// Smart Carts // Solution by Jacob Plachta #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #define LL long long #define LD long double #define PR pair #define Fox(i,n) for (i=0; i=0; i--) #define FoxR1(i,n) for (i=n; i>0; i--) #define FoxRI(i,a,b) for (i=b; i>=a; i--) #define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++) #define Min(a,b) a=min(a,b) #define Max(a,b) a=max(a,b) #define Sz(s) int((s).size()) #define All(s) (s).begin(),(s).end() #define Fill(s,v) memset(s,v,sizeof(s)) #define pb push_back #define mp make_pair #define x first #define y second template T Abs(T x) { return(x < 0 ? -x : x); } template T Sqr(T x) { return(x * x); } string plural(string s) { return(Sz(s) && s[Sz(s) - 1] == 'x' ? s + "en" : s + "s"); } const int INF = (int)1e9; const LD EPS = 1e-12; const LD PI = acos(-1.0); #define GETCHAR getchar_unlocked bool Read(int& x) { char c, r = 0, n = 0; x = 0; for (;;) { c = GETCHAR(); if ((c < 0) && (!r)) return(0); if ((c == '-') && (!r)) n = 1; else if ((c >= '0') && (c <= '9')) x = x * 10 + c - '0', r = 1; else if (r) break; } if (n) x = -x; return(1); } #define LIM 705 int N; int nxt[2][LIM], prv[2][LIM]; vector seq[2][2]; int L[2][2]; PR pos[2][LIM]; int F[2], subS[2]; vector CS; int csInd, sumC, baseAns; int ProcessQuery0(int* K) { int i, ans = 0; // check whether either initial line is too long to be valid Fox(i, 2) if (L[0][i] > K[i]) return(-1); // count initially-satisfied carts Fox(i, N) ans += nxt[0][i] == nxt[1][i]; return(ans); } void PrecomputeForQuery1(int C) { int i, j; // determine which carts are free Fox(i, 2) F[i] = min(C - L[0][1 - i], L[0][i]); auto IsFree = [&](int i, int e) { // if e=1, include non-free, accessible latches PR p = pos[0][i]; return(p.y > L[0][p.x] - F[p.x] - e); }; // compute number of potentially-satisfiable carts baseAns = 0; Fox(i, N) baseAns += nxt[0][i] == nxt[1][i] || // initially satisfied? (IsFree(i, 0) && IsFree(nxt[1][i], 1)); // free, and target accessible? // split free, potentially-satisfiable carts into chains // and compute achievable subset sums of chain lengths sumC = 0; Fill(subS, 0); bitset BC = 1; Fox(i, 2) { auto& s = seq[1][i]; int c = 0, f = -1; Fox(j, Sz(s)) { if (!IsFree(s[j], 0)) continue; c++; // chain forced to belong to a certain line? if (c == 1 && j && IsFree(s[j - 1], 1)) f = pos[0][s[j - 1]].x; // chain ends with this cart? if (j + 1 == Sz(s) || !IsFree(s[j + 1], 0)) { if (f < 0) sumC += c, BC |= (BC << c); else subS[f] += c; c = 0, f = -1; } } } // store results CS.clear(); Fox(i, sumC + 1) if (BC[i]) CS.pb(i); csInd = 0; } int ProcessQuery1(int* K) { // compute space for free carts in each line int i, S[2]; Fox(i, 2) S[i] = K[i] - (L[0][i] - F[i]) - subS[i]; // check whether all free cart chains may be packed into the lines if (min(S[0], S[1]) < 0) return(baseAns - 1); while (csInd + 1 < Sz(CS) && CS[csInd + 1] <= S[0]) csInd++; if (sumC - CS[csInd] <= S[1]) return(baseAns); return(baseAns - 1); // 1 cart must remain unsatisfied due to chain breakage } int ProcessQuery2(int* K) { int i; // check whether either target line is too long to be fully satisfied Fox(i, 2) if (L[1][i] > K[i]) return(N - 1); return(N); } int ProcessQuery(int d, int c, int x, int y) { int i, K[2] = { min(c, x), min(c, y) }; // check whether either initial line is too long to be valid Fox(i, 2) if (L[0][i] > c) return(-1); // check whether there are too many carts to form valid final lines if (N > K[0] + K[1]) return(-1); return d == 0 ? ProcessQuery0(K) : d == 1 ? ProcessQuery1(K) : ProcessQuery2(K); } void ProcessCase() { int i, j, z; // init Fill(prv, -1); // input Read(N); Fox(i, N) { Fox(z, 2) { Read(nxt[z][i]), nxt[z][i]--; prv[z][nxt[z][i]] = i; } } // split into lines (initial/target) Fox(z, 2) { Fox(i, 2) { seq[z][i].clear(); j = N + i; while (j >= 0) { pos[z][j] = mp(i, Sz(seq[z][i])); seq[z][i].pb(j); j = prv[z][j]; } L[z][i] = Sz(seq[z][i]) - 1; } } // process queries int d, c, x, y; LL G[LIM] = { 0 }; Fox(d, min(3, N + 1)) { Fox(c, N + 1) { if (d == 1) PrecomputeForQuery1(c); Fox(x, N + 1) { Fox(y, N + 1) G[ProcessQuery(d, c, x, y) + 1] += d == 2 ? N - 1 : 1; } } } Fox(i, N + 2) printf(" %lld", G[i]); printf("\n"); } int main() { int T, t; Read(T); Fox1(t, T) { printf("Case #%d:", t); ProcessCase(); } return(0); }