一個
對於第
求
特別的,如果
首先,最小生成樹的樹邊是可以無限制減少的,非樹邊是可以無限制增加的
然後對於樹邊增加的上限是所有跨過這條邊的非樹邊的權值最小的那個,如果沒有跨過這條邊的非樹邊,這條樹邊是無限制增加的
非樹邊減少的下限是他跨過的所有的樹邊的權值中最大的那個
以上的幾部分都可以樹鏈剖分+線段樹維護出來,於是就做完了
需要注意輸入的下標,節點的編號和樹剖之後點的重編號的對應關係
具體見代碼
#include<bits/stdc++.h>
using namespace std;
const int maxn = 11234,INF = 0x3f3f3f3f;
#define LL long long
#define root 1,1,n
#define Now int o,int l,int r
#define lson o<<1,l,m
#define rson o<<1|1,m+1,r
#define Mid int m = (l + r)>>1
int ma[maxn*4],mi[maxn*4],lazy[maxn*4];
int arr[maxn];
void seter(int o,int v){
lazy[o] = min(lazy[o],v);
mi[o] = min(mi[o],v);
}
void push_down(Now){
if(l != r){
seter(o<<1,lazy[o]);
seter(o<<1|1,lazy[o]);
}
lazy[o] = INF;
}
int query(Now,int pos){
if(l == r){
return mi[o];
}
if(lazy[o] != INF) push_down(o,l,r);
Mid;
if(pos <= m)
return query(lson,pos);
else
return query(rson,pos);
}
int handle(Now,int ul,int ur,int v){
if(ul <= l && r <= ur){
seter(o,v);
return ma[o];
}
if(lazy[o] != INF) push_down(o,l,r);
int ret = 0;
Mid;
if(ul <= m) ret = max(ret,handle(lson,ul,ur,v));
if(m+1<=ur) ret = max(ret,handle(rson,ul,ur,v));
return ret;
}
void segInit(Now){
lazy[o] = mi[o] = INF;
if(l == r){
ma[o] = arr[l];
return;
}
Mid;
segInit(lson),segInit(rson);
ma[o] = max(ma[o<<1],ma[o<<1|1]);
}
vector<int> edge[maxn];
int fa[maxn],son[maxn],siz[maxn];
int deep[maxn],top[maxn],tid[maxn];
int _cnt;
void dffs(int st,int Fa,int Deep){
siz[st] = 1,deep[st] = Deep;
fa[st] = Fa,son[st] = -1;
for(auto x : edge[st]){
if(x == Fa) continue;
dffs(x,st,Deep+1);
siz[st] += siz[x];
if(son[st] == -1 || siz[son[st]] < siz[x])
son[st] = x;
}
}
void dfss(int st,int Top){
top[st] = Top,tid[st] = _cnt++;
if(son[st] != -1) dfss(son[st],Top);
for(auto x : edge[st]){
if(son[st] != x && fa[st] != x)
dfss(x,x);
}
}
void splite(){
_cnt = 1;
dffs(1,-1,1);
dfss(1,1);
}
int n;
int handle(int x,int y,int v){
int ix,iy;
ix = iy = 0;
int tx = top[x],ty = top[y];
while(tx != ty){
if(deep[tx] < deep[ty])
swap(tx,ty),swap(x,y),swap(ix,iy);
ix = max(handle(root,tid[tx],tid[x],v),ix);
x = fa[tx],tx = top[x];
}
if(deep[x] < deep[y])
swap(x,y);
return max(max(ix,iy),handle(root,tid[y]+1,tid[x],v));
}
int x[maxn],y[maxn],v[maxn];
int main(){
int T,m;
scanf("%d",&T);
int icase = 1;
while(T-- && ~scanf("%d %d",&n,&m)){
LL ans = 0;
for(int i=1;i<=n;i++) edge[i].clear();
for(int i=1;i<n;i++){
scanf("%d %d %d",&x[i],&y[i],&v[i]);
edge[x[i]].push_back(y[i]);
edge[y[i]].push_back(x[i]);
}
splite();
for(int i=1;i<n;i++){
if(deep[x[i]] < deep[y[i]]) swap(x[i],y[i]);
arr[tid[x[i]]] = v[i];
}
segInit(root);
int l,r,w;
for(int i=n;i<=m;i++){
scanf("%d %d %d",&l,&r,&w);
int ops = w - handle(l,r,w);
ans -= 1ll * i;
ans += 1ll * i * i * ops;
}
for(int i=1;i<n;i++){
int temp = query(root,tid[x[i]]);
if(temp == INF) temp = -1;
else temp = temp - v[i];
ans += 1ll * i * temp;
ans -= 1ll * i * i;
}
printf("Case %d: %lld\n",icase++,ans);
}
return 0;
}