CSU 1663 2015湖南多校对抗赛06.22

题目链接

给定一棵50000个点的树，有以下三种操作：

1.将一条边权修改为X

2.将A到B路径上的所有边权乘以C

3.询问A到B路径上的边权和

思路

  看到点权50000以及树上路径操作，直接上树链剖分

一些细节：

  1.线段树共俩个标记区间和Sum,以及区间倍数Dt

  2.Dt初始为1，C可以为负数，所以用Dt != 1判断是否下放

Code

#include <cstdio>
#include <iostream>
#include <cstring>
#include <queue>
#include <algorithm>
#include <vector>
typedef long long ll;
using namespace std;
#define foru(i, a, b) for(ll i=(a); i<=(b); i++)
#define ford(i, a, b) for(ll i=(a); i>=(b); i--)
#define clr(a, b) memset(a, b, sizeof(a))

const int N = 50010;

struct Edge{
int a, b;
ll c;
}E
;

int n, tot;
int adj
, aim[2*N], nxt[2*N];

void add(int a, int b){
tot ++;
aim[tot] = b;
nxt[tot] = adj[a];
adj[a] = tot;
}

void init(){
tot = 0; clr(adj, 0);
scanf("%d", &n);
foru(i, 1, n-1){
scanf("%d %d %lld", &E[i].a, &E[i].b, &E[i].c);
add(E[i].a, E[i].b);
add(E[i].b, E[i].a);
}
}

int num, l, r;
int fa
, son
, siz
, dep
, idx
, top
;
int L[4*N], R[4*N], mid[4*N];
ll Sum[4*N], dt[4*N], ans;

void dfs(int x, int pre, int d){
fa[x] = pre; siz[x] = 1; dep[x] = d;
int k = adj[x];
while (k){
int tx = aim[k];
if (tx != pre){
dfs(tx, x, d+1);
siz[x] += siz[tx];
if (siz[tx] > siz[son[x]])
son[x] = tx;
}
k = nxt[k];
}
}

void get_tree(int x, int pre){
idx[x] = ++ num; top[x] = pre;
if (son[x]) get_tree(son[x], top[x]);
int k = adj[x];
while (k){
int tx = aim[k];
if (tx != son[x] && tx != fa[x]) get_tree(tx, tx);
k = nxt[k];
}
}

void build(int l, int r, int i){
L[i] = l; R[i] = r; dt[i] = 1;
if (l == r) return;
mid[i] = (l + r) >> 1;
build(l, mid[i], i<<1);
build(mid[i]+1, r, (i<<1)+1);
}

void down(int i){
Sum[i << 1] *= dt[i];
Sum[(i<<1)+1] *= dt[i];
dt[i<< 1] *= dt[i];
dt[(i<<1)+1] *= dt[i];
dt[i] = 1;
}

void modify(int k, ll x, int i){
if (L[i] == R[i]) {
Sum[i] = x;
return;
}
if (dt[i] != 1) down(i);
if (k <= mid[i]) modify(k, x, i<<1);
else modify(k, x, (i<<1)+1);
Sum[i] = Sum[i<<1] + Sum[(i<<1)+1];
}

int root;
void prepare(){
num = 0; root = (n + 1) >> 1;
clr(son, 0);
dfs(root, root, 1);
get_tree(root, root);
build(1, num, 1);
foru(i, 1, n-1){
if (dep[E[i].a] > dep[E[i].b]) swap(E[i].a, E[i].b);
modify(idx[E[i].b], E[i].c, 1);
}
}

void get(int a, int b, int i){
if (a <= L[i] && R[i] <= b){
ans = ans + Sum[i];
return;
}
if (dt[i] != 1) down(i);
if (a <= mid[i]) get(a, b, i<<1);
if (b >  mid[i]) get(a, b, (i<<1)+1);
}

ll query(int x, int y){
int fx = top[x], fy = top[y]; ans = 0;
while (fx != fy){
if (dep[fx] < dep[fy]){
swap(x, y);
swap(fx, fy);
}
get(idx[fx], idx[x], 1);
x = fa[fx]; fx = top[x];
}
if (x == y) return ans;
if (dep[x] > dep[y]) swap(x, y);
get(idx[son[x]], idx[y], 1);
return ans;
}

void change(int a, int b, ll c, int i){
if (a <= L[i] && R[i] <= b){
Sum[i] *= c;
dt[i] *= c;
return;
}
if (dt[i] != 1) down(i);
if (a <= mid[i]) change(a, b, c, i<<1);
if (b >  mid[i]) change(a, b, c, (i<<1)+1);
Sum[i] = Sum[i<<1] + Sum[(i<<1)+1];
}

void updata(int x, int y, ll c){
int fx = top[x], fy = top[y];
while (fx != fy){
if (dep[fx] < dep[fy]){
swap(x, y);
swap(fx, fy);
}
change(idx[fx], idx[x], c, 1);
x = fa[fx]; fx = top[x];
}
if (x == y) return;
if (dep[x] > dep[y]) swap(x, y);
change(idx[son[x]], idx[y], c, 1);
}

void solve(){
char cmd[10];
while (1){
int i, a, b; ll c;
scanf("%s", cmd);
if (cmd[0] == 'E') return;
if (cmd[0] == 'C'){
scanf("%d %lld", &i, &c);
modify(idx[E[i].b], c, 1);
continue;
}
if (cmd[0] == 'M'){
scanf("%d%d%lld", &a, &b, &c);
updata(a, b, c);
continue;
}
scanf("%d%d", &a, &b);
printf("%lld\n", query(a, b));
}
}

int main(){
freopen("G.txt", "r", stdin);
int T; scanf("%d", &T);
while (T--){
init();
prepare();
solve();
}

return 0;
}