[bzoj5017][Snoi2017]炸弹 tarjan缩点+线段树优化建图+拓扑

  1 #include<iostream>
  2 #include<cstring>
  3 #include<cstdlib>
  4 #include<cmath>
  5 #include<cstdio>
  6 #include<algorithm>
  7 #define maxn 500005
  8 #define ll long long
  9 #define mod 1000000007
 10 using namespace std;
 11 inline ll read() {
 12     char ch=getchar();ll x=0,f=1;
 13     for(;!isdigit(ch);ch=getchar()) if(ch==‘-‘) f=-1;
 14     for(;isdigit(ch);ch=getchar()) x=x*10+ch-‘0‘;
 15     return x*f;
 16 }
 17 int n,rt;
 18 ll s[maxn*5],a[maxn*5],id[maxn*5],tsz;
 19 struct seg {int s[2];ll mn,mx;}t[maxn*5];
 20 struct Edge {int fr,to,nxt;}e[maxn*20];
 21 int head[maxn*5],sz;
 22 void addedge(int u,int v) {e[sz].fr=u;e[sz].nxt=head[u];e[sz].to=v;head[u]=sz++;}
 23 void build(int l,int r,int &x) {
 24     x=++tsz;
 25     if(l==r) {id[l]=x;t[x].mn=t[x].mx=l;return;}
 26     int mid=l+r>>1;
 27     build(l,mid,t[x].s[0]);build(mid+1,r,t[x].s[1]);
 28     if(t[x].s[0]) addedge(x,t[x].s[0]);
 29     if(t[x].s[1]) addedge(x,t[x].s[1]);
 30     t[x].mn=l;t[x].mx=r;
 31     return ;
 32 }
 33 void add(int l,int r,int x,int L,int R,int p) {
 34     if(L<=l&&R>=r) {if(id[p]==x) return;addedge(id[p],x);return;}
 35     int mid=l+r>>1;
 36     if(L<=mid) add(l,mid,t[x].s[0],L,R,p);
 37     if(R>mid) add(mid+1,r,t[x].s[1],L,R,p);
 38     return;
 39 }
 40 bool inq[maxn*5];
 41 ll dfn[maxn*5],low[maxn*5],tim,q[maxn*5],top,lm[maxn*5],rm[maxn*5];
 42 int bel[maxn*5],scc;
 43 void tarjan(int x) {
 44     dfn[x]=low[x]=++tim;q[++top]=x;inq[x]=1;
 45     for(int i=head[x];i>=0;i=e[i].nxt) {
 46         int to=e[i].to;
 47         if(!dfn[to]){
 48             tarjan(to);low[x]=min(low[x],low[to]);
 49         }else if(inq[to]) low[x]=min(low[x],dfn[to]);
 50     }
 51     if(dfn[x]==low[x]) {
 52         scc++;
 53         lm[scc]=214748364700000000ll;
 54         ll now;
 55         do {
 56             now=q[top--];inq[now]=0;bel[now]=scc;
 57             lm[scc]=min(lm[scc],t[now].mn);rm[scc]=max(rm[scc],t[now].mx);
 58         }while(now!=x);
 59     }
 60 }
 61 ll rd[maxn*5];
 62 int main() {
 63     //freopen("bomb9.in","r",stdin);
 64     memset(head,-1,sizeof(head));
 65     n=read();
 66     for(int i=1;i<=n;i++) {s[i]=read();a[i]=read();}
 67     build(1,n,rt);
 68     for(int i=1;i<=n;i++) {
 69         int now=lower_bound(s+1,s+n+1,s[i])-s,L=lower_bound(s+1,s+n+1,s[i]-a[i])-s,R=upper_bound(s+1,s+n+1,s[i]+a[i])-s-1;
 70         if(L==R) continue;add(1,n,1,L,R,i);
 71     }
 72     for(int i=1;i<=tsz;i++) if(!dfn[i]) {tarjan(i);}
 73     int tmp=sz;sz=0;memset(head,-1,sizeof(head));
 74     for(int i=0;i<tmp;i++) {
 75         int u=bel[e[i].fr],v=bel[e[i].to];
 76         if(u==v) continue;
 77         rd[v]++;addedge(u,v);
 78     }
 79     int hd=0,tl=0;
 80     for(int i=1;i<=scc;i++) if(!rd[i]) q[tl++]=i;
 81     while(hd!=tl) {
 82         int now=q[hd++];
 83         for(int i=head[now];i>=0;i=e[i].nxt) {
 84             int to=e[i].to;rd[to]--;
 85             if(!rd[to]) q[tl++]=to;
 86         }
 87     }
 88     for(int i=scc;i>=1;i--) {
 89         int now=q[i];
 90         for(int j=head[now];j>=0;j=e[j].nxt) {
 91             int to=e[j].to;
 92             lm[now]=min(lm[now],lm[to]);rm[now]=max(rm[now],rm[to]);
 93         }
 94     }
 95     ll ans=0;
 96     for(int i=1;i<=n;i++) {
 97         ans+=(ll)i*(rm[bel[id[i]]]-lm[bel[id[i]]]+1);ans%=mod;
 98     }
 99     printf("%lld\n",ans);
100 }
101