#include <bits/stdc++.h> using namespace std; #define REP(i,a,b) for (int i = (a); i <= (b); ++i) #define REPD(i,a,b) for (int i = (a); i >= (b); --i) #define FORI(i,n) REP(i,1,n) #define FOR(i,n) REP(i,0,int(n)-1) #define mp make_pair #define pb push_back #define pii pair<int,int> #define vi vector<int> #define ll long long #define SZ(x) int((x).size()) #define DBG(v) cerr << #v << " = " << (v) << endl; #define FOREACH(i,t) for (typeof(t.begin()) i=t.begin(); i!=t.end(); i++) #define fi first #define se second typedef pair<ll, int> restype; // (-zysk, id) const int N = 100100; const ll infll = 1000100100200100100LL; const restype ini = mp(infll, -1); /// --------------------------- graf ----------------------------------- int n; /// krawedzie vi g[N]; /// wagi krawedzi vector<ll> vcst[N]; /// wielkosc skladowej, ojciec int siz[N], par[N]; /// koszt krawedzi do ojca ll cst[N]; /// zyski w wierzcholkach ll z[N]; /// najlepszy wybor nie z hld (-zysk, id) restype best_nhld[N], cur_nhld[N]; set<restype> set_nhld[N]; /// -------------------------- drzewa ---------------------------------- restype operator+ (const restype& le, const ll &ri) { return restype(le.fi-ri, le.se); } restype operator+ (const ll& le, const restype &ri) { return restype(ri.fi-le, ri.se); } struct Tree { int M; vi ids; /// 0 - najwyzszy w drzewie vector<ll> Tu, Td; /// zysk na calym przedziale idac w gore / dol (czyli lewo / prawo) vector<restype> Tbu, Tbd; /// najlepszy zysk w gore / dol startujacy na koncu przedzialu void build(vi v) { ids = v; M=1; while (M < SZ(v)) M *= 2; while (SZ(ids)<M) ids.pb(n); /*printf("robie drzewo M=%d\nids = ", M); FOR(i,SZ(ids)) printf("%d ", ids[i]); printf("\n");*/ Tu.resize(2*M); Td.resize(2*M); Tbu.resize(2*M); Tbd.resize(2*M); FOR(i,M) Tbd[i+M] = Tbu[i+M] = ini; FOR(i,SZ(v)) { Tbu[i+M] = Tbd[i+M] = min(best_nhld[ids[i]]+(-z[ids[i]]), mp(0LL,ids[i])); //Tbu[i+M] = Tbd[i+M] = min(best_nhld[ids[i]]+z[ids[i]], mp(-z[ids[i]], ids[i])); //printf("Tbu[%d] = %lld (%d)\n", i, -Tbu[i+M].fi, Tbu[i+M].se); } for (int i = M-1; i >= 1; i--) { int m = 2*i+1; while (m<M) m*=2; m -= M; //printf("M=%d, i=%d, m=%d\n", M, i, m); Td[i] = Td[2*i] - z[ids[m-1]] - cst[ids[m]] + z[ids[m]] + Td[2*i+1]; Tu[i] = Tu[2*i] - z[ids[m]] - cst[ids[m]] + z[ids[m-1]] + Tu[2*i+1]; Tbu[i] = min(Tbu[2*i] + (Tu[i] - Tu[2*i]), Tbu[2*i+1]); Tbd[i] = min(Tbd[2*i], (Td[i] - Td[2*i+1]) + Tbd[2*i+1]); //printf("Tbu[%d] = %lld (%d)\n", i, -Tbu[i].fi, Tbu[i].se); } } /// najlepszy (-zysk, id) w dol i w gore (razem) restype get_best(int pos, bool can_stay=false) { /*printf("get best %d\n", pos); FORI(i,M-1) printf("%lld ", Tu[i]); printf("\n"); FORI(i,M-1) printf("%lld ", Td[i]); printf("\n"); FORI(i,2*M-1) printf("(%lld %d) ", -Tbu[i].fi, Tbu[i].se); printf("\n"); FORI(i,2*M-1) printf("(%lld %d) ", -Tbd[i].fi, Tbd[i].se); printf("\n");*/ pos += M; restype best = can_stay ? Tbu[pos] : ini; ll le = 0, ri = 0; while (pos > 1) { //printf("pos=%d, best= %lld %d; ri=%lld, le=%lld\n", pos, -best.fi, best.se, ri, le); if (pos & 1) { best = min(best, Tbu[pos-1] + le + (Tu[pos/2] - Tu[pos] - Tu[pos-1])); le += Tu[pos/2] - Tu[pos]; } else { best = min(best, Tbd[pos+1] + ri + (Td[pos/2] - Td[pos] - Td[pos+1])); ri += Td[pos/2] - Td[pos]; } pos /= 2; } //printf("najlepszy to %lld (%d)\n", -best.fi, best.se); return best; } /// zysk z dojscia do konca do gory ll gain_up(int pos) { //printf("od %d do korzenia zyskam ", pos); pos += M; ll res = 0; while (pos > 1) { if (pos & 1) res += Tu[pos/2]-Tu[pos]; pos /= 2; } //printf("%lld\n", res); return res; } /// zmiana z[id[pos]] lub cst[id[pos]] (fst=true) lub best_nhld[id[pos]] (fst=false); void update(int pos, bool fst) { //printf("update %d (id=%d)\n", pos, ids[pos]); //Tbu[pos+M] = Tbd[pos+M] = min(best_nhld[ids[pos]]+z[ids[pos]], mp(-z[ids[pos]], ids[pos])); Tbu[pos+M] = Tbd[pos+M] = min(best_nhld[ids[pos]]+(-z[ids[pos]]), mp(0LL, ids[pos])); int le = pos, ri = pos+1, len = 1, mi; pos += M; //printf("z = "); //FOR(i,n) printf("%lld ", z[i]); //printf("\n"); while (pos > 1) { if (pos & 1) le -= len; else ri += len; len *= 2; mi = (le + ri) / 2; int R = pos | 1, L = R - 1, U = pos / 2; //printf("pos = %d; L=%d, R=%d, U=%d; le=%d, ri=%d, mi=%d\n", pos, L, R, U, le, ri, mi); Td[U] = Td[L] - z[ids[mi-1]] - cst[ids[mi]] + z[ids[mi]] + Td[R]; Tu[U] = Tu[L] - z[ids[mi]] - cst[ids[mi]] + z[ids[mi-1]] + Tu[R]; Tbu[U] = min(Tbu[L] + (Tu[U] - Tu[L]), Tbu[R]); Tbd[U] = min(Tbd[L], (Td[U] - Td[R]) + Tbd[R]); pos /= 2; } } }; Tree tr[N]; /// zawartosc drzew, od gory vi vtr[N]; /// liczba drzew int tn; /// numer drzewa dla wierzcholkow, pozycja w drzewie int ntr[N], ptr[N]; /// --------------------------- graf ----------------------------------- void dfs(int u, int pa) { par[u] = pa; siz[u] = 1; FOR(i,SZ(g[u])) { int v = g[u][i]; if (v != pa) { cst[v] = vcst[u][i]; dfs(v,u); siz[u] += siz[v]; } } } void dfs_hld(int u, int hn) { ptr[u] = SZ(vtr[hn]); ntr[u] = hn; vtr[hn].pb(u); int who = -1; FOR(i,SZ(g[u])) { int v = g[u][i]; if (v==par[u]) continue; if (who == -1 || siz[who] < siz[v]) who = v; } FOR(i,SZ(g[u])) { int v = g[u][i]; if (v == par[u]) continue; if (who == v) dfs_hld(v, hn); else dfs_hld(v, tn++); } } /// ------------------------ zapytania --------------------------------- int find_best(int u) { /// (-zysk, id) restype best = best_nhld[u] + (-z[u]); //printf("start best = %lld (%d)\n", -best.fi, best.se); ll path = 0; while (u != -1) { restype cand = tr[ntr[u]].get_best(ptr[u]); cand.fi -= path; if (cand < best) best = cand; path += tr[ntr[u]].gain_up(ptr[u]); u = vtr[ntr[u]][0]; if (par[u] != -1) { path += z[par[u]] - cst[u] - z[u]; //printf("path up is %lld\n", path); best = min(best, mp(-path, par[u])); restype cand2 = best_nhld[par[u]]; if (cand2.se != -1 && cand2 == cur_nhld[u]) { set<restype>::iterator it=set_nhld[par[u]].begin(); it++; if (it != set_nhld[par[u]].end()) cand2 = *it; else cand2=ini; } cand2.fi -= path; cand2 = cand2 + (-z[par[u]]); //printf("candidate 2: %lld (%d)\n", -cand2.fi, cand2.se); best = min(best, cand2); } u = par[u]; } return best.se; } void update(int u) { /// uwzglednia zmiane z[v] i cst[v] bool fst = true; while (u != -1) { tr[ntr[u]].update(ptr[u], fst); fst = false; u = vtr[ntr[u]][0]; if (par[u] != -1) { set_nhld[par[u]].erase(cur_nhld[u]); cur_nhld[u] = tr[ntr[u]].get_best(0, true) + (z[u] - cst[u]); set_nhld[par[u]].insert(cur_nhld[u]); best_nhld[par[u]] = *set_nhld[par[u]].begin(); //printf("%d ma mozliwosc pojscia do %d zyskujac %lld\n", par[u], best_nhld[par[u]].se, -best_nhld[par[u]].fi); } u = par[u]; } } int main() { int q; scanf("%d%d", &n, &q); FOR(i,n) scanf("%lld", &z[i]); FOR(i,n-1) { int a,b; ll c; scanf("%d%d%lld", &a, &b, &c); a--; b--; g[a].pb(b); g[b].pb(a); vcst[a].pb(c); vcst[b].pb(c); } /// budowanie hld dfs(0, -1); dfs_hld(0, tn++); FOR(i,n+1) best_nhld[i] = ini; for (int i = tn-1; i >= 0; i--) { tr[i].build(vtr[i]); int u = par[vtr[i][0]]; if (u == -1) continue; cur_nhld[vtr[i][0]] = tr[i].get_best(0, true) + (z[vtr[i][0]] - cst[vtr[i][0]]); set_nhld[u].insert(cur_nhld[vtr[i][0]]); best_nhld[u] = *set_nhld[u].begin(); //printf("%d ma mozliwosc pojscia do %d zyskujac %lld\n", u, best_nhld[u].se, -best_nhld[u].fi); } int cur = 0; /// miasto w ktorym jestem FOR(i,q) { int qt; scanf("%d", &qt); if (qt==1) { int v; ll d; scanf("%d%lld", &v, &d); v--; //printf("zysk %d to teraz %lld\n", v, d); z[v] = d; update(v); } else { int u,v; ll d; scanf("%d%d%lld", &u, &v, &d); u--; v--; if (u==par[v]) swap(u,v); assert(v==par[u]); /// todo wywalic po przetestowaniu //printf("koszt %d->%d to teraz %lld\n", u, v, d); cst[u] = d; update(u); } cur = find_best(cur); printf("%d ", cur+1); /// todo spacja } printf("\n"); return 0; }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 | #include <bits/stdc++.h> using namespace std; #define REP(i,a,b) for (int i = (a); i <= (b); ++i) #define REPD(i,a,b) for (int i = (a); i >= (b); --i) #define FORI(i,n) REP(i,1,n) #define FOR(i,n) REP(i,0,int(n)-1) #define mp make_pair #define pb push_back #define pii pair<int,int> #define vi vector<int> #define ll long long #define SZ(x) int((x).size()) #define DBG(v) cerr << #v << " = " << (v) << endl; #define FOREACH(i,t) for (typeof(t.begin()) i=t.begin(); i!=t.end(); i++) #define fi first #define se second typedef pair<ll, int> restype; // (-zysk, id) const int N = 100100; const ll infll = 1000100100200100100LL; const restype ini = mp(infll, -1); /// --------------------------- graf ----------------------------------- int n; /// krawedzie vi g[N]; /// wagi krawedzi vector<ll> vcst[N]; /// wielkosc skladowej, ojciec int siz[N], par[N]; /// koszt krawedzi do ojca ll cst[N]; /// zyski w wierzcholkach ll z[N]; /// najlepszy wybor nie z hld (-zysk, id) restype best_nhld[N], cur_nhld[N]; set<restype> set_nhld[N]; /// -------------------------- drzewa ---------------------------------- restype operator+ (const restype& le, const ll &ri) { return restype(le.fi-ri, le.se); } restype operator+ (const ll& le, const restype &ri) { return restype(ri.fi-le, ri.se); } struct Tree { int M; vi ids; /// 0 - najwyzszy w drzewie vector<ll> Tu, Td; /// zysk na calym przedziale idac w gore / dol (czyli lewo / prawo) vector<restype> Tbu, Tbd; /// najlepszy zysk w gore / dol startujacy na koncu przedzialu void build(vi v) { ids = v; M=1; while (M < SZ(v)) M *= 2; while (SZ(ids)<M) ids.pb(n); /*printf("robie drzewo M=%d\nids = ", M); FOR(i,SZ(ids)) printf("%d ", ids[i]); printf("\n");*/ Tu.resize(2*M); Td.resize(2*M); Tbu.resize(2*M); Tbd.resize(2*M); FOR(i,M) Tbd[i+M] = Tbu[i+M] = ini; FOR(i,SZ(v)) { Tbu[i+M] = Tbd[i+M] = min(best_nhld[ids[i]]+(-z[ids[i]]), mp(0LL,ids[i])); //Tbu[i+M] = Tbd[i+M] = min(best_nhld[ids[i]]+z[ids[i]], mp(-z[ids[i]], ids[i])); //printf("Tbu[%d] = %lld (%d)\n", i, -Tbu[i+M].fi, Tbu[i+M].se); } for (int i = M-1; i >= 1; i--) { int m = 2*i+1; while (m<M) m*=2; m -= M; //printf("M=%d, i=%d, m=%d\n", M, i, m); Td[i] = Td[2*i] - z[ids[m-1]] - cst[ids[m]] + z[ids[m]] + Td[2*i+1]; Tu[i] = Tu[2*i] - z[ids[m]] - cst[ids[m]] + z[ids[m-1]] + Tu[2*i+1]; Tbu[i] = min(Tbu[2*i] + (Tu[i] - Tu[2*i]), Tbu[2*i+1]); Tbd[i] = min(Tbd[2*i], (Td[i] - Td[2*i+1]) + Tbd[2*i+1]); //printf("Tbu[%d] = %lld (%d)\n", i, -Tbu[i].fi, Tbu[i].se); } } /// najlepszy (-zysk, id) w dol i w gore (razem) restype get_best(int pos, bool can_stay=false) { /*printf("get best %d\n", pos); FORI(i,M-1) printf("%lld ", Tu[i]); printf("\n"); FORI(i,M-1) printf("%lld ", Td[i]); printf("\n"); FORI(i,2*M-1) printf("(%lld %d) ", -Tbu[i].fi, Tbu[i].se); printf("\n"); FORI(i,2*M-1) printf("(%lld %d) ", -Tbd[i].fi, Tbd[i].se); printf("\n");*/ pos += M; restype best = can_stay ? Tbu[pos] : ini; ll le = 0, ri = 0; while (pos > 1) { //printf("pos=%d, best= %lld %d; ri=%lld, le=%lld\n", pos, -best.fi, best.se, ri, le); if (pos & 1) { best = min(best, Tbu[pos-1] + le + (Tu[pos/2] - Tu[pos] - Tu[pos-1])); le += Tu[pos/2] - Tu[pos]; } else { best = min(best, Tbd[pos+1] + ri + (Td[pos/2] - Td[pos] - Td[pos+1])); ri += Td[pos/2] - Td[pos]; } pos /= 2; } //printf("najlepszy to %lld (%d)\n", -best.fi, best.se); return best; } /// zysk z dojscia do konca do gory ll gain_up(int pos) { //printf("od %d do korzenia zyskam ", pos); pos += M; ll res = 0; while (pos > 1) { if (pos & 1) res += Tu[pos/2]-Tu[pos]; pos /= 2; } //printf("%lld\n", res); return res; } /// zmiana z[id[pos]] lub cst[id[pos]] (fst=true) lub best_nhld[id[pos]] (fst=false); void update(int pos, bool fst) { //printf("update %d (id=%d)\n", pos, ids[pos]); //Tbu[pos+M] = Tbd[pos+M] = min(best_nhld[ids[pos]]+z[ids[pos]], mp(-z[ids[pos]], ids[pos])); Tbu[pos+M] = Tbd[pos+M] = min(best_nhld[ids[pos]]+(-z[ids[pos]]), mp(0LL, ids[pos])); int le = pos, ri = pos+1, len = 1, mi; pos += M; //printf("z = "); //FOR(i,n) printf("%lld ", z[i]); //printf("\n"); while (pos > 1) { if (pos & 1) le -= len; else ri += len; len *= 2; mi = (le + ri) / 2; int R = pos | 1, L = R - 1, U = pos / 2; //printf("pos = %d; L=%d, R=%d, U=%d; le=%d, ri=%d, mi=%d\n", pos, L, R, U, le, ri, mi); Td[U] = Td[L] - z[ids[mi-1]] - cst[ids[mi]] + z[ids[mi]] + Td[R]; Tu[U] = Tu[L] - z[ids[mi]] - cst[ids[mi]] + z[ids[mi-1]] + Tu[R]; Tbu[U] = min(Tbu[L] + (Tu[U] - Tu[L]), Tbu[R]); Tbd[U] = min(Tbd[L], (Td[U] - Td[R]) + Tbd[R]); pos /= 2; } } }; Tree tr[N]; /// zawartosc drzew, od gory vi vtr[N]; /// liczba drzew int tn; /// numer drzewa dla wierzcholkow, pozycja w drzewie int ntr[N], ptr[N]; /// --------------------------- graf ----------------------------------- void dfs(int u, int pa) { par[u] = pa; siz[u] = 1; FOR(i,SZ(g[u])) { int v = g[u][i]; if (v != pa) { cst[v] = vcst[u][i]; dfs(v,u); siz[u] += siz[v]; } } } void dfs_hld(int u, int hn) { ptr[u] = SZ(vtr[hn]); ntr[u] = hn; vtr[hn].pb(u); int who = -1; FOR(i,SZ(g[u])) { int v = g[u][i]; if (v==par[u]) continue; if (who == -1 || siz[who] < siz[v]) who = v; } FOR(i,SZ(g[u])) { int v = g[u][i]; if (v == par[u]) continue; if (who == v) dfs_hld(v, hn); else dfs_hld(v, tn++); } } /// ------------------------ zapytania --------------------------------- int find_best(int u) { /// (-zysk, id) restype best = best_nhld[u] + (-z[u]); //printf("start best = %lld (%d)\n", -best.fi, best.se); ll path = 0; while (u != -1) { restype cand = tr[ntr[u]].get_best(ptr[u]); cand.fi -= path; if (cand < best) best = cand; path += tr[ntr[u]].gain_up(ptr[u]); u = vtr[ntr[u]][0]; if (par[u] != -1) { path += z[par[u]] - cst[u] - z[u]; //printf("path up is %lld\n", path); best = min(best, mp(-path, par[u])); restype cand2 = best_nhld[par[u]]; if (cand2.se != -1 && cand2 == cur_nhld[u]) { set<restype>::iterator it=set_nhld[par[u]].begin(); it++; if (it != set_nhld[par[u]].end()) cand2 = *it; else cand2=ini; } cand2.fi -= path; cand2 = cand2 + (-z[par[u]]); //printf("candidate 2: %lld (%d)\n", -cand2.fi, cand2.se); best = min(best, cand2); } u = par[u]; } return best.se; } void update(int u) { /// uwzglednia zmiane z[v] i cst[v] bool fst = true; while (u != -1) { tr[ntr[u]].update(ptr[u], fst); fst = false; u = vtr[ntr[u]][0]; if (par[u] != -1) { set_nhld[par[u]].erase(cur_nhld[u]); cur_nhld[u] = tr[ntr[u]].get_best(0, true) + (z[u] - cst[u]); set_nhld[par[u]].insert(cur_nhld[u]); best_nhld[par[u]] = *set_nhld[par[u]].begin(); //printf("%d ma mozliwosc pojscia do %d zyskujac %lld\n", par[u], best_nhld[par[u]].se, -best_nhld[par[u]].fi); } u = par[u]; } } int main() { int q; scanf("%d%d", &n, &q); FOR(i,n) scanf("%lld", &z[i]); FOR(i,n-1) { int a,b; ll c; scanf("%d%d%lld", &a, &b, &c); a--; b--; g[a].pb(b); g[b].pb(a); vcst[a].pb(c); vcst[b].pb(c); } /// budowanie hld dfs(0, -1); dfs_hld(0, tn++); FOR(i,n+1) best_nhld[i] = ini; for (int i = tn-1; i >= 0; i--) { tr[i].build(vtr[i]); int u = par[vtr[i][0]]; if (u == -1) continue; cur_nhld[vtr[i][0]] = tr[i].get_best(0, true) + (z[vtr[i][0]] - cst[vtr[i][0]]); set_nhld[u].insert(cur_nhld[vtr[i][0]]); best_nhld[u] = *set_nhld[u].begin(); //printf("%d ma mozliwosc pojscia do %d zyskujac %lld\n", u, best_nhld[u].se, -best_nhld[u].fi); } int cur = 0; /// miasto w ktorym jestem FOR(i,q) { int qt; scanf("%d", &qt); if (qt==1) { int v; ll d; scanf("%d%lld", &v, &d); v--; //printf("zysk %d to teraz %lld\n", v, d); z[v] = d; update(v); } else { int u,v; ll d; scanf("%d%d%lld", &u, &v, &d); u--; v--; if (u==par[v]) swap(u,v); assert(v==par[u]); /// todo wywalic po przetestowaniu //printf("koszt %d->%d to teraz %lld\n", u, v, d); cst[u] = d; update(u); } cur = find_best(cur); printf("%d ", cur+1); /// todo spacja } printf("\n"); return 0; } |