P10001 [集训队互测 2023] 优惠购物

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#include <bits/stdc++.h>
using namespace std;
#define int long long
#define ls rt<<1
#define rs (rt<<1|1)
const int N=1e6+5;
int T,n,len;
int m,c,ans;
int a[N],b[N],tlsh[N],s[N],use[N];
priority_queue<int>q;
struct node{
	int x,id;
}lsh[N];
bool cmp(node x,node y){return x.x<y.x;}
struct node1{
	int min,lz;
}tr[N<<2];
void pushup(int rt) {tr[rt].min=min(tr[ls].min,tr[rs].min);}
void pushdown(int rt)
{
	if(!tr[rt].lz) return ;
	tr[ls].min+=tr[rt].lz;
	tr[rs].min+=tr[rt].lz;
	tr[ls].lz+=tr[rt].lz;
	tr[rs].lz+=tr[rt].lz;
	tr[rt].lz=0;
}
void build(int rt,int l,int r)
{
	tr[rt].min=tr[rt].lz=0;
	if(l==r) return tr[rt].min=s[l-1]-use[l],void();
	int mid=(l+r)>>1;
	build(ls,l,mid);
	build(rs,mid+1,r);
	pushup(rt);
}

void update(int rt,int l,int r,int L,int R,int val)
{
	if(l>=L&&r<=R)
	{
		tr[rt].min+=val;
		tr[rt].lz+=val;
		return ;
	}
	int mid=(l+r)>>1;
	pushdown(rt);
	if(L<=mid) update(ls,l,mid,L,R,val);
	if(R>mid) update(rs,mid+1,r,L,R,val);
	pushup(rt);
}

int query(int rt,int l,int r,int L,int R)
{
	if(l>=L && r<=R) return tr[rt].min;
	pushdown(rt);
	int mid=(l+r)>>1;
	int ans=1e18;
	if(L<=mid) ans=min(ans,query(ls,l,mid,L,R));
	if(R>mid) ans=min(ans,query(rs,mid+1,r,L,R));
	return ans;
}

signed main()
{
	ios::sync_with_stdio(0);
	cin.tie(0),cout.tie(0);
	cin >>T;
	while(T--)
	{
		cin >>n>>m>>c;
		while(!q.empty()) q.pop();
		ans=0;
		for(int i=1;i<=n;i++)
		{
			cin >>a[i];
			ans+=a[i];
		}
		for(int i=1;i<=n;i++) cin >>b[i];
		s[0]=m;
		for(int i=1;i<=n;i++) s[i]=s[i-1]+a[i]/c;
		int minn=1e18;
		for(int i=n;i>=1;i--)
		{
			minn=min(minn,s[i-1]);
			int cnt=min(min(b[i],minn),a[i]%c);
			use[i]=cnt;
			minn-=cnt;
		}
		for(int i=1;i<=n;i++) s[i]=s[i-1]-use[i]+a[i]/c;
		minn=1e18;
		for(int i=n;i>=1;i--)
		{
			int cnt=min(min((b[i]-use[i])/c,minn/(c+1)),(s[i-1]-use[i])/c);
			use[i]+=cnt*c;
			minn-=cnt*(c+1);
			minn=min(minn,s[i-1]-use[i]);
		}
		for(int i=1;i<=n;i++) s[i]=s[i-1]-use[i]+(a[i]-use[i])/c;
		build(1,1,n);
		for(int i=1;i<=n;i++)
		{
			lsh[i]={b[i]-use[i],i};
			tlsh[i]=b[i]-use[i];
		}
		sort(lsh+1,lsh+1+n,cmp);
		sort(tlsh+1,tlsh+1+n);
		len=unique(tlsh+1,tlsh+n+1)-tlsh-1;
		for(int i=len,j=n;i>=1;i--)
		{
			while(j>=1 && lsh[j].x>=tlsh[i])
			{
				q.push(lsh[j].id);
				j--;
			}
			while(!q.empty())
			{
				int d=q.top();
				int min1=query(1,1,n,d,d),min2=(d==n?1e18:query(1,1,n,d+1,n)-1);
				int cnt=min(b[d]-use[d],min(min1,min2));
				if(cnt>=tlsh[i-1])
				{
					q.pop();
					use[d]+=cnt;
					update(1,1,n,d,d,-cnt);
					if(d<n) update(1,1,n,d+1,n,-cnt-1);
				}
				else break;
			}
		}
		for(int i=1;i<=n;i++) ans-=use[i];
		cout <<ans<<'\n';
	}
}