H問題の解法と雑な証明です。
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generated by indenter
以下ソースコードです。マクロ多くてごめんなさい。
#include略 #define fi first #define se second #define rep(i,n) for(int i = 0; i < (n); ++i) #define rrep(i,n) for(int i = 1; i <= (n); ++i) #define drep(i,n) for(int i = (n)-1; i >= 0; --i) #define gep(i,g,j) for(int i = g.head[j]; i != -1; i = g.e[i].next) #define each(it,c) for(__typeof((c).begin()) it=(c).begin();it!=(c).end();it++) #define rng(a) a.begin(),a.end() #define maxs(x,y) x = max(x,y) #define mins(x,y) x = min(x,y) #define pb push_back #define sz(x) (int)(x).size() #define pcnt __builtin_popcount #define uni(x) x.erase(unique(rng(x)),x.end()) #define snuke srand((unsigned)clock()+(unsigned)time(NULL)); #define df(x) int x = in() #define dame { puts("-1"); return 0;} #define show(x) cout<<#x<<" = "<<x<<endl; #define PQ(T) priority_queue<T,vector<T>,greater<T> > #define bn(x) ((1<<x)-1) using namespace std; typedef long long int ll; typedef pair<int,int> P; typedef vector<int> vi; typedef vector<vi> vvi; typedef vector<ll> vl; typedef vector<P> vp; inline int in() { int x; scanf("%d",&x); return x;} inline void priv(vi a) { rep(i,sz(a)) printf("%d%c",a[i],i==sz(a)-1?'\n':' ');} template<typename T>istream& operator>>(istream&i,vector<T>&v) {rep(j,sz(v))i>>v[j];return i;} template<typename T>string join(vector<T>&v) {stringstream s;rep(i,sz(v))s<<' '<<v[i];return s.str().substr(1);} template<typename T>ostream& operator<<(ostream&o,vector<T>&v) {if(sz(v))o<<join(v);return o;} template<typename T1,typename T2>istream& operator>>(istream&i,pair<T1,T2>&v) {return i>>v.fi>>v.se;} template<typename T1,typename T2>ostream& operator<<(ostream&o,pair<T1,T2>&v) {return o<<v.fi<<","<<v.se;} const int MX = 100005, INF = 1001001001; int n, m; vvi to, co; int cnt; int dfs(int v, int x, int p=-1) { int a = 0, b = INF; rep(i,sz(to[v])) { int u = to[v][i]; if (u == p) continue; int r = dfs(u,x,v)+co[v][i]; if (r*2 >= x) { mins(b,r); } else { --cnt; maxs(a,r); } } if (a+b < x) return b; ++cnt; return a; } int f(int x) { cnt = 0; dfs(0,x); return cnt; } int main() { scanf("%d%d",&n,&m); to = co = vvi(n); rep(i,n-1) { int a,b,c; scanf("%d%d%d",&a,&b,&c); --a; --b; to[a].pb(b); co[a].pb(c); to[b].pb(a); co[b].pb(c); } int l = 1, r = INF; while (l+1<r) { int c = (l+r)>>1; if (f(c) >= m) l = c; else r = c; } cout<<l<<endl; return 0; }