[BZOJ1984][Luogu4315]月下“毛景树”

题目大意

给出一棵 n 个点的无根树，待边权，要求维护一下操作：

• 修改某条边的边权
• 修改点 u 到点 v 路径上所有边的边权
• 点 u 到点 v 路径上所有边的边权加上某个值
• 查询点 u 到点 v 路径上所有边的边权最大值

Solution

边权下放后 是 树链剖分 裸题，代码略长；

用线段树维护区间加、改、查操作，关于线段树多操作优先级的处理可以看这里。

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;

const int maxn = 100007;
int n, a[maxn];

//edge-Table
int edgenum, head[maxn], nxt[maxn << 1], vet[maxn << 1], val[maxn << 1], id[maxn << 1], id_val[maxn];
inline void addedge(int u, int v, int cost, int ID){
	++edgenum;
	vet[edgenum] = v;
	val[edgenum] = cost;
	id[edgenum] = ID;
	nxt[edgenum] = head[u];
	head[u] = edgenum;
}

//Segment Tree
int Max[maxn << 2], changetag[maxn << 2], addtag[maxn << 2];
inline void PushUp(int rt){
    Max[rt] = max(Max[rt<<1], Max[rt<<1|1]);
}

inline void PushDown(int rt, int ln, int rn){
    if (changetag[rt] != -1){
        Max[rt<<1] = changetag[rt]; Max[rt<<1|1] = changetag[rt];
        changetag[rt << 1] = changetag[rt]; addtag[rt << 1] = 0;
        changetag[rt << 1 | 1] = changetag[rt]; addtag[rt << 1 | 1] = 0;
        changetag[rt] = -1;
    }else if (addtag[rt]){
        Max[rt<<1] += addtag[rt]; Max[rt<<1|1] += addtag[rt];
        if (changetag[rt<<1] != -1) changetag[rt<<1] += addtag[rt];
        else addtag[rt<<1] += addtag[rt];
        if (changetag[rt<<1|1] != -1) changetag[rt<<1|1] += addtag[rt];
        else addtag[rt<<1|1] += addtag[rt];
        addtag[rt] = 0;
    }
}

void Change(int rt, int l, int r, int L, int R, int C){
    if (L <= l && r <= R){
        Max[rt] = C;
        changetag[rt] = C;
        addtag[rt] = 0;
        return;
    }
    int m = (l + r) >> 1;
    PushDown(rt, m - l + 1, r - m);
    if (L <= m) Change(rt<<1, l, m, L, R, C);
    if (R > m) Change(rt<<1|1, m+1, r, L, R, C);
    PushUp(rt);
}

void Add(int rt, int l, int r, int L, int R, int C){
    if (L <= l && r <= R){
        Max[rt] = Max[rt] + C;
        if (changetag[rt] == -1) addtag[rt] += C;
        else changetag[rt] += C;
        return;
    }
    int m = (l + r) >> 1;
    PushDown(rt, m - l + 1, r - m);
    if (L <= m) Add(rt<<1, l, m, L, R, C);
    if (R > m) Add(rt<<1|1, m+1, r, L, R, C);
    PushUp(rt);
}

int Query(int rt, int l, int r, int L, int R){
    if (L <= l && r <= R) return Max[rt];
    int m = (l + r) >> 1, res = -1;
    PushDown(rt, m - l + 1, r - m);
    if (L <= m) res = max(res, Query(rt<<1, l, m, L, R));
    if (R > m) res = max(res, Query(rt<<1|1, m+1, r, L, R));
    return res;
}

//树剖
int size[maxn], tid[maxn], top[maxn], son[maxn], dep[maxn], stamp, dfspath[maxn], fa[maxn];
void dfs(int u, int D){
	size[u] = 1; dep[u] = D; son[u] = 0;
	for (int e = head[u]; e; e = nxt[e]){
		int v = vet[e], cost = val[e], ID = id[e];
		if (v == fa[u]) continue;
		fa[v] = u; a[v] = cost; id_val[ID] = v;
		dfs(v, D + 1);
		size[u] += size[v];
		if (size[v] > size[son[u]]) son[u] = v;
	}
}

void Dfs(int u, int ance){
	top[u] = ance; tid[u] = ++stamp; dfspath[stamp] = u;
	if (son[u])Dfs(son[u], ance);
	for (int e = head[u]; e; e = nxt[e]){
		int v = vet[e];
		if (v != fa[u] && v != son[u]){
			Dfs(v, v);
		}
	}
}

int query(int u, int v){
	int res = 0;
	while (top[u] != top[v]){
		if (dep[top[u]] < dep[top[v]]) swap(u, v);
		res = max(res, Query(1, 1, n, tid[top[u]], tid[u]));
		u = fa[top[u]];
	}
	if (dep[u] > dep[v]) swap(u, v);
	if (tid[u] < tid[v]) res = max(res, Query(1, 1, n, tid[u] + 1, tid[v]));
	return res;
}

void change(int u, int v, int val){
	while (top[u] != top[v]){
		if (dep[top[u]] < dep[top[v]]) swap(u, v);
		Change(1, 1, n, tid[top[u]], tid[u], val);
		u = fa[top[u]];
	}
	if (dep[u] > dep[v]) swap(u, v);
	if (tid[u] < tid[v]) Change(1, 1, n, tid[u] + 1, tid[v], val);
}

void add(int u, int v, int val){
	while (top[u] != top[v]){
		if (dep[top[u]] < dep[top[v]]) swap(u, v);
		Add(1, 1, n, tid[top[u]], tid[u], val);
		u = fa[top[u]];
	}
	if (dep[u] > dep[v]) swap(u, v);
	if (tid[u] < tid[v]) Add(1, 1, n, tid[u] + 1, tid[v], val);
}

inline int read(){
	int f = 1, val = 0; char ch = getchar();
	while ((ch < '0' || ch > '9') && (ch != '-')) ch = getchar();
	if (ch == '-') f = -1, ch = getchar();
	while (ch >= '0' && ch <= '9') val = (val << 3) + (val << 1) + ch - '0', ch = getchar();
	return val * f;
}

void Build(int rt, int l, int r){
    changetag[rt] = -1; addtag[rt] = 0;
    if (l == r){
        Max[rt] = a[dfspath[l]];
        return;
    }
    int m = (l + r) >> 1;
    Build(rt<<1, l, m);
    Build(rt<<1|1, m+1, r);
    PushUp(rt);
}

int main(){
	n = read();
	for (int i = 1; i < n; ++i){
		int u = read(), v = read(), cost = read();
		addedge(u, v, cost, i);
		addedge(v, u, cost, i);
	}
	dfs(1, 0);
	Dfs(1, 1);
	Build(1, 1, n);
	char order[20];
	scanf("%s", order);
	while (order[0] != 'S'){
		if (order[0] == 'M'){
			int u = read(), v = read();
			printf("%d\n", query(u, v));
		}else if (order[0] == 'C' && order[1] == 'h'){
			int k = read(), w = read();
			Change(1, 1, n, tid[id_val[k]], tid[id_val[k]], w);
		}else if (order[0] == 'C' && order[1] == 'o'){
			int u = read(), v = read(), w = read();
			change(u, v, w);
		}else{
			int u = read(), v = read(), w = read();
			add(u, v, w);
		}
		scanf("%s", order);
	}
	return 0;
}