笛卡尔树模版
按第一关键字排序，然后按第二关键字构建笛卡尔树即可。
#include <bits/stdc++.h>
#define INF 0x3f3f3f3f
#define full(a, b) memset(a, b, sizeof a)
#define __fastIn ios::sync_with_stdio(false), cin.tie(0)
#define pb push_back
using namespace std;
typedef long long LL;
inline int lowbit(int x){ return x & (-x); }
inline int read(){
int ret = 0, w = 0; char ch = 0;
while(!isdigit(ch)){
w |= ch == '-', ch = getchar();
}
while(isdigit(ch)){
ret = (ret << 3) + (ret << 1) + (ch ^ 48);
ch = getchar();
}
return w ? -ret : ret;
}
template <typename A>
inline A __lcm(A a, A b){ return a / __gcd(a, b) * b; }
template <typename A, typename B, typename C>
inline A fpow(A x, B p, C lyd){
A ans = 1;
for(; p; p >>= 1, x = 1LL * x * x % lyd)if(p & 1)ans = 1LL * x * ans % lyd;
return ans;
}
const int N = 60000;
int n, x, y;
vector< pair<pair<int, int>, int> > v;
struct Node{
int i, val;
Node *fa, *lf, *rf;
Node(){}
Node(int i, int val, Node *fa, Node *lf, Node *rf): i(i), val(val), fa(fa), lf(fa), rf(rf){}
}*null, *root;
bool cmp(Node *a, Node *b){ return a->i < b->i; }
Node *buildTree(){
stack<Node *> st;
Node *last = null;
for(int i = 0; i < v.size(); i ++){
Node *cur = new Node(v[i].second, v[i].first.second, null, null, null);
while(!st.empty()){
if(st.top()->val < cur->val){
Node *up = st.top();
if(up->rf != null) cur->lf = up->rf, up->rf->fa = cur;
up->rf = cur, cur->fa = up;
break;
}
last = st.top(), st.pop();
}
if(st.empty() && last) cur->lf = last, last->fa = cur;
st.push(cur);
}
Node *root = null;
while(!st.empty()) root = st.top(), st.pop();
return root;
}
vector<Node *> ans;
void dfs(Node *cur){
if(cur == null) return;
ans.pb(cur);
dfs(cur->lf), dfs(cur->rf);
}
int main(){
n = read();
for(int i = 0; i < n; i ++){
x = read(), y = read();
v.pb(make_pair(make_pair(x, y), i + 1));
}
sort(v.begin(), v.end());
null = new Node(0, 0, NULL, NULL, NULL);
root = buildTree();
dfs(root);
sort(ans.begin(), ans.end(), cmp);
puts("YES");
for(int i = 0; i < ans.size(); i ++){
printf("%d %d %d\n", ans[i]->fa->i, ans[i]->lf->i, ans[i]->rf->i);
}
return 0;
}