欢迎您访问程序员文章站本站旨在为大家提供分享程序员计算机编程知识!
您现在的位置是: 首页  >  IT编程

洛谷P4069 [SDOI2016]游戏(李超线段树)

程序员文章站 2022-11-22 08:22:57
题意 "题目链接" 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。 cpp // luogu judger enable o2 / 李超线段树板子题 / include define ......

题意

题目链接

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;
}