Brief description:
Problem D. Liars and Serge
.. 有 n 个人。。询问每个人有多少个 Liars。。。每个人都知道有多少 Liars。。。说真话的人返回的总是答案。。说假话的人从 [1, n] 中不是答案的某个值。。
。。问有多少种回答方案。。可以确定 恰好有 k 个 说谎者。。。
( 1 ≤ k ≤ n ≤ 2^8 …n 为 2 的整次幂。。
Problem E. Lucky Arrays
给定 n 个元素的数列。每个数字可以是 1、2、3 以及待定三种状态。。待定的话可以任取 1、2、3 三者之一。
给定一个 3*3 的合法相邻矩阵 aij。。表示相邻的位置如果是 i,j 的话是否合法。。。
初始所有位置都是待定。。m 个操作。。每个操作修改其中一个数的状态。。然后询问当前有多少合法数列。。。
(1 ≤ n, m ≤ 77777 ..
Analysis:
…
Problem D. Liars and Serge
组合 DP。。考虑到如果回答 i 的人数不是 i 那么这些一定都在说谎。。
dp[i][j][k] 表示当前考察的是回答 i 的一组，且已经有 j 个人回答过了其中确定 k 个人在说谎的方案数。
。。枚举回答答案 i 的有多少人即可。。O(n4) DP。。。
。。。会稍稍超时。。最后注意到 n 很稀疏可以打表。。
Problem E. Lucky Arrays
ただ普通のセグメント木だけ。。
//}/* .................................................................................................................................. */
const int N = 256 + 1;
int a[10][N] = { { 0 }, { 2, 1 }, { 32, 30, 80, 109 }, { 6824, 59808, 147224, 415870, 1757896, 1897056, 4898872, 7593125 }, { 776830421, 290516100, 746623577, 293783147, 33900006, 735127505,
565460332, 428982705, 472062098, 161873957, 117354594, 515619293, 578944191, 312106242, 569389279, 391464593 }, { 261086313, 584837659, 683961846, 468868529, 211593382, 736955478, 229471758,
157617135, 398169441, 360252438, 629394768, 264125799, 647490480, 342079395, 391579767, 225200475, 486011304, 513156108, 628771752, 132906648, 142138221, 20119449, 444199674, 195188679,
387329805, 44684703, 651912135, 737154512, 612549793, 519860281, 186175544, 212568440 }, { 240805271, 239509872, 581127897, 6511239, 156126222, 509425833, 672407328, 366667722, 459185405,
509737025, 554790222, 165216555, 703150560, 74806569, 398730015, 383350905, 506108358, 51326142, 298053147, 104256117, 391428765, 374020479, 206607807, 87664059, 275899176, 56407680,
551553401, 448939463, 582889860, 129676638, 226078251, 135769095, 61292868, 578972226, 190181628, 390739055, 184587732, 446575689, 732674124, 232198470, 676760679, 352474101, 611444862,
575661807, 628905585, 320813094, 522840969, 469781928, 156006018, 554473341, 239654268, 643714911, 433540170, 199307003, 496385218, 291740751, 67309914, 370826673, 202356819, 279421821,
421203111, 63744786, 520987612, 550671827 }, { 482164403, 768209115, 462063756, 154906374, 36099042, 341766705, 678182556, 621882744, 478771358, 231881111, 175889805, 243630450, 168908523,
671961765, 55761813, 652682670, 773939082, 517628076, 756201264, 124604900, 750976272, 498253248, 676047609, 137170026, 705610017, 495032139, 561797418, 703097347, 500815609, 95984586,
739707108, 265613565, 387099846, 777331779, 594676173, 591219559, 407997044, 208947235, 93337440, 478908360, 685013007, 487033953, 671903001, 39521181, 738490312, 33785059, 465470131,
310453920, 54648783, 346831137, 427694175, 474743430, 705296781, 435828036, 429824745, 663532359, 261388683, 244690731, 533997135, 596108961, 506813013, 371892402, 590145264, 104733162,
143420103, 654339672, 700348950, 685038942, 578826927, 286484229, 501639192, 434962491, 299270097, 27702486, 335375775, 111746817, 565603164, 294926121, 676063665, 735862995, 710035809,
437011960, 668528077, 138765186, 508213986, 615036450, 353784942, 624827616, 343900011, 241289776, 52410890, 72018835, 352406796, 415705878, 4802637, 376367145, 65589678, 333633477, 341834527,
303717460, 282387700, 42951006, 254706039, 423048528, 526429710, 68131467, 669954708, 12787348, 500636381, 317959019, 479433192, 657133515, 416259390, 610216692, 340129188, 44594256,
257373347, 138718678, 530767740, 292922628, 37220268, 605295159, 480722613, 458170419, 30540300, 487159055, 232966794, 149150650 }, { 412133651, 386543325, 139952108, 289303402, 102404925,
317067177, 396414708, 80515854, 663739304, 317300809, 228877044, 493725043, 715317967, 490300965, 315527373, 743539734, 488329191, 553627998, 533025234, 242583957, 706116537, 614109258,
645447222, 523195911, 492109128, 722623041, 111085128, 766395126, 654378921, 691964847, 496688157, 399056049, 654363234, 102052314, 191720088, 473910948, 259736526, 332840025, 388047555,
665791056, 627111387, 139696515, 441456687, 443032569, 283264821, 771641703, 452641455, 511306362, 117572859, 127701891, 721298331, 176520078, 357242229, 611296308, 696994956, 405628839,
429224274, 465336054, 695091546, 689828796, 574648641, 351220905, 507964023, 675326610, 517248963, 453528621, 220301928, 494463186, 681789969, 339589656, 44524053, 417125457, 339589404,
747135963, 341780733, 734158215, 396817281, 21997836, 5728464, 147611205, 456248898, 714128667, 377654949, 3862068, 128418948, 589390074, 304947090, 11703825, 228266073, 127304142, 429215724,
361541124, 521572968, 468358191, 341231688, 65323503, 613778508, 15985323, 291661029, 410970006, 591638112, 349541550, 89967528, 224922159, 361094166, 584206074, 640051812, 324264456,
652625388, 693768537, 11740617, 309238398, 211085469, 194905872, 639416484, 110110707, 296645895, 748118511, 131177718, 511142751, 775975599, 421403409, 475528473, 434685258, 1768977,
80301375, 708023862, 569195676, 56238084, 632887668, 88089750, 631539342, 396695565, 38780154, 695798271, 469819224, 439587099, 69045921, 682966116, 112310856, 64943298, 534475872, 40215357,
389728458, 286368453, 736006257, 501181650, 54829908, 603489402, 338032656, 512182818, 627500097, 462674016, 3103092, 157324491, 43978329, 596818971, 259025598, 9088632, 91991781, 577291428,
211245489, 429471231, 142626330, 172560633, 510907446, 444609585, 758102058, 375112647, 744786693, 276174402, 19259856, 233672418, 745389414, 225772848, 23385663, 324290610, 519804558,
120337812, 402578568, 360676008, 450089262, 551043738, 337388940, 512108856, 28879011, 690040638, 106017282, 558262341, 99972432, 608226003, 612152037, 42414435, 776201013, 39580443,
518796945, 494437752, 583194366, 723936555, 415359657, 309569589, 751104774, 166684527, 249229170, 353120823, 130668327, 753823584, 580966092, 561963717, 543672234, 393846327, 586278000,
327398400, 278403867, 156455586, 363920382, 190245195, 290039148, 547014447, 466218648, 146037150, 585462906, 666008595, 691786683, 374707494, 622498779, 231158277, 685740951, 115612245,
681825249, 545555745, 551718468, 277206615, 640171035, 757727334, 195193908, 658656684, 457760646, 225925875, 505761984, 18685233, 506832921, 112511021, 396846646, 290147622, 113924623,
669986155, 336008070, 63611061, 238586775, 119956662, 616557739, 772784623, 334527774, 410403148, 51933421 } };
int dp[N][N][N]; int comb[N][N];
int n, k;
void makeTable() {
cout << "int a[10][300]={";
FOR(i, 0, N){comb[i][0] = 1; REP_1(j, i) comb[i][j] = sum(comb[i-1][j-1], comb[i-1][j]);}
for (int n = 1; n <= 256; n <<= 1) {
cout << "{"; //cout << n << endl;
RST(dp); dp[0][0][0] = 1;
#define u dp[i-1][j][k]
#define v dp[i][j+ii][k+(ii!= i?ii:0)]
#define nn (n-j)
REP_1(i, n) FOR_1(j, 0, n) FOR_1(k, 0, j) if (u){
FOR_1(ii, 0, nn) INC(v, pdt(u, comb[nn][ii]));
}
for (int i = 1; i <= n; ++i) {
cout << dp[n][n][i];
if (i + 1 <= n) cout << ",";
}
cout << "},";
}
}
int main(){
#ifndef ONLINE_JUDGE
freopen("in.txt", "r", stdin);
#endif
//makeTable();
int n, k; RD(n, k), OT(a[lg2(n)][k-1]);
}
//}/* .................................................................................................................................. */
const int N = 1 << 17, NN = N * 2 + 9;
int a[NN][3][3]; bool f[3][3];
int n, m, p, v;
// Segment Tree
#define lx (x<<1)
#define rx (lx|1)
#define mid (l+r>>1)
#define lcc lx, l, mid
#define rcc rx, mid+1, r
void Upd(int x){
RST(a[x]); REP_2(i, j, 3, 3) if (f[i][j]) REP_2(s, t, 3, 3)
INC(a[x][s][t], pdt(a[lx][s][i], a[rx][j][t]));
}
void Set(int x){
RST(a[x]); if (v) a[x][v-1][v-1] = 1;
else REP(i, 3) a[x][i][i] = 1;
}
int Sum(int x = 1){
int res = 0; REP_2(i, j, 3, 3) INC(res, a[x][i][j]);
return res;
}
void Build(int x = 1, int l = 1, int r = n){
if (l == r) Set(x);
else {
Build(lcc), Build(rcc);
Upd(x);
}
}
void Modify(int x = 1, int l = 1, int r = n){
if (l == r) Set(x);
else {
if (p <= mid) Modify(lcc); else Modify(rcc);
Upd(x);
}
}
int main(){
#ifndef ONLINE_JUDGE
freopen("in.txt", "r", stdin);
#endif
RD(n, m); REP_2(i, j, 3, 3) RD(f[i][j]); Build();
DO(m) RD(p, v), Modify(), OT(Sum());
}
