#include <bits/stdc++.h> using namespace std; const int N = 1 << 17; const int LOG = 19; pair<long long, int> W[LOG][2*N]; long long w[LOG][2*N]; void upd(int lev, int a, int b, long long c) { if (a > b) return; a += N; b += N; w[lev][a] += c; W[lev][a].first += c; if (a != b) { w[lev][b] += c; W[lev][b].first += c; } while ((a>>1) != (b>>1)) { if ((a&1)== 0) { w[lev][a+1] += c; W[lev][a+1].first += c; } if ((b&1) == 1) { w[lev][b-1] += c; W[lev][b-1].first += c; } a >>= 1; b >>= 1; W[lev][a] = max(W[lev][2*a], W[lev][2*a+1]); W[lev][a].first += w[lev][a]; W[lev][b] = max(W[lev][2*b], W[lev][2*b+1]); W[lev][b].first += w[lev][b]; } while (a > 1) { a >>= 1; W[lev][a] = max(W[lev][2*a], W[lev][2*a+1]); W[lev][a].first += w[lev][a]; } } pair<long long, int> que(int lev, int a, int b) { if (a > b) return {-1e18, -1e9}; a += N; b += N; pair<long long, int> res_a = W[lev][a]; pair<long long, int> res_b = W[lev][b]; while ((a>>1) != (b>>1)) { if ((a&1) == 0) res_a = max(res_a, W[lev][a+1]); if ((b&1) == 1) res_b = max(res_b, W[lev][b-1]); a >>= 1; b >>= 1; res_a.first += w[lev][a]; res_b.first += w[lev][b]; } while (a > 1) { a >>= 1; b >>= 1; res_a.first += w[lev][a]; res_b.first += w[lev][b]; } return max(res_a, res_b); } int n, q; long long val[N]; vector<pair<int,long long>> adj[N]; int sz[N], blocked[N]; map<pair<int,int>, long long> waga; void dfs(int v) { sz[v] = 1; for (auto u: adj[v]) if (sz[u.first] == 0 && !blocked[u.first]) { dfs(u.first); sz[v] += sz[u.first]; } } int find_centroid(int v, int whole) { for (auto u: adj[v]) if (!blocked[u.first] && sz[u.first] < sz[v] && (2*sz[u.first] > whole)) return find_centroid(u.first, whole); return v; } long long dist[N][LOG]; int czas[LOG], preor[N][LOG], postor[N][LOG], parent[N], ktory[N]; void dfs_2(int v, int lev, int me, long long len) { sz[v] = 0; preor[v][lev] = ++czas[lev]; dist[v][lev] = len; W[lev][preor[v][lev]+N].second = -v; upd(lev, preor[v][lev], preor[v][lev], val[v] - len); for (auto u: adj[v]) if (!blocked[u.first] && parent[u.first] != me) { parent[u.first] = me; dfs_2(u.first, lev, me, len + u.second); } postor[v][lev] = czas[lev]; } void rozbij(int v, int lev) { dfs(v); v = find_centroid(v, sz[v]); ktory[v] = lev; blocked[v] = 1; dfs_2(v, lev, v, 0); for (auto u: adj[v]) if (!blocked[u.first]) rozbij(u.first, lev+1); } int32_t main() { scanf("%d%d", &n, &q); for (int i = 1; i <= n; i++) scanf("%lld", &val[i]); for (int i = 0; i < n-1; i++) { int a, b; long long c; scanf("%d%d%lld", &a, &b, &c); adj[a].push_back({b, c}); adj[b].push_back({a, c}); waga[{a,b}] = waga[{b,a}] = c; } rozbij(1, 0); int v = 1; for (int i = 0; i < q; i++) { /* zmianka */ int type; scanf("%d", &type); if (type == 1) { int u; long long d; scanf("%d%lld", &u, &d); for (int lev = 0; lev < LOG; lev++) upd(lev, preor[u][lev], preor[u][lev], d-val[u]); val[u] = d; } else { int a, b; long long d; scanf("%d%d%lld", &a, &b, &d); long long xd = waga[{a,b}]; for (int lev = 0; lev < LOG; lev++) upd(lev, max(preor[a][lev], preor[b][lev]), min(postor[a][lev], postor[b][lev]), -d+xd); waga[{a,b}] = waga[{b,a}] = d; } /* odpowiedz */ pair<long long, int> best = {-1e18, -1e9}; int roo = v; for (int lev = ktory[v]; lev >= 0; lev--) { long long diste = val[v] - que(lev, preor[v][lev], preor[v][lev]).first; pair<long long, int> kurcze = que(lev, preor[roo][lev], preor[v][lev]-1); best = max(best, {kurcze.first - diste, kurcze.second}); pair<long long, int> kurcze2 = que(lev, preor[v][lev]+1, postor[roo][lev]); best = max(best, {kurcze2.first - diste, kurcze2.second}); roo = parent[roo]; } printf("%d ", -best.second); v = -best.second; } 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 | #include <bits/stdc++.h> using namespace std; const int N = 1 << 17; const int LOG = 19; pair<long long, int> W[LOG][2*N]; long long w[LOG][2*N]; void upd(int lev, int a, int b, long long c) { if (a > b) return; a += N; b += N; w[lev][a] += c; W[lev][a].first += c; if (a != b) { w[lev][b] += c; W[lev][b].first += c; } while ((a>>1) != (b>>1)) { if ((a&1)== 0) { w[lev][a+1] += c; W[lev][a+1].first += c; } if ((b&1) == 1) { w[lev][b-1] += c; W[lev][b-1].first += c; } a >>= 1; b >>= 1; W[lev][a] = max(W[lev][2*a], W[lev][2*a+1]); W[lev][a].first += w[lev][a]; W[lev][b] = max(W[lev][2*b], W[lev][2*b+1]); W[lev][b].first += w[lev][b]; } while (a > 1) { a >>= 1; W[lev][a] = max(W[lev][2*a], W[lev][2*a+1]); W[lev][a].first += w[lev][a]; } } pair<long long, int> que(int lev, int a, int b) { if (a > b) return {-1e18, -1e9}; a += N; b += N; pair<long long, int> res_a = W[lev][a]; pair<long long, int> res_b = W[lev][b]; while ((a>>1) != (b>>1)) { if ((a&1) == 0) res_a = max(res_a, W[lev][a+1]); if ((b&1) == 1) res_b = max(res_b, W[lev][b-1]); a >>= 1; b >>= 1; res_a.first += w[lev][a]; res_b.first += w[lev][b]; } while (a > 1) { a >>= 1; b >>= 1; res_a.first += w[lev][a]; res_b.first += w[lev][b]; } return max(res_a, res_b); } int n, q; long long val[N]; vector<pair<int,long long>> adj[N]; int sz[N], blocked[N]; map<pair<int,int>, long long> waga; void dfs(int v) { sz[v] = 1; for (auto u: adj[v]) if (sz[u.first] == 0 && !blocked[u.first]) { dfs(u.first); sz[v] += sz[u.first]; } } int find_centroid(int v, int whole) { for (auto u: adj[v]) if (!blocked[u.first] && sz[u.first] < sz[v] && (2*sz[u.first] > whole)) return find_centroid(u.first, whole); return v; } long long dist[N][LOG]; int czas[LOG], preor[N][LOG], postor[N][LOG], parent[N], ktory[N]; void dfs_2(int v, int lev, int me, long long len) { sz[v] = 0; preor[v][lev] = ++czas[lev]; dist[v][lev] = len; W[lev][preor[v][lev]+N].second = -v; upd(lev, preor[v][lev], preor[v][lev], val[v] - len); for (auto u: adj[v]) if (!blocked[u.first] && parent[u.first] != me) { parent[u.first] = me; dfs_2(u.first, lev, me, len + u.second); } postor[v][lev] = czas[lev]; } void rozbij(int v, int lev) { dfs(v); v = find_centroid(v, sz[v]); ktory[v] = lev; blocked[v] = 1; dfs_2(v, lev, v, 0); for (auto u: adj[v]) if (!blocked[u.first]) rozbij(u.first, lev+1); } int32_t main() { scanf("%d%d", &n, &q); for (int i = 1; i <= n; i++) scanf("%lld", &val[i]); for (int i = 0; i < n-1; i++) { int a, b; long long c; scanf("%d%d%lld", &a, &b, &c); adj[a].push_back({b, c}); adj[b].push_back({a, c}); waga[{a,b}] = waga[{b,a}] = c; } rozbij(1, 0); int v = 1; for (int i = 0; i < q; i++) { /* zmianka */ int type; scanf("%d", &type); if (type == 1) { int u; long long d; scanf("%d%lld", &u, &d); for (int lev = 0; lev < LOG; lev++) upd(lev, preor[u][lev], preor[u][lev], d-val[u]); val[u] = d; } else { int a, b; long long d; scanf("%d%d%lld", &a, &b, &d); long long xd = waga[{a,b}]; for (int lev = 0; lev < LOG; lev++) upd(lev, max(preor[a][lev], preor[b][lev]), min(postor[a][lev], postor[b][lev]), -d+xd); waga[{a,b}] = waga[{b,a}] = d; } /* odpowiedz */ pair<long long, int> best = {-1e18, -1e9}; int roo = v; for (int lev = ktory[v]; lev >= 0; lev--) { long long diste = val[v] - que(lev, preor[v][lev], preor[v][lev]).first; pair<long long, int> kurcze = que(lev, preor[roo][lev], preor[v][lev]-1); best = max(best, {kurcze.first - diste, kurcze.second}); pair<long long, int> kurcze2 = que(lev, preor[v][lev]+1, postor[roo][lev]); best = max(best, {kurcze2.first - diste, kurcze2.second}); roo = parent[roo]; } printf("%d ", -best.second); v = -best.second; } printf("\n"); return 0; } |