[HZOI] CSP-S模拟38 赛后总结

[HZOI] CSP-S模拟38 赛后总结

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T1:最小生成树（tree）

#include<bits/stdc++.h>
#define lid (id << 1)
#define rid (id << 1 | 1)
#define Blue_Archive return 0
#define int long long 
using namespace std;
constexpr int N = 1e5 + 3;

int n;
int m;
int ans;

struct miku
{
	int l,r,val;
	friend bool operator < (miku a,miku b){return a.val < b.val;}
}a[N];

struct mika
{
	int laz,sum;
}tr[N << 2];

inline void pushdown(int id,int l,int r,int mid)
{
	if(!tr[id].laz) return;
	tr[lid].laz = 1;
	tr[rid].laz = 1;
	tr[lid].sum = (mid - l + 1);
	tr[rid].sum = (r - mid);
	tr[id].laz = 0;
}

inline void ins(int id,int l,int r,int L,int R)
{
	if(L <= l && r <= R) 
	{
		tr[id].laz = 1;
		tr[id].sum = r - l + 1;
		return;
	}
	int mid = (l + r) >> 1;
	pushdown(id,l,r,mid);
	if(L <= mid) ins(lid,l,mid,L,R);
	if(R > mid) ins(rid,mid + 1,r,L,R);
	tr[id].sum = tr[lid].sum + tr[rid].sum;
}

inline int query(int id,int l,int r,int L,int R)
{
	if(L <= l && r <= R) return tr[id].sum;
	int mid = (l + r) >> 1,res = 0;
	pushdown(id,l,r,mid);
	if(L <= mid) res += query(lid,l,mid,L,R);
	if(R > mid) res += query(rid,mid + 1,r,L,R);
	tr[id].sum = tr[lid].sum + tr[rid].sum;
	return res;
} 

signed main()
{
	freopen("tree.in","r",stdin);freopen("tree.out","w",stdout);
	// freopen("data.in","r",stdin);freopen("data.out","w",stdout);
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	cin >> n >> m;
	for(int i = 1;i <= m;i ++) cin >> a[i].l >> a[i].r >> a[i].val;
	sort(a + 1,a + m + 1);
	for(int i = 1,val,l,r;i <= m;i ++)
	{
		l = a[i].l;
		r = a[i].r - 1;
		val = query(1,1,n - 1,l,r);
		if(val == r - l + 1) continue;
		ans += a[i].val * (r - l + 1 - val);
		ins(1,1,n - 1,l,r);
	}
	if(query(1,1,n - 1,1,n - 1) != n - 1) cout << -1 << '\n';
	else cout << ans << '\n';
	Blue_Archive;
}

T2：最短路（roads）

#include<bits/stdc++.h>
#define Blue_Archive return 0
#define int long long 
#define fi first
#define se second
#define add(u,v,a) to[++ tot] = v,w[tot] = a,nxt[tot] = h[u],h[u] = tot
using namespace std;
constexpr int N = 4e5 + 3;
constexpr int M = 2e6 + 3;
constexpr int INF = 1e18;

int n;
int m;
int tot;
int cnt;
int h[N];
int w[M];
int to[M];
int nxt[M];
int dis[M];
int ans[N];

bool vis[M];

struct miku 
{
	int u,v,a,b;
}a[N];

struct mika
{
	int id,val;
}p[M];

priority_queue<pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>> > q;

vector<int> vec[N];

inline void dijk()
{
	memset(dis,0x3f,sizeof(dis));
	q.push({0,vec[1].back()});
	dis[vec[1].back()] = 0;
	while(!q.empty())
	{
		int u = q.top().se;
		q.pop();
		if(vis[u]) continue;
		vis[u] = 1;
		for(int i = h[u];i;i = nxt[i])
		{
			if(!vis[to[i]] && dis[to[i]] > dis[u] + w[i])
			{
				dis[to[i]] = dis[u] + w[i];
				q.push({dis[to[i]],to[i]});
			}
		}
	}
}

signed main()
{
	// freopen("data.in","r",stdin);freopen("data.out","w",stdout);
	freopen("roads.in","r",stdin);freopen("roads.out","w",stdout);
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0); // 366746381
	cin >> n >> m;
	for(int i = 1;i <= m;i ++)
	{
		cin >> a[i].u >> a[i].v >> a[i].a >> a[i].b;
		a[i].b = a[i].a - a[i].b;
		p[++ cnt] = {a[i].v,a[i].a};
		vec[a[i].v].push_back(cnt);
	}
	for(int i = 1;i <= n;i ++) p[++ cnt] = {i,-INF},vec[i].push_back(cnt);
	for(int i = 1;i <= n;i ++) p[++ cnt] = {i,INF},vec[i].push_back(cnt);
	for(int i = 1;i <= n;i ++)
	{
		sort(vec[i].begin(),vec[i].end(),[](int a,int b){return p[a].val < p[b].val;});
		for(int j = 0;j + 1 < (int)vec[i].size();j ++) add(vec[i][j],vec[i][j + 1],0); // 给每个点按入边排序
	}
	for(int i = 1,l,r,mid,res,as;i <= m;i ++)
	{
		l = 0,r = vec[a[i].v].size() - 1;
		res = 0,as = 0;
		while(l <= r)
		{
			mid = (l + r) >> 1;
			if(p[vec[a[i].v][mid]].val <= a[i].a) l = mid + 1,res = mid;
			else r = mid - 1;
		}
		add(vec[a[i].u].back(),vec[a[i].v][res],a[i].a);
		l = 0,r = (int)vec[a[i].u].size() - 1;
		while(l <= r)
		{
			mid = (l + r) >> 1;
			if(p[vec[a[i].u][mid]].val < a[i].a) l = mid + 1,as = mid;
			else r = mid - 1; 
		}
		add(vec[a[i].u][as],vec[a[i].v][res],a[i].b);
	}
	dijk();
	for(int i = 1;i <= n;i ++) ans[i] = -1;
	for(int i = 1;i <= cnt;i ++)
	{
		if(!vis[i]) continue;
		if(ans[p[i].id] == -1) ans[p[i].id] = dis[i];              
		else ans[p[i].id] = min(ans[p[i].id],dis[i]);
	} 
	for(int i = 1;i <= n;i ++) cout << ans[i] << ' ';
	cout << '\n';
	Blue_Archive;
}

T3：计算任务（mission）

#include<bits/stdc++.h>
#define Blue_Archive return 0
#define int long long 
#define fi first
#define se second
using namespace std;
constexpr int N = 2e5 + 3;
constexpr int INF = 1e18;

int n;
int m;
int tot;
int top;
int tpp;
int ans;
int laz[N];
int stk[N];
int tim[N];
int skk[N];

bool del[N];

struct miku
{
	int id;
	int val;
	friend bool operator < (miku a,miku b){return a.val < b.val;}
	friend bool operator > (miku a,miku b){return a.val > b.val;}
};

vector<int> bel[N];

priority_queue<miku,vector<miku>,greater<miku>> q[N];

inline void change(int x,int val)
{
	if(del[x]) return;
	tim[x] = val;
	for(int v : bel[x]) tim[x] += laz[v];
	for(int v : bel[x]) q[v].push((miku){x,(val / bel[x].size()) + laz[v]});
}

inline int query(int x)
{
	int res = 0;
	for(int v : bel[x]) res += laz[v];
	return res;
}

signed main()
{
	freopen("mission.in","r",stdin);freopen("mission.out","w",stdout);
	// freopen("data.in","r",stdin);freopen("data.out","w",stdout);
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	cin >> n >> m;
	for(int i = 1,op,k,x,pos;i <= m;i ++)
	{
		cin >> op;
		if(op == 1)
		{
			tot ++;
			cin >> x >> k;
			x ^= ans;
			for(int j = 1;j <= k;j ++)
			{
				cin >> pos;
				pos ^= ans;
				bel[tot].push_back(pos);
			}
			change(tot,x);
		}
		else 
		{
			top = tpp = 0;
			cin >> pos >> x;
			pos ^= ans,x ^= ans;
			laz[pos] += x;
			while(q[pos].size() && (q[pos].top().val <= laz[pos] || del[q[pos].top().id]))
			{
				if(del[q[pos].top().id])
				{
					q[pos].pop();
					continue;
				} 
				if(query(q[pos].top().id) >= tim[q[pos].top().id]) stk[++ top] = q[pos].top().id,del[q[pos].top().id] = 1;
				else skk[++ tpp] = q[pos].top().id;
				q[pos].pop();
			}
			for(int j = 1;j <= tpp;j ++) change(skk[j],tim[skk[j]] - query(skk[j])); 
			ans = top;
			sort(stk + 1,stk + top + 1);
			cout << top << ' ';
			for(int i = 1;i <= top;i ++) cout << stk[i] << ' ';
			cout << '\n';
		}
	}
	Blue_Archive;
}
// 不是她努力就一定能听懂相似三角形的题目。不是她想就可以和他们相似。
// "欢迎回来少年，机房为你开敞"

T4：树上纯树（ture）

#include<bits/stdc++.h>
#define int long long 
#define Blue_Archive return 0
#define putchar_unlocked putchar
#define getchar_unlocked getchar
#define con putchar_unlocked(' ')
#define ent putchar_unlocked('\n')
#define add(x,y) to[++ tot] = y,nxt[tot] = h[x],h[x] = tot
#define calc(x,pos) (lin[pos].k * x + lin[pos].b)
using namespace std;
const int N = 1e5 + 3;
const int M = 2e5 + 3;
const int V = 1e6 + 3;
const int INF = 0x7f7f7f7f7f7f7f7f;

int n;
int cnt;
int tot;
int tim;
int a[N];
int b[N];// k
int h[N];
int rt[N];
int dp[N];// b
int to[M];
int nxt[M];

struct mika
{
	int k;
	int b;
}lin[N];

struct miku
{
	int ls;
	int rs;
	int mn;
}tr[N << 5];

inline int read()
{
	int k = 0,f = 1;
	char c = getchar_unlocked();
	while(c < '0' || c > '9')
	{
		if(c == '-') f = -1;
		c = getchar_unlocked();
	}
	while(c >= '0' && c <= '9') k = (k << 3) + (k << 1) + c - '0',c = getchar_unlocked();
	return k * f;
}

inline void write(int u)
{
	if(u < 0) putchar_unlocked('-'),u = -u;
	if(u > 9) write(u / 10);
	putchar_unlocked(u % 10 + '0');
}

inline void ins(int &id,int l,int r,int L,int R,int pos)
{
	if(l > R || L > r) return;
	if(!id) id = ++ cnt;
	if(!tr[id].mn) 
	{
		tr[id].mn = pos;
		return;
	}
	int mid = (l + r) >> 1;
	if(L <= l && r <= R)
	{
		if(calc(mid,pos) < calc(mid,tr[id].mn)) swap(pos,tr[id].mn);
		if(calc(l,pos) < calc(l,tr[id].mn)) ins(tr[id].ls,l,mid,L,R,pos);
		if(calc(r,pos) < calc(r,tr[id].mn)) ins(tr[id].rs,mid + 1,r,L,R,pos);
		return; 
	}
	ins(tr[id].ls,l,mid,L,R,pos);
	ins(tr[id].rs,mid + 1,r,L,R,pos);
}

inline int query(int id,int l,int r,int pos)
{
	if(!id) return INF;
	if(l == r) return calc(pos,tr[id].mn);
	int mid = (l + r) >> 1;
	int res = calc(pos,tr[id].mn);
	if(pos <= mid) return min(res,query(tr[id].ls,l,mid,pos));
	else return min(res,query(tr[id].rs,mid + 1,r,pos));
}

inline int meg(int p,int q,int l,int r)
{
	if(!p || !q) return p | q;
	if(l == r) return calc(l,tr[p].mn) > calc(l,tr[q].mn) ? q : p;
	int mid = (l + r) >> 1;
	tr[p].ls = meg(tr[p].ls,tr[q].ls,l,mid);
	tr[p].rs = meg(tr[p].rs,tr[q].rs,mid + 1,r);
	ins(p,l,r,-V,V,tr[q].mn);
	return p;
}

inline void dfs(int x,int fa)
{
	for(int i = h[x];i;i = nxt[i])
	{
		if(to[i] == fa) continue;
		dfs(to[i],x);
		rt[x] = meg(rt[x],rt[to[i]],-V,V);
	}
	if(rt[x]) dp[x] = query(rt[x],-V,V,a[x]);
	lin[++ tim] = (mika){b[x],dp[x]};
	ins(rt[x],-V,V,-V,V,tim);
}

signed main()
{
	freopen("ture.in","r",stdin);freopen("ture.out","w",stdout);
	n = read();
	for(int i = 1;i <= n;i ++) a[i] = read();
	for(int i = 1;i <= n;i ++) b[i] = read();
	for(int i = 1,x,y;i < n;i ++)
	{
		x = read();
		y = read();
		add(x,y);
		add(y,x);
	}
	dfs(1,0);
	for(int i = 1;i <= n;i ++) write(dp[i]),con;
	ent;
	Blue_Archive;
}
//dp[i] = min{dp[j] + a[i] * b[j]}//b[j] == k,dp[j] == b