526互联

P4069 [SDOI2016]游戏 李超线段树 维护区间优势线段的线段树

发布时间 2023-04-17 16:19:12作者: qdhys

传送门

#include <iostream>
#include <algorithm>
#include <cstring>

typedef long long ll;
typedef std::pair<double, int> PDI;

const int N = 1e5, M = 2e5 + 10;
const ll INF = 123456789123456789;
int n, m, cnt;

int h[N], e[M], ne[M], idx;
int id[N], cnt1;
int dep[N], sz[N], top[N], fa[N], son[N];
ll len[N], w[M], nw[N];

inline void add(int a, int b, ll c){
	ne[idx] = h[a], e[idx] = b, w[idx] = c, h[a] = idx ++;
}

struct Segment {
    ll k, b;
}seg[M << 1];

struct node {
    int l, r;
    ll mn;
    int id;
}tr[N << 2];

inline void ADD(ll k, ll b) {
	seg[++ cnt] = {k, b};
}

inline int cmp(ll x, ll y) {
    if(x < y)   return 1;
    else if(y > x)  return -1;
    return 0;
}

inline ll calc(int id, ll x) {
    return seg[id].k * x + seg[id].b;
}

inline void pushup(int u) {
	tr[u].mn = std::min(std::min(tr[u << 1].mn, tr[u].mn), tr[u << 1 | 1].mn);
}

inline void build_tree(int u, int l, int r) {
    tr[u] = {l, r, INF};
    if(l == r)	return ;
	
    int mid = l + r >> 1;
    build_tree(u << 1, l, mid);
    build_tree(u << 1 | 1, mid + 1, r);
}
 
inline void update(int u, int v) {
    int& k = tr[u].id;
    int mid = tr[u].l + tr[u].r >> 1;
    tr[u].mn = std::min(std::min(tr[u].mn, calc(v, nw[tr[u].l])), calc(v, nw[tr[u].r]));
    tr[u].mn = std::min(std::min(tr[u].mn, calc(k, nw[tr[u].r])), calc(k, nw[tr[u].r]));
    if(cmp(calc(v, nw[mid]), calc(k, nw[mid])) == 1)   std::swap(k, v);
    int d1 = cmp(calc(v, nw[tr[u].l]), calc(k, nw[tr[u].l])), d2 = cmp(calc(v, nw[tr[u].r]), calc(k, nw[tr[u].r]));

    if(d1 == 1)    update(u << 1, v);
    if(d2 == 1)    update(u << 1 | 1, v);
}

inline void modify(int u, int l, int r) {
    if(tr[u].l >= l && tr[u].r <= r){//定位update区间
        update(u, cnt);
        return ;
    }
    int mid = tr[u].l + tr[u].r >> 1;
    if(l <= mid)    modify(u << 1, l, r);
    if(r > mid) modify(u << 1 | 1, l, r);
    
    pushup(u);
}


inline ll query(int u, int l, int r) {
	ll res = INF;
	if(tr[u].l >= l && tr[u].r <= r)	return tr[u].mn;
    
    int mid = tr[u].l + tr[u].r >> 1;
    
	res = std::min({res, calc(tr[u].id, nw[std::max(tr[u].l, l)]), calc(tr[u].id, nw[std::min(tr[u].r, r)])});
	if (l <= mid)	res = std::min(res, query(u << 1, l, r));
	if (r > mid)	res = std::min(res, query(u << 1 | 1, l, r));
	
	return res;
}

//统计子树大小 并且 找出重儿子
inline void dfs1(int u, int father, int depth, ll cd){
    dep[u] = depth, fa[u] = father, sz[u] = 1;
    len[u] = cd;
    
    for (int i = h[u]; ~i; i = ne[i]){
        int j = e[i];
        if (j == father) continue;
        dfs1(j, u, depth + 1, cd + w[i]);
        sz[u] += sz[j];
        if (sz[son[u]] < sz[j]) son[u] = j;
    }
}

//dfs序 nw标记dfs为cnt的时候对应的树上点的权值 top标记父亲是谁
inline void dfs2(int u, int t){
    id[u] = ++ cnt1,  top[u] = t, nw[cnt1] = len[u];
    if (!son[u]) return;
    dfs2(son[u], t);
    for (int i = h[u]; ~i; i = ne[i]){
        int j = e[i];
        if (j == fa[u] || j == son[u]) continue;
        dfs2(j, j);
    }
}

inline int LCA(int u, int v) {
	while (top[u] != top[v]) {
        if (dep[top[u]] < dep[top[v]]) std::swap(u, v);
        if(u == fa[top[u]])	return u;
        u = fa[top[u]];
    }
    if (dep[u] < dep[v]) return u;
    return v;
}
//传进来想要爬的两个点
inline void update_path(int u, int v) { 

    while (top[u] != top[v]) {
        if (dep[top[u]] < dep[top[v]]) std::swap(u, v);
        modify(1, id[top[u]], id[u]);
        u = fa[top[u]];
    }
    
    if (dep[u] < dep[v]) std::swap(u, v);
	modify(1, id[v], id[u]);
}

inline ll query_path(int u, int v){
	ll mn = INF;
    while (top[u] != top[v])
    {
        if (dep[top[u]] < dep[top[v]]) std::swap(u, v);
        mn = std::min(mn, query(1, id[top[u]], id[u]));
        u = fa[top[u]];
    }
    if (dep[u] < dep[v]) std::swap(u, v);
    mn = std::min(mn, query(1, id[v], id[u]));
    
    return mn;
}

inline void Init(){
	dfs1(1, -1, 1, 0);
    dfs2(1, 1);
}

inline void solve(){
	memset(h, -1, sizeof h);
	
	std::cin >> n >> m;
	
	for(int i = 1; i < n; i ++) {
		int a, b;
		ll c;
		std::cin >> a >> b >> c;
		add(a, b, c);
		add(b, a, c);
	}
	
	Init();

    build_tree(1, 1, n);
	
	seg[0] = {0, INF};
	
	int op, u, v;
	ll a, b;
	while(m --) {
		std::cin >> op >> u >> v;
		if(op == 1){
			int lca = LCA(u, v);
			std::cin >> a >> b;
			
			ll k = -a, c = b + a * len[u];
			ADD(k, c);
			update_path(u, lca);
			
			k = a, c = a * (len[u] - len[lca] * 2) + b;
			ADD(k, c);
			update_path(lca, v);
		}else{
			std::cout << query_path(u, v) << '\n';
		}
	}
}

int main(void) {
    std::ios::sync_with_stdio(false);
    std::cin.tie(0);
    std::cout.tie(0);
    
    int _ = 1;
    while(_ --)
    	solve();

    return 0;
}