10.23考试

T1
显然贪心+维护小根堆；
注意边界条件，以及一些细节问题

#include<iostream>
#include<cstdio>
#include<queue>
#include<algorithm>
#define LL long long
using namespace std;
const int N=3e5+7;
struct node{
	LL v,w,cha;
	int id;
	friend bool operator <(const node x,const node y){
		return x.cha>y.cha;
	}
}a[N];
int n,k,ans=1<<30;
priority_queue<node> q;
int cmp(node x,node y){
	if(x.v==y.v) return x.id<y.id;
	return x.v>y.v;
}
int main(){
	freopen("rank.in","r",stdin);
	freopen("rank.out","w",stdout);
	scanf("%lld",&n);
	for(int i=1;i<=n;i++){
		scanf("%lld%lld",&a[i].v,&a[i].w);
		a[i].cha=a[i].w-a[i].v;
		a[i].id=i;
	}
	sort(a+1,a+n+1,cmp);
	for(int i=1;i<=n;i++){
		if(a[i].id==1){
			k=i;
			break;
		}
	}
	for(int i=1;i<=n;i++){
		if(a[i].v>a[k].v) q.push(a[i]);
		else break;
	}
	int num=k+1;
	LL sum=a[k].v;
	ans=(int)q.size()+1;
	a[n+1].v=-1;
	while(1){
		node now=q.top();
		if(sum==0) break;
		if(sum<now.cha+1) break;
		sum-=(now.cha+1);
		q.pop();
		for(int i=num;i<=n;i++){
			if(a[i].v>sum){
				q.push(a[i]);
				if(i==n) num=n+1;
			}
			else{
				num=i;
				break;
			}
		}
		ans=min(ans,(int)q.size()+1);
		if(ans==1) break;
 	}
	cout<<ans;
	fclose(stdin);
	fclose(stdout);
	return 0;
}
/*
8
20 1000
32 37
40 1000
45 50
16 16
16 16
14 1000
2 1000

8
40 1000
32 37
40 42
45 50
16 16
16 16
14 1000
2 1000

10
25 38
45 48
9 13
49 50
12 14
41 42
34 37
46 49
14 15
23 26
*/

T2
由于是对链进行操作所以考虑树上查分；
又因为双向边，对答案影响不同，所以要分别算，
还有这题比较坑，注意体面

#include<iostream>
#include<cstdio>
#define LL long long
using namespace std;
inline long long read() {
    long long s = 0, f = 1; char ch;
    while(!isdigit(ch = getchar())) (ch == '-') && (f = -f);
    for(s = ch ^ 48;isdigit(ch = getchar()); s = (s << 1) + (s << 3) + (ch ^ 48));
    return s * f;
}
const int N=1e5+7;
const int p=1e9+7;
struct edge{
	int v,id,nxt;
}e[N<<1];
int n,cnt=1,m,maxn;
LL ans;
int a[N],fa[N],head[N],dep[N],top[N],siz[N],hs[N],f[N],d[N],ba[N];
void add_edge(int u,int v,int w){
	e[++cnt]=(edge){v,w,head[u]};
	head[u]=cnt;
}

void get_tree(int u){
	dep[u]=dep[fa[u]]+1;
	siz[u]=1;
	for(int i=head[u];i;i=e[i].nxt){
		int to=e[i].v;
		if(to!=fa[u]){
			fa[to]=u;
			get_tree(to);
			siz[u]+=siz[to];
			if(siz[hs[u]]<siz[to]) hs[u]=to;
		}
	}
}

void dfs(int u,int fat){
	top[u]=fat;
	if(hs[u]) dfs(hs[u],fat);
	for(int i=head[u];i;i=e[i].nxt){
		int to=e[i].v;
		if(to!=fa[u]&&to!=hs[u]){
			dfs(to,to);
		}
	}
}


int lca(int x,int y){
	while(top[x]!=top[y]){
		if(dep[top[x]]<dep[top[y]]) swap(x,y);
		x=fa[top[x]];
	}
	return dep[x]<dep[y]?x:y;
}

void dfs1(int u){
	for(int i=head[u];i;i=e[i].nxt){
		int to=e[i].v;
		if(to!=fa[u]){
			dfs1(to);
			f[u]+=f[to];
			d[u]+=d[to];
		}
	}
	maxn=max(maxn,max(f[u],d[u]));
}

void dfs2(int u){
	for(int i=head[u];i;i=e[i].nxt){
		int to=e[i].v;
		if(to!=fa[u]){
			if(e[i].id==1){
				ans+=ba[d[to]]-1;
			}else{
				if(e[i^1].id==1){
					ans+=ba[f[to]]-1;
				}
			}
			dfs2(to);
		}
	}
}

int main(){
	freopen("task.in","r",stdin);
	freopen("task.out","w",stdout);
	n=read();
	for(int i=1;i<n;i++){
		int x,y,z;
		x=read();
		y=read();
		z=read();
		add_edge(x,y,0);
		add_edge(y,x,z);
	}
	get_tree(1);
	dfs(1,1);
//	return 0;
	scanf("%d",&m);
	for(int i=1;i<=m;i++){
		a[i]=read();
	}
	a[0]=1;
	for(int i=1;i<=m;i++){
		int x=a[i-1];
		int y=a[i];
		int ff=lca(x,y);
//		cout<<ff<<"\n";
		f[x]++;
		d[y]++;
		f[ff]--;
		d[ff]--;
	}
	dfs1(1);
//	for(int i=1;i<=n;i++){
//		cout<<i<<" "<<f[i]<<" "<<d[i]<<"\n";
//	}
//	cout<<"----"<<maxn<<"\n";
	ba[0]=1;
	for(int i=1;i<=maxn+1;i++){
		ba[i]=1LL*ba[i-1]*2%p;
	}
//	for(int i=1;i<=maxn;i++){
//		cout<<sum[i]<<"\n";
//	}
//	for(int u=1;u<=n;u++){
//		for(int i=head[u];i;i=e[i].nxt){
//			int to=e[i].v;
//			if(e[i].id==1){
////				cout<<u<<" "<<to<<" "<<dep[u]<<" "<<dep[to]<<"\n";
//				int tt=dep[u]>dep[to]?u:to;
//				if(dep[u]<dep[to]){
//					ans=(1LL*ans+ba[d[tt]]-1)%p;
//				}else ans=(1LL*ans+ba[f[tt]]-1)%p;
////				cout<<ans<<"\n";
//			}
//		}
//	}
	dfs2(1);
	cout<<ans;
	fclose(stdin);
	fclose(stdout);
	return 0;
}
/*
5
1 2 0
2 3 0
5 1 1
3 4 1
5
5 4 5 2 2
*/