Laying Cables （单调栈）

One-dimensional country has n cities, the i-th of which is located at the point xi and has population pi, and all xi, as well as all pi, are distinct. When one-dimensional country got the Internet, it was decided to place the main server in the largest city, and to connect any other city j to the city k that has bigger population than j and is the closest to it (if there are many such cities, the largest one should be chosen). City k is called a parent of city j in this case.

Unfortunately, the Ministry of Communications got stuck in determining from where and to where the Internet cables should be laid, and the population of the country is suffering. So you should solve the problem. For every city, find its parent city.

Input
The first line contains a single integer n (1 ≤ n ≤ 200000) — the number of cities.

Each of the next n lines contains two space-separated integers xi and pi (1 ≤ xi,  pi ≤ 109) — the coordinate and the population of the i-th city.

Output
Output n space-separated integers. The i-th number should be the parent of the i-th city, or  - 1, if the i-th city doesn’t have a parent. The cities are numbered from 1 by their order in the input.

Examples
Input
4
1 1000
7 10
9 1
12 100
Output
-1 4 2 1
Input
3
1 100
2 1
3 10
Output
-1 1 1
Input
3
1 10
3 100
2 1
Output
2 -1 2

#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 10;
struct node {
    int x, sum, id;
} s[N];
int cmp(node a, node b) { return a.x < b.x; }
int n, ans[N];
node a[N];
int main() {
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) {
        scanf("%d%d", &s[i].x, &s[i].sum);
        s[i].id = i;
    }
    sort(s + 1, s + 1 + n, cmp);
    int cnt = 0;
    for (int i = 1; i <= n; i++) {
        if (cnt == 0)
            a[++cnt] = s[i];
        else {
            while (s[i].sum > a[cnt].sum && cnt >= 1) {
                if (cnt == 1)
                    ans[a[cnt].id] = s[i].id;
                else {
                    if (a[cnt].x - a[cnt - 1].x == s[i].x - a[cnt].x) {
                        if (a[cnt - 1].sum > s[i].sum)
                            ans[a[cnt].id] = a[cnt - 1].id;
                        else
                            ans[a[cnt].id] = s[i].id;
                    } else if (a[cnt].x - a[cnt - 1].x < s[i].x - a[cnt].x) {
                        ans[a[cnt].id] = a[cnt - 1].id;
                    } else
                        ans[a[cnt].id] = s[i].id;
                }
                cnt--;
            }
            a[++cnt] = s[i];
        }
    }
    for (int i = cnt; i >= 2; i--) {
        ans[a[i].id] = a[i - 1].id;
    }
    ans[a[1].id] = -1;
    for (int i = 1; i <= n; i++) {
        if (i == n)
            printf("%d\n", ans[i]);
        else
            printf("%d ", ans[i]);
    }
}