18,86,77,28,11,98,45,47,23,14,55,67,60,29,86,3,20,3,38,98,2,71,95,92,53,78,18,63,21,58,85,99,5,35,10,89,27,84,42,54,0},{1,12,56,25,73,66,60,38,87,23,102,1,68,14,41,87,73,30,92,50,35,21,80,78,58,95,82,76,3,21,97,19,100,13,72,46,35,56,59,5,31,95,75,94,49,17,43,45,18,74,14,0},{1,100,31,74,69,7,56,56,86,21,29,7,75,26,78,46,82,47,54,64,11,72,30,84,94,53,14,23,43,81,60,41,91,73,75,3,87,77,28,7,94,57,61,79,9,59,11,31,43,75,69,0},{1,9,73,90,42,84,105,78,40,98,17,74,52,34,108,106,12,51,9,103,99,78,28,20,58,4,20,104,16,84,43,14,30,33,34,52,35,67,42,25,30,97,72,98,76,100,65,68,100,46,64,0},{1,80,108,27,11,22,25,35,62,65,29,53,84,26,59,63,108,57,109,73,13,103,64,60,82,23,5,103,98,74,83,38,112,42,94,60,38,24,82,48,18,9,70,59,35,62,7,36,26,100,105,0},{1,13,49,107,9,55,112,39,115,34,99,38,110,75,24,11,73,52,101,32,85,58,92,61,96,50,125,102,99,72,10,13,59,100,99,15,53,67,126,86,56,98,77,126,77,13,63,97,99,118,50,0},{1,31,92,42,16,6,34,125,121,67,99,40,121,1,60,81,123,90,9,55,98,74,77,100,42,37,71,7,27,1,20,99,97,43,69,119,77,72,14,49,11,93,38,79,104,89,105,41,113,6,102,0},{1,25,36,70,18,112,71,18,77,118,67,42,19,73,123,120,50,12,21,8,85,59,36,4,71,19,86,123,97,85,69,69,89,44,14,125,5,127,91,42,62,67,120,38,131,28,25,116,87,57,79,0},{1,69,5,114,119,53,82,89,135,118,7,25,86,15,108,49,89,10,65,117,122,24,20,117,121,135,95,84,25,37,73,55,104,64,21,33,75,22,80,103,44,58,14,106,105,95,26,17,94,26,104,0},{1,56,32,7,83,40,128,45,44,27,67,47,23,20,23,125,100,146,118,133,52,87,143,143,108,70,44,103,57,129,75,83,20,56,104,91,118,107,133,125,13,8,66,119,92,5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847,760,977,367,661,610,359,237,1062,704,1426,1054,812,24,1227,0},{1,1205,1460,281,1212,1287,1516,850,267,264,1287,1696,195,868,748,1569,1311,538,814,125,1481,874,577,1211,1640,1676,1175,758,968,371,1279,261,995,687,74,386,379,1389,789,357,1593,1500,9,630,939,15,214,595,968,852,1135,0},{1,1606,699,1606,40,1736,954,661,426,1595,306,317,1036,506,1561,1135,1461,886,866,1608,1260,1507,628,952,1337,1040,1288,499,1703,1822,1650,619,569,136,443,1813,1078,1769,378,224,106,1766,158,251,1777,1670,1455,1023,949,572,393,0},{1,820,710,621,1756,1403,207,1226,1193,1752,1277,1588,445,340,1499,794,92,556,498,704,968,632,1477,1260,1437,706,269,50,43,1832,1628,57,1271,247,991,1307,15,754,869,1665,1565,1347,805,219,615,1471,1702,916,1470,1813,1506,0},{1,1116,706,692,162,1130,854,297,952,1761,144,776,939,456,93,1464,81,1220,863,1038,898,858,1779,4,1517,957,1832,204,1034,317,112,1043,364,401,708,1856,1091,1420,466,1611,1758,1071,372,1642,246,638,1178,1757,1609,1063,1143,0},{1,972,857,1735,1849,613,670,848,1059,727,606,1569,1607,116,326,1482,1459,1017,852,1789,619,1078,1495,1428,1337,956,1242,285,483,1043,359,1075,1102,1649,778,829,1010,1420,1788,1638,19,186,1444,1065,1378,1593,1326,1449,411,738,375,0},{1,366,1126,714,754,968,1683,1342,322,537,244,1082,1202,1599,401,1560,1289,1517,815,1537,486,1169,1530,1217,382,77,696,972,176,1557,796,1279,1659,99,1256,1759,1476,417,121,729,849,790,379,707,447,1593,152,925,56,711,1766,0},{1,471,11,1680,1625,512,840,1412,243,1019,75,1491,287,30,1560,537,1136,725,1045,1503,1210,208,1561,1867,1233,1559,1298,463,416,1029,346,1380,429,490,197,1191,213,934,1340,249,336,1214,45,1267,1842,1359,1457,1216,285,1046,476,0},{1,1209,615,959,1806,1077,256,692,1516,994,339,324,1569,1020,90,990,933,135,1640,745,1739,769,1343,644,1606,1304,1194,1804,1331,801,1631,157,1503,836,702,870,844,949,312,133,267,387,1206,67,601,1208,1563,5,160,369,877,0},{1,620,1861,1200,905,1698,1563,603,579,762,1648,1267,1488,1721,320,1808,1426,1073,1239,278,1572,1276,639,765,1204,319,872,715,712,723,639,1591,130,1836,380,1452,246,1530,964,1196,1844,1822,1518,1584,485,1171,1155,1683,1693,340,1724,0},{1,889,1605,1729,977,1459,1282,980,777,659,1289,741,749,1550,1690,925,1198,1372,552,902,774,256,297,149,488,1215,599,1860,403,1551,1685,1734,588,61,235,854,93,43,25,398,1742,943,501,1189,984,1647,138,1478,854,1476,664,0},{1,1499,268,75,1486,1091,1479,501,94,415,268,1176,1454,235,1267,1086,44,637,1493,1438,1750,310,319,301,1776,877,583,788,761,378,32,1453,593,1068,427,410,273,324,576,251,1006,408,615,1123,1686,60,1417,1318,324,1307,1369,0},{1,509,187,5,389,906,1272,1289,1230,1380,445,911,1574,1830,904,345,410,1862,318,259,323,1887,770,495,1606,843,698,860,1101,507,253,443,1657,1343,894,259,696,1660,1222,186,631,488,382,452,1235,1500,1154,1615,1227,641,3,0},{1,362,1217,1188,1439,1618,301,488,1285,984,977,103,1650,1151,861,1597,271,1577,878,1459,642,347,281,1687,721,1089,1770,1033,1586,291,1675,1380,1749,1589,164,1171,963,1705,612,309,975,1862,1484,691,1616,970,1757,40,337,329,1368,0},{1,1890,194,799,575,907,1068,1360,419,666,1836,169,220,307,283,372,1212,1012,1258,370,1762,903,1602,390,24,43,1793,1792,1592,562,1841,649,401,727,1036,307,1106,565,299,1217,756,1916,844,43,1299,433,87,1912,1908,136,59,0},{1,867,1187,783,1131,1465,199,104,1325,1022,1487,1101,72,1818,52,700,310,740,734,397,94,977,908,313,816,1710,1523,1080,327,1387,920,1456,23,1709,1081,454,11,905,632,1595,1761,1525,1125,1908,637,384,951,1663,589,1386,217,0},{1,1646,1842,377,1828,1118,635,1267,1415,1501,531,1704,1569,1520,1819,691,1433,1183,928,224,453,1765,213,34,161,1468,387,1412,131,1621,886,1461,1589,1505,775,1876,1943,1701,1720,372,1325,702,31,1109,1703,932,1376,1569,307,885,480,0},{1,1757,1493,802,1345,1968,1183,437,1030,1269,629,1293,86,907,1504,42,1886,496,1820,1632,1803,1141,592,1429,1953,938,726,399,435,288,903,626,620,51,959,1445,1434,1201,727,1963,384,63,840,561,513,910,936,1316,1373,996,712,0},{1,1703,1654,591,1399,241,1578,677,293,1713,394,191,511,215,253,855,375,983,203,1004,1045,585,1513,91,1662,531,895,1627,970,1204,1256,865,830,1483,1131,1786,1970,655,121,623,1902,322,1392,760,378,90,1691,563,909,272,613,0},{1,107,1830,1226,1613,1745,196,1841,983,309,1760,144,1135,1872,1755,660,517,42,1570,47,1815,871,1447,1649,633,1955,1908,27,1062,240,1974,1333,1884,1180,663,1716,267,349,117,964,1539,867,1907,577,1324,534,1864,36,1124,187,1849,0},{1,208,1313,965,132,1941,1051,8,110,522,1297,1331,1588,606,689,646,1883,1425,878,43,1784,1136,1545,801,1212,771,1231,120,1681,1923,1600,1150,860,1009,453,1825,1278,994,201,1836,865,52,1798,319,357,75,847,495,4,1962,942,0},{1,417,193,1292,812,1963,1819,1269,1303,153,650,365,43,630,11,230,218,1859,1,1809,1494,1918,1791,246,12,12,415,560,1777,407,1147,585,1881,1339,95,219,1234,1818,672,811,482,752,969,1389,40,1925,1595,116,739,1303,1301,0},{1,552,317,244,451,1391,987,182,1359,939,1075,1971,1365,444,113,955,910,304,1504,1108,216,286,1293,1777,1203,456,498,753,849,507,1278,273,1634,865,705,1453,372,936,1030,905,1754,1002,1775,1765,164,928,1238,801,1457,665,95,0}};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;}

• TLE代码

#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;}