Educational Codeforces Round 7 D. Optimal Number Permutation（構造）

題意:

N≤5×105,有1∼N各出現2次的序列

如果數i在xi,yi位置,設di=yi−xi

試構造一個序列使得s=∑i=1n(n−i)⋅|di+i−n|最小

分析:

我們發現i=n的貢獻一定是0,也就是說2個n可以随意放

其實可以發現一定可以構造出s=0的序列

奇數n=5：13X31   2442,缺個X填n就好了

偶數n=6:24X42    135531,缺個X填n就好了

其實規律一樣的,不用分開,賽上寫的急,而且也不用算n的位置,直接填到沒填的地方就可以了。。。

代碼:

//
//  Created by TaoSama on 2016-02-11
//  Copyright (c) 2016 TaoSama. All rights reserved.
//
#pragma comment(linker, "/STACK:1024000000,1024000000")
#include <algorithm>
#include <cctype>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <string>
#include <set>
#include <vector>

using namespace std;
#define pr(x) cout << #x << " = " << x << "  "
#define prln(x) cout << #x << " = " << x << endl
const int N =  + , INF = , MOD =  + ;

int n, a[N];

int main() {
#ifdef LOCAL
    freopen("C:\\Users\\TaoSama\\Desktop\\in.txt", "r", stdin);
//  freopen("C:\\Users\\TaoSama\\Desktop\\out.txt","w",stdout);
#endif
    ios_base::sync_with_stdio();

    while(scanf("%d", &n) == ) {
        int i, j;
        if(n & ) {
            for(i = , j = ; j < n; ++i, j += )
                a[i] = a[i + n - j] = j;
            a[i] = a[i + n /  + ] = n;
            for(i = n + , j = ; j < n; ++i, j += )
                a[i] = a[i + n - j] = j;
        } else {
            for(i = , j = ; j < n; ++i, j += )
                a[i] = a[i + n - j] = j;
            a[i] = a[i + n / ] = n;
            for(i = n + , j = ; j < n; ++i, j += )
                a[i] = a[i + n - j] = j;
        }
        for(int i = ; i <= n << ; ++i)
            printf("%d%c", a[i], " \n"[i == (n << )]);
    }
    return ;
}