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super_log
欧拉降幂，需要正确的欧拉降幂姿势。
欧拉函数收敛的很快，搞一下就过了。
#include <bits/stdc++.h>
#define maxn 1000005
using namespace std;
int prime[maxn], isnprime[maxn], fai[maxn], cnt;
void sieve()
{
isnprime[1] = 1;
fai[1] = 1;
for (register long long i = 1; i <= 1000000; i++)
{
if (!isnprime[i])
prime[++cnt] = i, fai[i] = i - 1;
for (int j = 1; j <= cnt && prime[j] * i <= 1000000; j++)
{
isnprime[i * prime[j]] = 1;
if (i % prime[j] == 0)
{
fai[i * prime[j]] = fai[i] * prime[j];
break;
}
fai[i * prime[j]] = fai[i] * (prime[j] - 1);
}
}
}
int t, m, a, b, phi[maxn], ct;
int my_pow(int a, int p, int m)
{
long long ret = 1, tem = a;
while (p)
{
if (p & 1)
ret = ret * tem % m;
tem = tem * tem % m;
p >>= 1;
}
return ret;
}
int my_pow2(int a, int p)
{
long long ret = 1, tem = a;
while (p)
{
if (p & 1)
ret = ret * tem;
tem = tem * tem;
p >>= 1;
}
return ret;
}
int get2(int b)
{
if (b == 0)
return 1;
if (b == 1)
return a;
return my_pow2(a, get2(b - 1));
}
int get(int b, int m)
{
if (m == 1)
return 0;
if (b == 0)
return 1;
int ans;
if (b > ct)
ans = get(b - 1, fai[m]), ans += fai[m];
else
ans = get2(b - 1);
return my_pow(a, ans, m);
}
int main(void)
{
scanf("%d", &t);
sieve();
while (t--)
{
scanf("%d%d%d", &a, &b, &m);
if (a == 1)
{
cout << 1 % m << endl;
continue;
}
if (m == 1)
{
cout << "0\n";
continue;
}
if (b == 0)
{
printf("1\n");
continue;
}
if (a >= 8)
ct = 1;
else if (a >= 4)
ct = 2;
else if (a == 3)
ct = 2;
else if (a == 2)
ct = 3;
printf("%d\n", get(b, m));
}
}
Tsy’s number 5
正解是 NTT，然而这里每十二个打个表（代码长度限制 96KB，下面这个代码 92KB）就莽过去了…
注意要写$O(N^2)$的算法，否则可能会 T。
去掉注释就是一个很好的打表程序。
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
struct Mod
{
const ll M, SM;
Mod(ll M) : M(M), SM(sqrt(M) + 0.5) {}
ll qadd(ll &a, ll b) const { return a += b, a < M ? a : (a -= M); } //假如a和b都已经在同余系内，就不必取模了，取模运算耗时很高
ll add(ll a, ll b) const { return qadd(a = (a + b) % M, M); } //考虑a和b不在同余系内甚至为负数的情况
ll mul(ll a, ll b) const { return add(a * b, M); }
/*
ll mul(ll a, ll b) const { return add(a * b, -M * ll((long double)a / M * b)); }
ll mul(ll a, ll b) const //无循环快速计算同余乘法，根据a*b是否爆ll替换a*b%M，需要a<M且b<M，可以调用时手动取模
{
ll c = a / SM, d = b / SM;
a %= SM, b %= SM;
ll e = add(add(a * d, b * c), c * d / SM * (SM * SM - M));
return add(add(a * b, e % SM * SM), add(c * d % SM, e / SM) * (SM * SM - M));
}
*/
ll pow(ll a, ll b) const
{
ll r = 1;
for (a = add(a, M); b; b >>= 1, a = mul(a, a))
if (b & 1)
r = mul(r, a);
return r;
}
ll inv(ll a) const { return pow(a, M - 2); } //要求M为素数
/*
ll inv(ll a) const //模m下a的乘法逆元，不存在返回-1（m为素数时a不为0必有逆元）
{
ll x, y, d = gcd(a, M, x, y);
return d == 1 ? add(x, M) : -1; //return pow(a, phi(M) - 1);
}
vector<ll> sol(ll a, ll b) const //解同余方程，返回ax=b(mod M)循环节内所有解
{
vector<ll> ans;
ll x, y, d = gcd(a, M, x, y);
if (b % d)
return ans;
ans.push_back(mul((b / d) % (M / d), x));
for (ll i = 1; i < d; ++i)
ans.push_back(add(ans.back(), M / d));
return ans;
}
*/
ll log(ll a, ll b) const
{
unordered_map<ll, ll> x;
for (ll i = 0, e = 1; i <= SM; ++i, e = mul(e, a))
if (!x.count(e))
x[e] = i;
for (ll i = 0, v = inv(pow(a, SM)); i <= SM; ++i, b = mul(b, v))
if (x.count(b))
return i * SM + x[b];
return -1;
}
} M(998244353);
struct EulerSieve
{
vector<int> p, m, phi, mu; //素数序列，最小素因子，欧拉函数，莫比乌斯函数
EulerSieve(int N) : m(N, 0), phi(N, 0), mu(N, 0)
{
phi[1] = mu[1] = 1; //m[1]=0,m[i]==i可判断i是素数
for (long long i = 2, k; i < N; ++i) //防i*p[j]爆int
{
if (!m[i])
p.push_back(m[i] = i), phi[i] = i - 1, mu[i] = -1; //i是素数
for (int j = 0; j < p.size() && (k = i * p[j]) < N; ++j)
{
phi[k] = phi[i] * p[j];
if ((m[k] = p[j]) == m[i])
{
mu[k] = 0;
break;
}
phi[k] -= phi[i];
mu[k] = -mu[i];
}
}
}
} e(1e5 + 9);
ll a[] = {0, 535977894, 824090374, 966355039, 844688201, 642370795, 275302155, 412496450, 351516858, 758344268, 410326949, 885337764, 833437643, 538941894, 271795048, 447629209, 717437611, 656631107, 247231186, 169703783, 990456193, 501845081, 925025543, 594413550, 207768571, 927850544, 70897603, 955296959, 694095430, 180420785, 203871433, 927818684, 239425325, 753017780, 983651693, 816765852, 173664845, 578432829, 189259009, 390230583, 523151811, 861880791, 82787274, 207422220, 438956898, 983406554, 784578299, 262392277, 804955230, 314170684, 971594286, 224938360, 819980744, 237762570, 647272052, 158541460, 71655539, 478183961, 69213427, 212142319, 40641371, 351615372, 109219314, 215457754, 839274293, 471635686, 656110335, 412179567, 353272899, 162747922, 323873941, 290750052, 20055930, 320615278, 808314734, 586254171, 770146490, 801987924, 375201768, 973354358, 64288140, 30045836, 18769272, 139134951, 340469322, 741089853, 152465175, 88311691, 984030370, 776930584, 752386088, 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423435323, 308333281, 686987517, 787634249, 476684612, 54218607, 157099372, 761420709, 986225022, 746783818, 496684535, 434700191, 788549250, 445459518, 256246645, 63600604, 402792725, 124701313, 319334141, 893021981, 386170341, 524461150, 667117316, 639909762, 260385300, 816614545, 388407204, 17718038, 983697729, 895972898, 510816595, 660743096, 80537445, 33702443, 599770711, 215982973, 438865781, 514238553, 843597259, 387249488, 600831751, 360334793, 11051982, 492235401, 347626519, 742680023, 149544889, 631055497, 309320992, 48186648, 736859429, 395532883, 429678077, 194070161, 414290631, 89120410, 450220048, 848180743, 616406692, 714115048, 493858031, 785681782, 271326458, 550169680, 38026413, 830640013, 493792762, 556039882, 859569602, 753148171, 227720189, 265978392, 825854274, 348046681, 78868363, 923496365, 518818339, 207845153, 804051804, 560972237, 279613699, 642976081, 495422354, 607741877, 111997445, 204905789, 474365739, 975599226, 668867572, 90503463, 32946535, 508779295, 39104475, 884740649, 623999720, 627988354, 952182330, 923541702, 745890847, 359954593, 632621537, 200697656, 588518369, 586335274, 925224598, 784556582, 257961241, 98664155, 114965313, 150375411, 504951265, 385959114, 202170862, 15564909, 942990332, 192404122, 48981154, 611429290, 878467220, 15922653, 235408928, 515694245, 991422427, 968660530, 200138098, 57556630, 60323338, 749754675, 258626747, 698436112, 210347689, 190712090, 264040999, 892426739, 645622403, 679891775, 814577040, 950922764, 306273330, 871429019, 322885798, 182327421, 448751091, 110439113, 598690201, 655610148, 693738261, 741320691, 424743909, 203071698, 30623192, 151893755, 167917706, 845569134, 362806291, 908139881, 288476812, 216667318, 364610414, 927352113, 634981576, 128472195, 303992638, 473726623, 766154459, 200057456, 192814991, 44014021, 986262473, 110399125, 876230934, 165226991, 886532912, 220815659, 751175480, 376586125, 705104812, 595503944, 807925431, 636393200, 472775663, 969989266, 991859731, 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122731916, 95856504, 989161250, 762830034, 114143994, 986575945, 281533542, 919376657, 321335591, 397300690, 886790005, 801134929, 95715218, 365987608, 249776848, 944550396, 212887510, 994898025, 842530395, 405049115, 714954022, 380811988, 522872061, 621611908, 466261719, 258651441, 175671850, 255412245, 519267384, 598452451, 731192350, 797820382, 823200339, 842838117, 822477520, 130860908, 723675651, 67500858, 197997080, 44003452, 616858383, 616107229, 984015043, 355125358, 818001857, 378404211, 333588830, 417665949, 783242054, 674149844, 341824385, 744051420, 742848555, 462890375, 347500178, 172807750, 84326212, 6947838, 901797089, 187469124, 525785362, 677805988, 419611277, 948420949, 358826522, 171527776, 882406094, 952429901, 649635238, 39137973, 558542282, 630053870, 815280670, 93423904, 919861934, 698460479, 907009055, 101131928, 51011223, 853749333, 398118602, 270066117, 374899095, 718435060, 733294599, 611776431, 505709523, 462907004, 936983563, 430460412, 516734416, 191502371, 627625137, 265282339, 526578270, 449518192, 712140726, 282615038, 278500232, 18774660, 517013709, 845277268, 101762052, 326880127, 660625156, 685710711, 136911027, 155738765, 629154182, 18273394, 92198734, 978300601, 466873157, 584349640, 413532164, 786162240, 831385374, 297513069, 966090131, 448916051, 83938740, 195971336, 485141380, 750109423, 204217937, 849794923, 54572665, 610363458, 189680264, 947370178, 913405747, 551099517, 789836465, 132001992, 950562100, 454158557, 157141904, 62573993, 133731376, 109239251, 213639840, 645754347, 562534016, 959624377, 562883485, 871071543, 584242820, 5946241, 864340587, 839543350, 817321180, 754376407, 556877904, 654039902, 863173388, 610264276, 739112199, 726867451, 76346179, 99424183, 448814391, 201817141, 341061602, 515887097, 811986671, 841535639, 683813892, 498997571, 20204997, 446892476, 188213374, 263074111, 433340042, 313069877, 885914635, 263907230, 162422794, 754177278, 372532354, 817916764, 106849142, 536816795, 436823112, 124926459, 312684068, 976683959, 667006071, 302815127, 503787062, 695221300, 354471685, 139345719, 664923353, 266531205, 602090739, 298500204, 549323563, 955048624, 691309734, 695615384, 579115163, 54967279, 268340822, 410011851, 883576456, 472511998, 163026422, 328377061, 589393111, 803262068, 861878852, 891229460, 353295059, 611780802, 951004426, 479401177, 620112229, 563092319, 932636462, 19806101, 234339608, 703714556, 897547753, 317075050, 591424637, 873644121, 542824532, 626698328, 321346698, 733177141, 635775978, 301017766, 124832010, 711560007, 436431924, 232160005, 686904113, 217706081, 371981820, 744651097, 54384517, 70172591, 191430148, 352161670, 831800296, 230028513, 468494914, 498093407, 333609240, 258906459, 804143948, 119354381, 982508603, 600140318, 376784300, 142890651, 202131889, 753862248, 135024420, 651874528, 186366076, 618505846, 585216400, 323874769, 73306054, 200184746, 604115795, 871452782, 434783207, 765445255, 525510404, 66510829, 822246978, 7526362, 970072510, 757193177, 591770293, 26593501, 537875513, 544321577, 460167422, 260092894, 340249925, 233888104, 609662249, 159668964, 695369107, 108626018, 501233684, 129807049, 627448727, 775475428, 595697346, 463291469, 204387534, 623578882, 96933760, 14132999, 431773976, 519348947, 41301867, 627608205, 511667664, 663996895, 439528348, 401718922, 344359959, 223117187, 90666066, 683744762, 513163276, 821067531, 371335945, 639320206, 717640143, 171989490, 58280351, 896014107, 857912548, 550566261, 432001223, 647911847, 336043802, 753846227, 541913562, 325372123, 505378779, 2684055, 301584761, 569452264, 577275248, 585591841, 773123767, 83702566, 378567758, 810806103, 94616060, 42363467, 916420954, 247794204, 223597165, 683582209, 74007833, 913434706, 612271796, 3529544, 346750273, 513541684, 145310012, 226329059, 994278607, 936737719, 171821863, 676470533, 833826882, 718352590, 165162077, 496509583, 911086736, 841774466, 625724182, 942708489, 956887697, 496019292, 930547945, 242150425, 872551706, 272038665, 93465441, 857065526, 935915615, 839092457, 762248989, 254462589, 408032391, 384574978, 342663214, 411968287, 257051790, 338516676, 836274101, 561417455, 111217289, 321015844, 195944067, 798454860, 562695272, 954666728, 459878566, 924395799, 199473842, 349757974, 558564438, 453569905, 318551303, 597530589, 290934394, 261005055, 203578476, 237672105, 143525500, 693841372, 648846888, 139872616, 426223943, 409536848, 635746268, 562544417, 879888883, 656165231, 119498917, 319472714, 408655865, 109761696, 435449497, 846762171, 318784336, 34946318, 83496325, 454783214, 734056540, 426115847, 728967922, 70930353, 16768688, 29478707, 453594706, 55014968, 858400834, 867975609, 752611064, 64595167, 974858963, 160412219, 455087252, 626293858, 776975777, 768394385, 55925173, 399567743, 314367379, 804563593, 823451220, 2307013, 220801876, 676666538, 146643136, 187846211, 236683752, 382195669, 828144532, 241193010, 101280997, 139800231, 754021397, 182160838, 143851370, 928573820, 773044848, 59459860, 751656657, 499641056, 165392734, 438308341, 24987358, 734004517, 617640345, 117089477, 882862475, 995620920, 738924867, 193254834, 753418793, 650629896, 712253893, 293263088, 513150554, 131768625, 707522155, 859395355, 35904827, 711819656, 699472061, 68864432, 553792558, 418252087, 451488095, 780428953, 108203254, 777659480, 976248066, 342486737, 943135338, 660056949, 501278584, 356222008, 303820844, 720529393, 241916347, 845475727, 357652419, 155168566, 916958457, 950633291, 241270304, 268248418, 206788363, 327944176, 363705024, 262781892, 814805433, 814758713, 212806250, 613204648, 76449365, 429700605, 620179826, 211215996, 171604626, 491305000, 629555816, 788617850, 206923633, 897496306, 994810556, 346860176, 994247550, 299236041, 881444506, 699111772, 615111568, 643357209, 283580559, 660390832, 793607713, 461694548, 75737531, 653551593, 279644003, 822171780, 213174010, 540492939, 364063446, 687589658, 696340255, 471438470, 838500325, 207767876, 416916378, 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229387318, 836033062, 123921006, 905807278, 964062294, 202280561, 967452882, 79371202, 709049810, 554866152, 208875733, 936039369, 677996034, 124954582, 584672265, 790129244, 904875016, 522636522, 819176564, 202036570, 154467418, 110346094, 259161877, 112339418, 218209033, 741006833, 611976369, 203938656, 86685423, 2829377, 524588907, 173773443, 72147293, 370827600, 149176849, 844051742, 819836595, 728967381, 327299495, 411152789, 4580485, 73566702, 632011767, 395900191, 888290039, 583172447, 605223781, 564546817, 741068072, 225426786, 417621692, 583946575, 477517987, 730179200, 721625169, 291119896, 581110129, 571710731, 336976901, 251582952, 668125961, 435410668, 399288405, 213019661, 153760870, 311151205, 832138031, 196060976, 671621139, 27199692, 591942123, 294270118, 254086069, 146939041, 492756932, 601226590, 377558243, 698477980, 211770594, 398639455, 800799469, 905920193, 875831425, 330418130, 882165181, 804335972, 801950710, 494012365, 833154971, 900254250, 638850711, 135405557, 940138736, 9111740, 865156626, 64679365, 18983036, 946885739, 222976951, 376850196, 520227145, 596695108, 818422287, 594227206, 436538427, 297666886, 332597489, 743243870, 384067239, 953079398, 132490936, 886748625, 861960678, 284099948, 640729023, 80341935, 130735510, 432740713, 123362673, 712669135, 581978098, 484882077, 556158004, 557053310, 520679985, 113038899, 216337756, 925887251, 454288369, 248885032, 885627778, 978012260, 544280508, 557912382, 230390334, 780820520, 788735389, 472815700, 116933179, 212088719, 401168746, 159562236, 381139438, 454224784, 209781690, 675118001, 972620522, 55357115, 221798291, 172065449, 780772483, 955130695, 250649924, 33492544, 851534196, 98187505, 350244090, 389156879, 601325005, 113373433, 894737619, 691011705, 287422304, 563295923, 68749410, 412850866, 367925585, 316914995, 220800708, 922217911, 779772475, 831024578, 663460168, 498974869, 103850713, 344470565, 944194046, 575637912, 179538673, 166217018, 145304329, 286548516, 873963533, 964511267, 611058858, 328023599, 680795549, 120067508, 597989334, 472711914, 927960473, 988416567, 919193710, 974509394, 357552085, 260998610, 368831944, 898538361, 840083646, 705408144, 641751590, 261041462, 309235339, 881187094, 748520624, 226433712, 527934852, 32574127, 68082025, 780897588, 408377686, 5763340, 48456367, 944428905, 965224851, 562133375, 661306181, 626133775, 940540612, 334048570, 194695271, 615729050, 366624880, 866605805, 965240578, 462977847, 777679239, 461155637, 893323426, 768943360, 135739900, 472500397, 562119052, 362849902, 892081958, 357620566, 810636792, 168013307, 328872413, 530767273, 280413140, 570361941, 73790733, 721486032, 320360575, 366651617, 550495476, 449359521, 683063735, 670790498, 886640621, 721954327, 423049354, 176671948, 903143976, 757528967, 720359454, 985259103, 344796751, 677814437, 333327384, 33358556, 524125840, 858109016, 836343663, 609724202, 762081061, 877514221, 881906803, 83985175, 658004455, 771020745, 44959913, 977428391, 301887706, 176777664, 488654075, 2578760, 659427674, 843218989};
const ll N = 1e5 + 9, B = 12;
int main()
{
int t, n;
//ofstream fout("a.txt");
for (scanf("%d", &t); t--;)
{
scanf("%d", &n);
vector<ll> p(n + 1, 1);
ll pos = n / B, ans = a[pos];
//ll pos = 0, ans = 0;
for (ll i = pos * B + 1; i <= n; ++i)
{
for (ll j = 1, t = M.pow(2, e.phi[i]); j <= i; ++j)
p[j] = M.mul(p[j - 1], t);
for (int j = 1; j <= i; ++j)
{
ll tmp = M.mul(p[e.phi[j]], M.mul(e.phi[i], e.phi[j]));
M.qadd(ans, tmp);
if (j != i)
M.qadd(ans, tmp);
}
//if (i % B == 0)
//fout << ',' << ans, clog << i << '\n';
}
printf("%lld\n", ans);
}
}
Greedy Sequence
标准解法是 set 上二分，不过我暴力就搞过去了。
#include <bits/stdc++.h>
using namespace std;
int main()
{
int t, n, k;
for (scanf("%d", &t); t--;)
{
scanf("%d%d", &n, &k);
vector<int> f(n + 1, 1), p(f);
for (int i = 1, a; i <= n; ++i)
scanf("%d", &a), p[a] = i;
for (int i = 1; i <= n; ++i)
{
for (int j = i - 1; j > 0; --j)
if (abs(p[i] - p[j]) <= k)
{
f[i] = f[j] + 1;
break;
}
printf("%d%c", f[i], i < n ? ' ' : '\n');
}
}
}
Holy Grail
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll INF = 1e18;
struct Graph
{
struct Vertex
{
vector<int> o;
};
struct Edge
{
int first, second;
ll len; //边长、容量，图论算法使用
};
vector<Vertex> v; //点集
vector<Edge> e; //边集
Graph(int n) : v(n) {}
void add(const Edge &ed)
{
v[ed.first].o.push_back(e.size());
e.push_back(ed);
}
};
struct BellmanFord : Graph
{
vector<ll> d;
//vector<int> p;
BellmanFord(int n) : Graph(n) {}
bool ask(int s)
{
d.assign(v.size(), INF);
//p.assign(v.size(), e.size());
vector<int> cnt(v.size(), 0), flag(v.size(), d[s] = 0);
for (deque<int> q(cnt[s] = flag[s] = 1, s); !q.empty(); q.pop_front())
for (int u = q.front(), i = flag[u] = 0, k, to; i < v[u].o.size(); ++i)
if (k = v[u].o[i], to = e[k].second,
d[to] > d[u] + e[k].len)
{
d[to] = d[u] + e[k].len /*, p[to] = k*/;
if (!flag[to])
{
if (v.size() == ++cnt[to])
return 0;
flag[to] = 1, q.push_back(to);
}
}
return 1;
}
};
int t, n, m;
int main()
{
for (scanf("%d", &t); t--;)
{
scanf("%d%d", &n, &m);
BellmanFord g(n);
for (int i = 0, x, y, z; i < m; ++i)
{
scanf("%d%d%d", &x, &y, &z);
g.add({x, y, z});
}
for (int i = 0, s, t; i < 6; ++i)
{
scanf("%d%d", &s, &t);
g.ask(t);
printf("%lld\n", -g.d[s]);
g.add({s, t, -g.d[s]});
}
}
}