#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> pli; const int N = 333; const int infi = 1000100200; const ll infll = 1000100200300400500LL; struct Answer { ll s; int w; vector<pli> all; Answer() { s=infll; w=infi; all.emplace_back(s,w); } Answer(ll s_, int w_) { s=s_; w=w_; all.emplace_back(s,w); } Answer(vector<pli> tmp) { all = tmp; recalc(); } void recalc() { vector<pli> tmp = all; sort(tmp.begin(), tmp.end()); int pos = 0, cnt = 1; for (int i = 1; i < SZ(tmp); i++) { if (tmp[i].se < tmp[pos].se) { pos = i; cnt++; } } s = tmp[0].fi; w = tmp[0].se; all.resize(cnt); all[0] = tmp[0]; cnt = 1; pos = 0; for (int i = 1; i < SZ(tmp); i++) { if (tmp[i].se < tmp[pos].se) { all[cnt] = tmp[i]; pos = i; cnt++; } } //cerr << "\t\t\t\t"; //for (auto x : all) cerr << x.fi << "\t"; //cerr << "\n\t\t\t\t"; //for (auto x : all) cerr << x.se << "\t"; //cerr << "\n\t\t\t\t\ttmp was "; //for (auto x : tmp) cerr << "(" << x.fi << " " << x.se << ")\t"; //cerr << "\n\n"; } void update(Answer a) { if (a.s < s) { s = a.s; w = a.w; } all.insert(all.end(), a.all.begin(), a.all.end()); recalc(); } Answer add(ll s0) { Answer res(*this); res.s += s0; for (auto &x : res.all) x.fi += s0; return res; } Answer combine(Answer a) { //cerr << "\t\t\t"; //for (auto x : all) cerr << x.fi << "\t"; //cerr << "\\/\t"; //for (auto x : a.all) cerr << x.fi << "\t"; //cerr << "\t_\n\t\t\t"; //for (auto x : all) cerr << x.se << "\t"; //cerr << "/\\\t"; //for (auto x : a.all) cerr << x.se << "\t"; //cerr << "\t-\n"; //return Answer(s+a.s+2LL*w*a.w, w+a.w); vector<pli> tmp; tmp.reserve(SZ(all)*SZ(a.all)); for (auto x : all) for (auto y : a.all) { tmp.emplace_back(x.fi + y.fi + 2LL*x.se*y.se, x.se + y.se); } //return Answer(tmp[0].fi, tmp[0].se); return Answer(tmp); } }; int n, kk; int a[N]; int siz[N], sum[N], ord[N], par[N]; vector<int> g[N]; Answer dp[N][N]; void calc(int u) { //cerr << "Tree " << u+1 << "[" << a[u] << "] : \n"; Answer dpc[N], dpp[N]; dpp[1] = Answer(1LL*a[u]*a[u], a[u]); FOR(i,SZ(g[u])) { int v = g[u][i]; if (v==par[u]) continue; for (int ks = 1; ks <= siz[u]; ks++) { for (int k = 1; k <= siz[v] && k <= ks; k++) { ll s0 = dp[v][k].s, s1 = dpp[ks-k].s, s2 = dpp[ks-k+1].s; int w0 = dp[v][k].w, w1 = dpp[ks-k].w, w2 = dpp[ks-k+1].w; //cerr << "\t\tUsing dp[" << v << "][" << k << "] = " << s0 << ", " << w0 << " to update ks = " << ks << "\n"; //cerr << "\t\tOption 1: " << s1 << ", " << w1 << "\n"; //cerr << "\t\tOption 2: " << s2 << ", " << w2 << "\n"; dpc[ks].update(dpp[ks-k].add(s0)); //Answer(s1 + s0, w1)); dpc[ks].update(dpp[ks-k+1].combine(dp[v][k])); //Answer(s2 + s0 + 2LL*w2*w0, w2 + w0)); } } //cerr << "\tAfter processing " << v+1 << " the options are \n\tk = \t"; //for (int ks = 1; ks <= siz[u]; ks++) cerr << ks << "\t"; cerr << "\n\ts = \t"; //for (int ks = 1; ks <= siz[u]; ks++) cerr << dpc[ks].s << "\t"; cerr << "\n\tw = \t"; //for (int ks = 1; ks <= siz[u]; ks++) cerr << dpc[ks].w << "\t"; cerr << "\n\n"; for (int ks = 1; ks <= siz[u]; ks++) { dpp[ks]=dpc[ks]; dpc[ks]=Answer(); } } for (int ks = 1; ks <= siz[u]; ks++) { dp[u][ks] = dpp[ks]; } //cerr << "Final options are\n\tk = \t"; //for (int ks = 1; ks <= siz[u]; ks++) cerr << ks << "\t"; cerr << "\n\ts = \t"; //for (int ks = 1; ks <= siz[u]; ks++) cerr << dp[u][ks].s << "\t"; cerr << "\n\tw = \t"; //for (int ks = 1; ks <= siz[u]; ks++) cerr << dp[u][ks].w << "\t"; cerr << "\n\n"; } void dfs_cnt(int u, int pp) { siz[u] = 1; sum[u] = a[u]; ord[--kk] = u; par[u] = pp; FOR(i,SZ(g[u])) { int v = g[u][i]; if (v!=pp) { dfs_cnt(v,u); siz[u] += siz[v]; sum[u] += sum[v]; } } } void clear() { kk = n; FOR(i,n) g[i].clear(); } void test() { scanf("%d", &n); clear(); FOR(i,n) scanf("%d", &a[i]); FOR(i,n-1) { int b,c; scanf("%d%d", &b, &c); b--; c--; g[b].push_back(c); g[c].push_back(b); } dfs_cnt(0,-1); FOR(ii,n) { int u = ord[ii]; calc(u); } //FORI(i,n) printf("%.2lf ", 1.0*dp[0][i].s*i/sum[0]/sum[0]); FORI(i,n) printf("%lld ", dp[0][i].s); printf("\n"); } int main() { int tt; scanf("%d", &tt); while (tt--) test(); 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 | #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> pli; const int N = 333; const int infi = 1000100200; const ll infll = 1000100200300400500LL; struct Answer { ll s; int w; vector<pli> all; Answer() { s=infll; w=infi; all.emplace_back(s,w); } Answer(ll s_, int w_) { s=s_; w=w_; all.emplace_back(s,w); } Answer(vector<pli> tmp) { all = tmp; recalc(); } void recalc() { vector<pli> tmp = all; sort(tmp.begin(), tmp.end()); int pos = 0, cnt = 1; for (int i = 1; i < SZ(tmp); i++) { if (tmp[i].se < tmp[pos].se) { pos = i; cnt++; } } s = tmp[0].fi; w = tmp[0].se; all.resize(cnt); all[0] = tmp[0]; cnt = 1; pos = 0; for (int i = 1; i < SZ(tmp); i++) { if (tmp[i].se < tmp[pos].se) { all[cnt] = tmp[i]; pos = i; cnt++; } } //cerr << "\t\t\t\t"; //for (auto x : all) cerr << x.fi << "\t"; //cerr << "\n\t\t\t\t"; //for (auto x : all) cerr << x.se << "\t"; //cerr << "\n\t\t\t\t\ttmp was "; //for (auto x : tmp) cerr << "(" << x.fi << " " << x.se << ")\t"; //cerr << "\n\n"; } void update(Answer a) { if (a.s < s) { s = a.s; w = a.w; } all.insert(all.end(), a.all.begin(), a.all.end()); recalc(); } Answer add(ll s0) { Answer res(*this); res.s += s0; for (auto &x : res.all) x.fi += s0; return res; } Answer combine(Answer a) { //cerr << "\t\t\t"; //for (auto x : all) cerr << x.fi << "\t"; //cerr << "\\/\t"; //for (auto x : a.all) cerr << x.fi << "\t"; //cerr << "\t_\n\t\t\t"; //for (auto x : all) cerr << x.se << "\t"; //cerr << "/\\\t"; //for (auto x : a.all) cerr << x.se << "\t"; //cerr << "\t-\n"; //return Answer(s+a.s+2LL*w*a.w, w+a.w); vector<pli> tmp; tmp.reserve(SZ(all)*SZ(a.all)); for (auto x : all) for (auto y : a.all) { tmp.emplace_back(x.fi + y.fi + 2LL*x.se*y.se, x.se + y.se); } //return Answer(tmp[0].fi, tmp[0].se); return Answer(tmp); } }; int n, kk; int a[N]; int siz[N], sum[N], ord[N], par[N]; vector<int> g[N]; Answer dp[N][N]; void calc(int u) { //cerr << "Tree " << u+1 << "[" << a[u] << "] : \n"; Answer dpc[N], dpp[N]; dpp[1] = Answer(1LL*a[u]*a[u], a[u]); FOR(i,SZ(g[u])) { int v = g[u][i]; if (v==par[u]) continue; for (int ks = 1; ks <= siz[u]; ks++) { for (int k = 1; k <= siz[v] && k <= ks; k++) { ll s0 = dp[v][k].s, s1 = dpp[ks-k].s, s2 = dpp[ks-k+1].s; int w0 = dp[v][k].w, w1 = dpp[ks-k].w, w2 = dpp[ks-k+1].w; //cerr << "\t\tUsing dp[" << v << "][" << k << "] = " << s0 << ", " << w0 << " to update ks = " << ks << "\n"; //cerr << "\t\tOption 1: " << s1 << ", " << w1 << "\n"; //cerr << "\t\tOption 2: " << s2 << ", " << w2 << "\n"; dpc[ks].update(dpp[ks-k].add(s0)); //Answer(s1 + s0, w1)); dpc[ks].update(dpp[ks-k+1].combine(dp[v][k])); //Answer(s2 + s0 + 2LL*w2*w0, w2 + w0)); } } //cerr << "\tAfter processing " << v+1 << " the options are \n\tk = \t"; //for (int ks = 1; ks <= siz[u]; ks++) cerr << ks << "\t"; cerr << "\n\ts = \t"; //for (int ks = 1; ks <= siz[u]; ks++) cerr << dpc[ks].s << "\t"; cerr << "\n\tw = \t"; //for (int ks = 1; ks <= siz[u]; ks++) cerr << dpc[ks].w << "\t"; cerr << "\n\n"; for (int ks = 1; ks <= siz[u]; ks++) { dpp[ks]=dpc[ks]; dpc[ks]=Answer(); } } for (int ks = 1; ks <= siz[u]; ks++) { dp[u][ks] = dpp[ks]; } //cerr << "Final options are\n\tk = \t"; //for (int ks = 1; ks <= siz[u]; ks++) cerr << ks << "\t"; cerr << "\n\ts = \t"; //for (int ks = 1; ks <= siz[u]; ks++) cerr << dp[u][ks].s << "\t"; cerr << "\n\tw = \t"; //for (int ks = 1; ks <= siz[u]; ks++) cerr << dp[u][ks].w << "\t"; cerr << "\n\n"; } void dfs_cnt(int u, int pp) { siz[u] = 1; sum[u] = a[u]; ord[--kk] = u; par[u] = pp; FOR(i,SZ(g[u])) { int v = g[u][i]; if (v!=pp) { dfs_cnt(v,u); siz[u] += siz[v]; sum[u] += sum[v]; } } } void clear() { kk = n; FOR(i,n) g[i].clear(); } void test() { scanf("%d", &n); clear(); FOR(i,n) scanf("%d", &a[i]); FOR(i,n-1) { int b,c; scanf("%d%d", &b, &c); b--; c--; g[b].push_back(c); g[c].push_back(b); } dfs_cnt(0,-1); FOR(ii,n) { int u = ord[ii]; calc(u); } //FORI(i,n) printf("%.2lf ", 1.0*dp[0][i].s*i/sum[0]/sum[0]); FORI(i,n) printf("%lld ", dp[0][i].s); printf("\n"); } int main() { int tt; scanf("%d", &tt); while (tt--) test(); return 0; } |