题意
题目链接 https://www.luogu.org/problemnew/show/P4069
Sol
这题细节好多啊 qwq.. 稍不留神写出一个小 bug 就要调 1h+..
思路就不多说了, 把询问区间拆成两段就是李超线段树板子题了.
关于 dis 的问题可以直接维护.
- // luogu-judger-enable-o2
- /*
- 李超线段树板子题
- */
- #include<bits/stdc++.h>
- #define Pair pair<int, int>
- #define MP(x, y) make_pair(x, y)
- #define fi first
- #define se second
- #define int long long
- #define LL long long
- #define Fin(x) {freopen(#x".in","r",stdin);}
- #define Fout(x) {freopen(#x".out","w",stdout);}
- using namespace std;
- const int MAXN = 1e6 + 10;
- template <typename A, typename B> inline bool chmin(A &a, B b){if(a> b) {a = b; return 1;} return 0;}
- template <typename A, typename B> inline bool chmax(A &a, B b){if(a <b) {a = b; return 1;} return 0;}
- inline int read() {
- char c = getchar(); int x = 0, f = 1;
- while(c < '0' || c> '9') {if(c == '-') f = -1; c = getchar();}
- while(c>= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
- return x * f;
- }
- int N, M, dis[MAXN], son[MAXN], fa[MAXN], top[MAXN], dep[MAXN], siz[MAXN], ID[MAXN], rev[MAXN], root, tot;
- LL val[MAXN];
- vector<Pair> v[MAXN];
- struct Line {
- int k, b;
- }s[MAXN];
- int ls[MAXN], rs[MAXN], ll[MAXN], rr[MAXN], mn[MAXN];
- void dfs1(int x, int _fa) {
- fa[x] = _fa; dep[x] = dep[_fa] + 1; siz[x] = 1;
- for(auto &to : v[x]) {
- if(to.fi == _fa) continue;
- dis[to.fi] = dis[x] + to.se;
- dfs1(to.fi, x);
- siz[x] += siz[to.fi];
- if(siz[to.fi]> siz[son[x]]) son[x] = to.fi;
- }
- }
- void dfs2(int x, int topf) {
- top[x] = topf; ID[x] = ++ID[0]; rev[ID[0]] = x;
- if(!son[x]) return ;
- dfs2(son[x], topf);
- for(auto &to : v[x]) {
- if(top[to.fi]) continue;
- dfs2(to.fi, to.fi);
- }
- }
- int LCA(int x, int y) {
- while(top[x] ^ top[y]) {
- if(dep[top[x]] <dep[top[y]]) swap(x, y);
- x = fa[top[x]];
- }
- return dep[x]> dep[y] ? y : x;
- }
- int calc(Line s, int x) {
- return s.k * dis[rev[x]] + s.b;
- }
- double GetPoint(Line x, Line y) {
- return (double) (y.b - x.b) / (x.k - y.k);
- }
- void update(int k) {
- if(s[k].k || s[k].b) chmin(mn[k], min(calc(s[k], ll[k]), calc(s[k], rr[k])));
- chmin(mn[k], min(mn[ls[k]], mn[rs[k]]));
- }
- void IntAdd(int &k, int l, int r, int ql, int qr, Line seg) {
- if(!k) k = ++tot, mn[k] = val[0], ll[k] = l, rr[k] = r;
- int mid = l + r>> 1;
- if(ql <= l && r <= qr) {
- int pl = calc(s[k], l), pr = calc(s[k], r), nl = calc(seg, l), nr = calc(seg, r);
- if(!s[k].k && !s[k].b) {s[k] = seg; update(k); return ;}
- if(pl <= nl && pr <= nr) return ;// 这里必须要写等号
- if(pl> nl && pr> nr) {s[k] = seg; update(k); return ;}
- double xx = GetPoint(s[k], seg);
- int m = dis[rev[mid]];
- if(pl> nl) {
- if(xx> m) IntAdd(rs[k], mid + 1, r, ql, qr, s[k]), s[k] = seg;
- else IntAdd(ls[k], l, mid, ql, qr, seg);
- } else {
- if(xx> m) IntAdd(rs[k], mid + 1, r, ql, qr, seg);
- else IntAdd(ls[k], l, mid, ql, qr, s[k]), s[k] = seg;
- }
- update(k);
- return ;
- }
- if(ql <= mid) IntAdd(ls[k], l, mid, ql, qr, seg);
- if(qr> mid) IntAdd(rs[k], mid + 1, r, ql, qr, seg);
- update(k);
- }
- int IntMin(int k, int l, int r, int ql, int qr) {
- int ret = val[0];
- if(ql <= l && r <= qr)
- return mn[k];
- int mid = l + r>> 1;
- if(s[k].k || s[k].b)
- chmin(ret, min(calc(s[k], max(l, ql)), calc(s[k], min(r, qr))));
- if(ql <= mid) chmin(ret, IntMin(ls[k], l, mid, ql, qr));
- if(qr> mid) chmin(ret, IntMin(rs[k], mid + 1, r, ql, qr));
- return ret;
- }
- void Modify(int x, int y, int k, int b) {
- while(top[x] != top[y]) {
- if(dep[top[x]] < dep[top[y]]) swap(x, y);
- IntAdd(root, 1, N, ID[top[x]], ID[x], {k, b});
- x = fa[top[x]];
- }
- if(dep[x] < dep[y]) swap(x, y);
- IntAdd(root, 1, N, ID[y], ID[x], {k, b});
- }
- void Change(int s, int t, int a, int b) {
- int lca = LCA(s, t);
- Modify(s, lca, -a, b + a * dis[s]);
- Modify(t, lca, a, -a * dis[lca] + b + a * (dis[s] - dis[lca]));
- }
- LL Query(int x, int y) {
- int ans = val[0];
- while(top[x] != top[y]) {
- if(dep[top[x]] < dep[top[y]]) swap(x, y);
- chmin(ans, IntMin(root, 1, N, ID[top[x]], ID[x]));
- x = fa[top[x]];
- }
- if(dep[x] < dep[y]) swap(x, y);
- chmin(ans, IntMin(root, 1, N, ID[y], ID[x]));
- return ans;
- }
- signed main() {
- N = read(); M = read();
- for(int i = 0; i <= N; i++) mn[i] = val[i] = 123456789123456789ll;
- for(int i = 1; i <= N - 1; i++) {
- int x = read(), y = read(), z = read();
- v[x].push_back(MP(y, z));
- v[y].push_back(MP(x, z));
- }
- dfs1(1, 0);
- dfs2(1, 1);
- int GG =0;
- for(int i = 1; i <= M; i++) {
- int opt = read(), s = read(), t = read();
- if(opt == 1) {
- int a = read(), b = read();
- Change(s, t, a, b);
- } else {
- cout << Query(s, t) << '\n';
- }
- }
- return 0;
- }
来源: http://www.bubuko.com/infodetail-2947334.html