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Submission #222488

# Submission time Handle Problem Language Result Execution time Memory
222488 2020-04-13T08:18:56 Z haojiandan Constellation 3 (JOI20_constellation3) C++11
100 / 100
 985 ms 131960 KB 
#include <bits/stdc++.h>
using namespace std;
template <typename T> void read(T &t) {
	t=0; char ch=getchar(); int f=1;
	while (ch<'0'||ch>'9') { if (ch=='-') f=-1; ch=getchar(); }
	do { (t*=10)+=ch-'0'; ch=getchar(); } while ('0'<=ch&&ch<='9'); t*=f;
}
typedef long long ll;
const int maxn=(4e5)+10;
const int INF=(1e6);
int n,m,tot,a[maxn],rt,fa[maxn];
int L[maxn],R[maxn],p[maxn],back[maxn];
ll f[maxn],g[maxn],tmp;
vector<int> son[maxn];
struct star { int x,y,c; } d[maxn];
map<pair<int,int>,int> dy;
vector<int> G[maxn]; // stars in this region
ll sum[maxn];
int dfn[maxn],Son[maxn],sz[maxn],cnt,top[maxn];
namespace Seg1 {
	int st[maxn][20],lg[maxn],pos[maxn][20],mn[maxn][20]; // mx -> first in the left & right >= me
	int Querymx(int l,int r) {
		int j=lg[r-l+1];
		int x=st[l][j],y=st[r-(1<<j)+1][j];
		return max(x,y);
	}
	int querymx(int l,int r) {
		int j=lg[r-l+1];
		int x=pos[l][j],y=pos[r-(1<<j)+1][j];
		if (a[x]>=a[y]) return x;
		return y;
	}
	int Querymn(int l,int r) {
		int j=lg[r-l+1];
		int x=mn[l][j],y=mn[r-(1<<j)+1][j];
		return min(x,y);
	}
	void init() {
		int x,y;
		for (int i=0;i<=n+1;i++) st[i][0]=mn[i][0]=a[i],pos[i][0]=i;
		for (int i=2;i<=n+2;i++) lg[i]=lg[i/2]+1;
		for (int j=1;j<=19;j++)
		for (int i=0;i+(1<<j)-1<=n+1;i++) {
			x=st[i][j-1],y=st[i+(1<<(j-1))][j-1];
			st[i][j]=max(x,y);
			x=pos[i][j-1],y=pos[i+(1<<(j-1))][j-1];
			if (a[x]>=a[y]) pos[i][j]=x;
			else pos[i][j]=y;
			x=mn[i][j-1],y=mn[i+(1<<(j-1))][j-1];
			mn[i][j]=min(x,y);
		}
	}
	void solve() {
		int l,r,mid,res,x,y;
		for (int i=1;i<=m;i++) {
			l=0,r=d[i].x-1; res=0;
			while (l<=r) {
				mid=(l+r)/2;
				if (Querymx(mid,d[i].x-1)>=d[i].y) l=mid+1,res=mid;
				else r=mid-1;
			}
			x=res+1;
			l=d[i].x+1,r=n+1; res=0;
			while (l<=r) {
				mid=(l+r)/2;
				if (Querymx(d[i].x+1,mid)>=d[i].y) r=mid-1,res=mid;
				else l=mid+1;
			}
			y=res-1;
			//printf("find id=%d l=%d r=%d\n",i,x,y);
			x=dy[make_pair(x,y)];
			sum[x]+=d[i].c;
			G[x].push_back(i);
		}
	}
};
namespace Seg2 {
	int tr[maxn*4],lazy[maxn*4]; // mx -> belong to the deepest node
	void pushdown(int root) {
		if (!lazy[root]) return;
		tr[root*2]=max(tr[root*2],lazy[root]);
		tr[root*2+1]=max(tr[root*2+1],lazy[root]);
		lazy[root*2]=max(lazy[root*2],lazy[root]);
		lazy[root*2+1]=max(lazy[root*2+1],lazy[root]);
		lazy[root]=0;
	}
	void add(int L,int R,int l,int r,int root,int delta) {
		if (L<=l&&r<=R) {
			tr[root]=max(tr[root],delta);
			lazy[root]=max(lazy[root],delta);
			return;
		}
		pushdown(root);
		int mid=(l+r)/2;
		if (L<=mid) add(L,R,l,mid,root*2,delta);
		if (mid<R) add(L,R,mid+1,r,root*2+1,delta);
		tr[root]=max(tr[root*2],tr[root*2+1]);
	}
	int query(int x,int l,int r,int root) {
		if (l==r) return tr[root];
		pushdown(root);
		int mid=(l+r)/2;
		if (x<=mid) return query(x,l,mid,root*2);
		return query(x,mid+1,r,root*2+1);
	}
};
int build(int l,int r) {
	tot++;
	dy[make_pair(l,r)]=tot;
	L[tot]=l,R[tot]=r;
	int u=tot,mx=Seg1::Querymx(l,r),mn=Seg1::Querymn(l,r);
	if (mn==mx) return u;
	int x=Seg1::querymx(l,r),y;
	if (l<=x-1) son[u].push_back(build(l,x-1));
	while (x<=r) {
		y=Seg1::querymx(x+1,r);
		if (a[y]==mx) {
			if (x+1<=y-1) son[u].push_back(build(x+1,y-1));
			x=y;
		} else {
			if (x+1<=r) son[u].push_back(build(x+1,r));
			break;
		}
	}
	return u;
}
void dfs(int u) {
	sz[u]=1;
	for (int i=0,v;i<son[u].size();i++) {
		v=son[u][i];
		dfs(v);
		fa[v]=u;
		sz[u]+=sz[v];
		if (sz[v]>sz[Son[u]]) Son[u]=v;
	}
}
void dfs(int u,int t) {
	dfn[u]=++cnt; back[cnt]=u;
	top[u]=t;
	Seg2::add(L[u],R[u],1,n,1,dfn[u]);
	if (Son[u]) dfs(Son[u],t);
	for (int i=0,v;i<son[u].size();i++) {
		v=son[u][i];
		if (v==Son[u]) continue;
		dfs(v,v);
	}
}
namespace Seg3 {
	ll tr[maxn]; // sum -> DP
	void add(int x,ll delta) {
		x=dfn[x];
		for (;x<=tot;x+=x&(-x)) tr[x]+=delta;
	}
	ll query(int x) {
		ll res=0;
		for (;x;x-=x&(-x)) res+=tr[x];
		return res;
	}
	ll Query(int l,int r) {
		return query(r)-query(l-1);
	}
	ll query(int x,int y) {
		if (x==y) return 0;
		ll res=0;
		while (top[x]!=top[y]) {
			res+=Query(dfn[top[x]],dfn[x]);
			x=fa[top[x]];
		}
		if (x==y) return res;
		return res+Query(dfn[y]+1,dfn[x]);
	}
};
void solve(int u) {
	f[u]=sum[u];
	for (int i=0,v;i<son[u].size();i++) {
		v=son[u][i];
		solve(v);
		f[u]+=f[v];
	}
	ll first=f[u];
	for (int i=0;i<G[u].size();i++) {
		tmp=first-d[G[u][i]].c+Seg3::query(p[d[G[u][i]].x],u);
		f[u]=min(f[u],tmp);
	}
	g[u]=first-f[u];
//	printf("dp[%d]: %lld %lld %lld\n",u,first,f[u],g[u]);
	Seg3::add(u,g[u]);
}
int main() {
	//freopen("1.txt","r",stdin);
	int x,y;
	read(n);
	for (int i=1;i<=n;i++) read(a[i]);
	read(m);
	for (int i=1;i<=m;i++) read(d[i].x),read(d[i].y),read(d[i].c);
	a[0]=a[n+1]=INF;
	Seg1::init();
	rt=build(1,n);
	Seg1::solve();
	dfs(rt);
	dfs(rt,rt);
	for (int i=1;i<=n;i++) {
		p[i]=back[Seg2::query(i,1,n,1)];//,printf("p[%d]=%d\n",i,p[i]);
	}
	solve(rt);
	printf("%lld\n",f[rt]);
	return 0;
}

Compilation message

constellation3.cpp: In function 'void dfs(int)':
constellation3.cpp:129:18: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for (int i=0,v;i<son[u].size();i++) {
                 ~^~~~~~~~~~~~~~
constellation3.cpp: In function 'void dfs(int, int)':
constellation3.cpp:142:18: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for (int i=0,v;i<son[u].size();i++) {
                 ~^~~~~~~~~~~~~~
constellation3.cpp: In function 'void solve(int)':
constellation3.cpp:175:18: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for (int i=0,v;i<son[u].size();i++) {
                 ~^~~~~~~~~~~~~~
constellation3.cpp:181:16: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for (int i=0;i<G[u].size();i++) {
               ~^~~~~~~~~~~~
constellation3.cpp: In function 'int main()':
constellation3.cpp:191:6: warning: unused variable 'x' [-Wunused-variable]
  int x,y;
      ^
constellation3.cpp:191:8: warning: unused variable 'y' [-Wunused-variable]
  int x,y;
        ^

Subtask #1
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 20 ms 19456 KB Output is correct
2 Correct 20 ms 19456 KB Output is correct
3 Correct 19 ms 19456 KB Output is correct
4 Correct 15 ms 19456 KB Output is correct
5 Correct 16 ms 19328 KB Output is correct
6 Correct 16 ms 19328 KB Output is correct
7 Correct 18 ms 19456 KB Output is correct
8 Correct 16 ms 19456 KB Output is correct
9 Correct 16 ms 19328 KB Output is correct
10 Correct 16 ms 19456 KB Output is correct
11 Correct 16 ms 19456 KB Output is correct
12 Correct 17 ms 19456 KB Output is correct
13 Correct 16 ms 19456 KB Output is correct
14 Correct 16 ms 19304 KB Output is correct
15 Correct 16 ms 19328 KB Output is correct
16 Correct 16 ms 19456 KB Output is correct
17 Correct 20 ms 19456 KB Output is correct
18 Correct 16 ms 19456 KB Output is correct
19 Correct 17 ms 19328 KB Output is correct
20 Correct 16 ms 19456 KB Output is correct
21 Correct 16 ms 19456 KB Output is correct
22 Correct 16 ms 19328 KB Output is correct

Subtask #2
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 20 ms 19456 KB Output is correct
2 Correct 20 ms 19456 KB Output is correct
3 Correct 19 ms 19456 KB Output is correct
4 Correct 15 ms 19456 KB Output is correct
5 Correct 16 ms 19328 KB Output is correct
6 Correct 16 ms 19328 KB Output is correct
7 Correct 18 ms 19456 KB Output is correct
8 Correct 16 ms 19456 KB Output is correct
9 Correct 16 ms 19328 KB Output is correct
10 Correct 16 ms 19456 KB Output is correct
11 Correct 16 ms 19456 KB Output is correct
12 Correct 17 ms 19456 KB Output is correct
13 Correct 16 ms 19456 KB Output is correct
14 Correct 16 ms 19304 KB Output is correct
15 Correct 16 ms 19328 KB Output is correct
16 Correct 16 ms 19456 KB Output is correct
17 Correct 20 ms 19456 KB Output is correct
18 Correct 16 ms 19456 KB Output is correct
19 Correct 17 ms 19328 KB Output is correct
20 Correct 16 ms 19456 KB Output is correct
21 Correct 16 ms 19456 KB Output is correct
22 Correct 16 ms 19328 KB Output is correct
23 Correct 19 ms 20096 KB Output is correct
24 Correct 18 ms 20096 KB Output is correct
25 Correct 19 ms 20224 KB Output is correct
26 Correct 19 ms 20224 KB Output is correct
27 Correct 19 ms 20096 KB Output is correct
28 Correct 19 ms 20096 KB Output is correct
29 Correct 19 ms 20096 KB Output is correct
30 Correct 19 ms 20224 KB Output is correct
31 Correct 19 ms 20096 KB Output is correct
32 Correct 19 ms 20480 KB Output is correct
33 Correct 20 ms 20224 KB Output is correct
34 Correct 19 ms 20224 KB Output is correct
35 Correct 20 ms 20224 KB Output is correct
36 Correct 17 ms 19840 KB Output is correct
37 Correct 17 ms 19840 KB Output is correct
38 Correct 18 ms 20352 KB Output is correct
39 Correct 18 ms 20096 KB Output is correct
40 Correct 19 ms 20352 KB Output is correct
41 Correct 18 ms 19968 KB Output is correct
42 Correct 19 ms 20096 KB Output is correct
43 Correct 18 ms 20224 KB Output is correct
44 Correct 18 ms 19968 KB Output is correct

Subtask #3
65.0 / 65.0

# Verdict Execution time Memory Grader output
1 Correct 20 ms 19456 KB Output is correct
2 Correct 20 ms 19456 KB Output is correct
3 Correct 19 ms 19456 KB Output is correct
4 Correct 15 ms 19456 KB Output is correct
5 Correct 16 ms 19328 KB Output is correct
6 Correct 16 ms 19328 KB Output is correct
7 Correct 18 ms 19456 KB Output is correct
8 Correct 16 ms 19456 KB Output is correct
9 Correct 16 ms 19328 KB Output is correct
10 Correct 16 ms 19456 KB Output is correct
11 Correct 16 ms 19456 KB Output is correct
12 Correct 17 ms 19456 KB Output is correct
13 Correct 16 ms 19456 KB Output is correct
14 Correct 16 ms 19304 KB Output is correct
15 Correct 16 ms 19328 KB Output is correct
16 Correct 16 ms 19456 KB Output is correct
17 Correct 20 ms 19456 KB Output is correct
18 Correct 16 ms 19456 KB Output is correct
19 Correct 17 ms 19328 KB Output is correct
20 Correct 16 ms 19456 KB Output is correct
21 Correct 16 ms 19456 KB Output is correct
22 Correct 16 ms 19328 KB Output is correct
23 Correct 19 ms 20096 KB Output is correct
24 Correct 18 ms 20096 KB Output is correct
25 Correct 19 ms 20224 KB Output is correct
26 Correct 19 ms 20224 KB Output is correct
27 Correct 19 ms 20096 KB Output is correct
28 Correct 19 ms 20096 KB Output is correct
29 Correct 19 ms 20096 KB Output is correct
30 Correct 19 ms 20224 KB Output is correct
31 Correct 19 ms 20096 KB Output is correct
32 Correct 19 ms 20480 KB Output is correct
33 Correct 20 ms 20224 KB Output is correct
34 Correct 19 ms 20224 KB Output is correct
35 Correct 20 ms 20224 KB Output is correct
36 Correct 17 ms 19840 KB Output is correct
37 Correct 17 ms 19840 KB Output is correct
38 Correct 18 ms 20352 KB Output is correct
39 Correct 18 ms 20096 KB Output is correct
40 Correct 19 ms 20352 KB Output is correct
41 Correct 18 ms 19968 KB Output is correct
42 Correct 19 ms 20096 KB Output is correct
43 Correct 18 ms 20224 KB Output is correct
44 Correct 18 ms 19968 KB Output is correct
45 Correct 790 ms 112308 KB Output is correct
46 Correct 755 ms 111240 KB Output is correct
47 Correct 774 ms 110200 KB Output is correct
48 Correct 759 ms 112504 KB Output is correct
49 Correct 739 ms 109432 KB Output is correct
50 Correct 752 ms 109432 KB Output is correct
51 Correct 785 ms 109760 KB Output is correct
52 Correct 771 ms 111864 KB Output is correct
53 Correct 755 ms 111480 KB Output is correct
54 Correct 982 ms 124092 KB Output is correct
55 Correct 972 ms 118648 KB Output is correct
56 Correct 938 ms 115704 KB Output is correct
57 Correct 973 ms 113392 KB Output is correct
58 Correct 568 ms 80120 KB Output is correct
59 Correct 580 ms 79992 KB Output is correct
60 Correct 384 ms 131960 KB Output is correct
61 Correct 724 ms 101624 KB Output is correct
62 Correct 985 ms 117016 KB Output is correct
63 Correct 730 ms 96168 KB Output is correct
64 Correct 760 ms 98908 KB Output is correct
65 Correct 966 ms 117900 KB Output is correct
66 Correct 738 ms 95204 KB Output is correct