[CF1500A] Going Home

[CF1500A] Going Home

Description

给定长度为 (n) 的序列 (a)，求出任意一组 (x,y,z,w) 满足：

1. (x,y,z,w) 互不相同；
2. (a_x+a_y=a_z+a_w)；

如果有解，输出一行 YES 后输出任意一组解；否则输出一行 NO。

(4leq nleq 2 imes10^5;1leq a_ileq 2.5 imes10^6;)

Solution

这是一个过于复杂的做法

无非四种形式，AAAA,AABB,AABC,ABCD

对前三种，随便暴力即可

对第四种，根号分治一下，对稀疏情况枚举数字，对稠密情况枚举差

---

正经做法是，直接暴力 (O(n^2)) 枚举，记录每一对的 sum，遇到相同的直接退出，根据鸽巢原理，显然只要 (O(n)) 次后就一定会撞到一样的

#include <bits/stdc++.h>
using namespace std;

#define int long long

const int N = 2500005;
int n, a[N];

struct pii
{
    int first;
    int second;
    bool operator<(const pii &b) const
    {
        return first < b.first;
    }
    bool operator==(const pii &b) const
    {
        return first == b.first;
    }
};
pii aa[N];

signed main()
{
    ios::sync_with_stdio(false);
    cin >> n;
    for (int i = 1; i <= n; i++)
        cin >> a[i];

    map<int, int> mp;
    for (int i = 1; i <= n; i++)
        mp[a[i]]++;
    vector<int> v4, v2;
    for (auto [x, y] : mp)
    {
        if (y >= 4)
            v4.push_back(x);
        if (y >= 2)
            v2.push_back(x);
    }
    if (v4.size())
    {
        int val = v4[0];
        vector<int> ans;
        for (int i = 1; i <= n; i++)
            if (a[i] == val)
                ans.push_back(i);
        cout << "YES" << endl;
        cout << ans[0] << " " << ans[1] << " " << ans[2] << " " << ans[3] << endl;
    }
    else if (v2.size() >= 2)
    {
        vector<int> ans1, ans2;
        {
            int val = v2[0];
            for (int i = 1; i <= n; i++)
                if (a[i] == val)
                    ans1.push_back(i);
        }
        {
            int val = v2[1];
            for (int i = 1; i <= n; i++)
                if (a[i] == val)
                    ans2.push_back(i);
        }
        cout << "YES" << endl;
        cout << ans1[0] << " " << ans2[0] << " " << ans1[1] << " " << ans2[1] << endl;
    }
    else
    {

        int flag = 0, vp = 0, vq = 0;
        if (v2.size())
        {
            int val = v2[0];
            set<int> s;
            for (int i = 1; i <= n; i++)
                if (a[i] != val)
                    s.insert(a[i]);
            for (int i = 1; i <= n; i++)
                if (a[i] != val)
                {
                    if (s.find(2 * val - a[i]) != s.end())
                    {
                        flag = 1;
                        vp = val;
                        vq = a[i];
                    }
                }
        }
        if (flag == 1)
        {
            vector<int> ans;
            {
                int val = v2[0];
                for (int i = 1; i <= n; i++)
                    if (a[i] == val)
                        ans.push_back(i);
            }
            ans.resize(2);
            for (int i = 1; i <= n; i++)
                if (a[i] == vq)
                    ans.push_back(i);
            for (int i = 1; i <= n; i++)
                if (a[i] == 2 * vp - vq)
                    ans.push_back(i);
            cout << "YES" << endl;
            cout << ans[0] << " " << ans[1] << " " << ans[2] << " " << ans[3] << endl;
        }
        else
        {
            for (int i = 1; i <= n; i++)
                aa[i] = {a[i], i};

            sort(aa + 1, aa + n + 1);
            n = unique(aa + 1, aa + n + 1) - aa - 1;
            for (int i = 1; i <= n; i++)
                a[i] = aa[i].first;
            if (n < 20000)
            {
                vector<int> b(N * 2);
                for (int i = 1; i <= n; i++)
                    for (int j = 1; j < i; j++)
                        b[a[i] + a[j]]++;
                if (*max_element(b.begin(), b.end()) > 1)
                {
                    int tmp = max_element(b.begin(), b.end()) - b.begin();
                    vector<int> ans;
                    for (int i = 1; i <= n; i++)
                        for (int j = 1; j < i; j++)
                            if (a[i] + a[j] == tmp)
                                ans.push_back(i), ans.push_back(j);
                    cout << "YES" << endl;
                    cout << aa[ans[0]].second << " " << aa[ans[1]].second << " " << aa[ans[2]].second << " " << aa[ans[3]].second << endl;
                }
                else
                {
                    cout << "NO" << endl;
                }
            }
            else
            {

                vector<int> b(N * 2);
                for (int i = 1; i <= n; i++)
                    b[a[i]] = i;
                for (int d = 1; d <= 130; d++)
                {
                    int a00 = 0, a01 = 0, a10 = 0, a11 = 0;
                    for (int i = 1; i < N; i++)
                        if (b[i] && b[i + d])
                        {
                            if (a00 == 0)
                            {
                                a00 = b[i];
                                a01 = b[i + d];
                            }
                            else
                            {
                                if (a00 != b[i] && a00 != b[i + d] && a01 != b[i] && a01 != b[i + d])
                                {
                                    a10 = b[i];
                                    a11 = b[i + d];
                                    break;
                                }
                            }
                        }

                    if (a10)
                    {
                        cout << "YES" << endl;
                        cout << aa[a00].second << " " << aa[a11].second << " " << aa[a01].second << " " << aa[a10].second << endl;
                        return 0;
                    }

                    // if (vec.size() > 1)
                    // {
                    //     cout << "YES" << endl;

                    //     cout << aa[vec[0].first].second << " " << aa[vec[1].second].second << " " << aa[vec[1].first].second << " " << aa[vec[0].second].second << endl;
                    //     return 0;
                    // }
                }
                cout << "NO" << endl;
            }
        }
    }
}