树上路径区间更新，单点查询。
线段树和树状数组都可以用于本题的维护。
线段树：
#include<cstdio> #include<iostream> #include<algorithm> #include<cstring> #define lson rt<<1 #define rson rt<<1|1 #define Lson l,m,lson #define Rson m+1,r,rson #define max(a,b) a>b? a:b using namespace std; const int maxn =5e4+5; struct Edge{ int to,next; }E[2*maxn]; int n,head[maxn],tot; int cnt,idx,size[maxn],fa[maxn],son[maxn],dep[maxn],top[maxn],id[maxn],rnk[maxn]; int a[maxn]; struct Node{ int sum,add; }tree[maxn<<2]; void init() { cnt=idx=tot=0; memset(head,-1,sizeof(head)); dep[1]=0,fa[1]=1,size[0]=0; memset(son,0,sizeof(son)); } void AddEdge(int u,int v) { E[tot] = (Edge){v,head[u]}; head[u]=tot++; } void dfs1(int u) { size[u]=1; for(int i=head[u];~i;i=E[i].next){ int v=E[i].to; if(v!=fa[u]){ fa[v]=u; dep[v]=dep[u]+1; dfs1(v); size[u]+=size[v]; if(size[son[u]]<size[v]) son[u]=v; } } } void dfs2(int u,int topu) { top[u]= topu; id[u] = ++idx; rnk[idx] = u; if(!son[u]) return; dfs2(son[u],top[u]); for(int i=head[u];~i;i=E[i].next){ int v=E[i].to; if(v!=fa[u]&&v!=son[u]) dfs2(v,v); } } void pushup(int rt){ tree[rt].sum = tree[lson].sum + tree[rson].sum; } void pushdown(int l,int r,int rt){ if(tree[rt].add){ tree[lson].add += tree[rt].add; tree[rson].add += tree[rt].add; int m = (l+r)>>1; tree[lson].sum += (m-l+1)*tree[rt].add; tree[rson].sum += (r-m)*tree[rt].add; tree[rt].add =0; } } void build(int l,int r,int rt) { tree[rt].add = 0; if(l==r){ tree[rt].sum = a[rnk[l]]; return; } int m = (l+r)>>1; build(Lson); build(Rson); pushup(rt); } void update(int L,int R,int v,int l,int r,int rt){ if(L<=l && R>=r){ tree[rt].sum +=v; tree[rt].add +=v; return ; } pushdown(l,r,rt); int m =(l+r)>>1; if(L<=m) update(L,R,v,Lson); if(R>m) update(L,R,v,Rson); pushup(rt); } int query(int p,int l,int r,int rt){ //单点更新 if(l==r) return tree[rt].sum; pushdown(l,r,rt); int m = (l+r)>>1,ans=0; if(p<=m) ans= query(p,Lson); else ans =query(p,Rson); pushup(rt); return ans; } void UPDATE(int u,int v,int w) { while(top[u]!=top[v]){ if(dep[top[u]]<dep[top[v]]) swap(u,v); update(id[top[u]],id[u],w,1,n,1); u = fa[top[u]]; } if(dep[u]>dep[v])swap(u,v); update(id[u],id[v],w,1,n,1); } int main() { #ifndef ONLINE_JUDGE freopen("in.txt","r",stdin); freopen("out.txt","w",stdout); #endif int m,q,u,v; char op[5]; while(scanf("%d%d%d",&n,&m,&q)==3){ init(); for(int i=1;i<=n;++i) scanf("%d",&a[i]); while(m--){ scanf("%d%d",&u,&v); AddEdge(u,v); AddEdge(v,u); } dfs1(1); dfs2(1,1); build(1,n,1); while(q--){ scanf("%s",op); if(op[0]=='Q'){ scanf("%d",&u); printf("%d\n",query(id[u],1,n,1)); } else{ int w; scanf("%d%d%d",&u,&v,&w); if(op[0]=='D') w = -w; UPDATE(u,v,w); } } } return 0; }
树状数组：
#include<cstdio> #include<iostream> #include<algorithm> #include<cstring> #define lson rt<<1 #define rson rt<<1|1 #define Lson l,m,lson #define Rson m+1,r,rson #define max(a,b) a>b? a:b using namespace std; const int maxn =5e4+5; struct Edge{ int to,next; }E[2*maxn]; int n,head[maxn],tot; int idx,size[maxn],fa[maxn],son[maxn],dep[maxn],top[maxn],id[maxn],rnk[maxn]; int a[maxn]; struct Node{ int sum,add; }tree[maxn<<2]; void init() { idx=tot=0; memset(head,-1,sizeof(head)); dep[1]=0,fa[1]=1,size[0]=0; memset(son,0,sizeof(son)); } void AddEdge(int u,int v) { E[tot] = (Edge){v,head[u]}; head[u]=tot++; } void dfs1(int u) { size[u]=1; for(int i=head[u];~i;i=E[i].next){ int v=E[i].to; if(v!=fa[u]){ fa[v]=u; dep[v]=dep[u]+1; dfs1(v); size[u]+=size[v]; if(size[son[u]]<size[v]) son[u]=v; } } } void dfs2(int u,int topu) { top[u]= topu; id[u] = ++idx; rnk[idx] = u; //建树用 if(!son[u]) return; dfs2(son[u],top[u]); for(int i=head[u];~i;i=E[i].next){ int v=E[i].to; if(v!=fa[u]&&v!=son[u]) dfs2(v,v); } } void pushup(int rt){ tree[rt].sum = max(tree[lson].sum ,tree[rson].sum); } void pushdown(int l,int r,int rt){ if(tree[rt].add){ tree[lson].add += tree[rt].add; tree[rson].add += tree[rt].add; int m = (l+r)>>1; tree[lson].sum += (m-l+1)*tree[rt].add; tree[rson].sum += (r-m)*tree[rt].add; tree[rt].add =0; } } void build(int l,int r,int rt) { tree[rt].add = 0; if(l==r){ tree[rt].sum = a[rnk[l]]; return; } int m = (l+r)>>1; build(Lson); build(Rson); pushup(rt); } void update(int L,int R,int v,int l,int r,int rt){ if(L<=l && R>=r){ tree[rt].sum +=v; tree[rt].add +=v; return ; } pushdown(l,r,rt); int m =(l+r)>>1; if(L<=m) update(L,R,v,Lson); if(R>m) update(L,R,v,Rson); pushup(rt); } int query(int p,int l,int r,int rt){ //单点更新 if(l==r) return tree[rt].sum; pushdown(l,r,rt); int m = (l+r)>>1,ans=0; if(p<=m) ans= query(p,Lson); else ans =query(p,Rson); pushup(rt); return ans; } int bit[maxn]; void add(int pos,int val){ for(int i=pos;i<=n;i+= i&(-i)) bit[i]+=val; } inline int sum(int pos){ int res=0; for(int i=pos;i;i-= i&(-i)) res+=bit[i]; return res; } void UPDATE2(int u,int v,int w) //树状数组维护 { while(top[u]!=top[v]){ if(dep[top[u]]<dep[top[v]]) swap(u,v); add(id[top[u]],w); add(id[u]+1,-w); u = fa[top[u]]; } if(dep[u]>dep[v]) swap(u,v); add(id[u],w); add(id[v]+1,-w); } void UPDATE(int u,int v,int w) //线段树维护 { while(top[u]!=top[v]){ if(dep[top[u]]<dep[top[v]]) swap(u,v); update(id[top[u]],id[u],w,1,n,1); u = fa[top[u]]; } if(dep[u]>dep[v])swap(u,v); update(id[u],id[v],w,1,n,1); } int main() { #ifndef ONLINE_JUDGE freopen("in.txt","r",stdin); freopen("out.txt","w",stdout); #endif int m,q,u,v; char op[5]; while(scanf("%d%d%d",&n,&m,&q)==3){ init(); for(int i=1;i<=n;++i) scanf("%d",&a[i]); while(m--){ scanf("%d%d",&u,&v); AddEdge(u,v); AddEdge(v,u); } dfs1(1); dfs2(1,1); //build(1,n,1); memset(bit,0,sizeof(bit)); for(int i=1;i<=n;++i){ add(id[i],a[i]); add(id[i]+1,-a[i]); } while(q--){ scanf("%s",op); if(op[0]=='Q'){ scanf("%d",&u); printf("%d\n",sum(id[u])); //printf("%d\n",query(id[u],1,n,1)); } else{ int w; scanf("%d%d%d",&u,&v,&w); if(op[0]=='D') w = -w; UPDATE2(u,v,w); //UPDATE(u,v,w); } } } return 0; }