题解 计蒜客题
签到题
建出来笛卡尔树
一个子树是原序列上的一个区间,所以可以预处理出 ST 表
然后二分一下两个子树中最小值 \(>x-a_u\) 和 \(\geqslant x-a_u\) 的位置就好了
复杂度 \(O(n\log n)\),听说也有 \(O(n)\) 做法
点击查看代码
#include <bits/stdc++.h>
using namespace std;
#define INF 0x3f3f3f3f
#define N 1000010
#define fir first
#define sec second
#define ll long long
//#define int long long
char buf[1<<21], *p1=buf, *p2=buf;
#define getchar() (p1==p2&&(p2=(p1=buf)+fread(buf, 1, 1<<21, stdin)), p1==p2?EOF:*p1++)
inline int read() {
int ans=0, f=1; char c=getchar();
while (!isdigit(c)) {if (c=='-') f=-f; c=getchar();}
while (isdigit(c)) {ans=(ans<<3)+(ans<<1)+(c^48); c=getchar();}
return ans*f;
}
int n, x;
int a[N];
// namespace force{
// ll ans;
// int st1[22][N], st2[22][N], lg[N];
// inline int qmin(int l, int r) {
// int t=lg[r-l+1]-1;
// return min(st1[t][l], st1[t][r-(1<<t)+1]);
// }
// inline int qmax(int l, int r) {
// int t=lg[r-l+1]-1;
// return max(st2[t][l], st2[t][r-(1<<t)+1]);
// }
// void solve() {
// for (int i=1; i<=n; ++i) lg[i]=lg[i-1]+(1<<lg[i-1]==i);
// for (int i=1; i<=n; ++i) st1[0][i]=a[i];
// int t=lg[n]-1;
// for (int i=1; i<=t; ++i)
// for (int j=1; j+(1<<i)-1<=n; ++j)
// st1[i][j]=min(st1[i-1][j], st1[i-1][j+(1<<i-1)]);
// for (int i=1; i<=n; ++i) st2[0][i]=a[i];
// for (int i=1; i<=t; ++i)
// for (int j=1; j+(1<<i)-1<=n; ++j)
// st2[i][j]=max(st2[i-1][j], st2[i-1][j+(1<<i-1)]);
// for (int l=1; l<=n; ++l)
// for (int r=l; r<=n; ++r)
// if (qmax(l, r)+qmin(l, r)==x)
// ++ans;
// printf("%lld\n", ans);
// }
// }
namespace task1{
ll ans;
pair<int, int> sta[N];
int ls[N], rs[N], st[22][N], lg[N], siz[N], top;
inline int qmin(int l, int r) {
int t=lg[r-l+1]-1;
return min(st[t][l], st[t][r-(1<<t)+1]);
}
void dfs(int u) {
siz[u]=1;
if (ls[u]) dfs(ls[u]), siz[u]+=siz[ls[u]];
if (rs[u]) dfs(rs[u]), siz[u]+=siz[rs[u]];
int l, r, mid;
int l_l, l_r, r_l, r_r;
// cout<<"calc: "<<u<<endl;
l=u+1, r=u+siz[rs[u]];
while (l<=r) {
mid=(l+r)>>1;
if (qmin(u, mid)>x-a[u]) l=mid+1;
else r=mid-1;
}
r_l=l-1;
l=u+1, r=u+siz[rs[u]];
while (l<=r) {
mid=(l+r)>>1;
if (qmin(u, mid)>=x-a[u]) l=mid+1;
else r=mid-1;
}
r_r=l-1;
l=u-siz[ls[u]], r=u-1;
while (l<=r) {
mid=(l+r)>>1;
if (qmin(mid, u)>=x-a[u]) r=mid-1;
else l=mid+1;
}
l_l=r+1;
l=u-siz[ls[u]], r=u-1;
while (l<=r) {
mid=(l+r)>>1;
if (qmin(mid, u)>x-a[u]) r=mid-1;
else l=mid+1;
}
l_r=r+1;
// cout<<"range: "<<l_l<<' '<<l_r<<' '<<r_l<<' '<<r_r<<endl;
if (x-a[u]<=0) {/* cout<<"case1"<<endl; */ return ;}
else if (x-a[u]==a[u]) ans+=1ll*(u-l_l+1)*(r_r-u+1); //, cout<<"case2"<<endl;
else ans+=1ll*(u-l_l+1)*(r_r-u+1)-1ll*(u-l_r+1)*(r_l-u+1); //, cout<<"case3"<<endl;
}
void solve() {
for (int i=1; i<=n; ++i) lg[i]=lg[i-1]+(1<<lg[i-1]==i);
for (int i=1; i<=n; ++i) st[0][i]=a[i];
int t=lg[n]-1;
for (int i=1; i<=t; ++i)
for (int j=1; j+(1<<i)-1<=n; ++j)
st[i][j]=min(st[i-1][j], st[i-1][j+(1<<i-1)]);
for (int i=1; i<=n; ++i) {
pair<int, int> t={a[i], i};
int k=top;
while (k && sta[k].fir<t.fir) --k;
if (k!=top) ls[t.sec]=sta[k+1].sec;
if (k) rs[sta[k].sec]=t.sec;
sta[top=++k]=t;
}
// cout<<"ls: "; for (int i=1; i<=n; ++i) cout<<ls[i]<<' '; cout<<endl;
// cout<<"rs: "; for (int i=1; i<=n; ++i) cout<<rs[i]<<' '; cout<<endl;
dfs(sta[1].sec);
printf("%lld\n", ans);
}
}
signed main()
{
freopen("garlic.in", "r", stdin);
freopen("garlic.out", "w", stdout);
n=read(); x=read();
for (int i=1; i<=n; ++i) a[i]=read();
// force::solve();
task1::solve();
return 0;
}