AtCoder ABC 127F Absolute Minima

题目链接：https://atcoder.jp/contests/abc127/tasks/abc127_f

题目大意

　　初始状态下$f(x) = 0$，现在有 2 种模式的询问，第一种以“1 a b”的形式，需要进行操作$f(x) = f(x) + |x - a| + b$；第二种以“2”的形式，求使得 f(x) 取得最小值的 x 取值和 f(x) 值，如果有多个 x，输出任意一个即可。

分析

　　考虑第一种询问已经出现了 k 次，现在遇到第二种询问。此时$f(x) = sum_{i = 1}^k (|x - a_i| + b_i)$，可以发现$b_i$完全是独立于 x 的，所以只要讨论$sum_{i = 1}^k |x - a_i|$的最小值即可。

　　于是问题就退化成在数轴上找一个点，使得它到给定的 k 个点的距离之和最短。

　　当点个数为奇数，最优解是中位数。 
　　当点个数为偶数，最优解是位于中间的两个数中任取一个。

　　所以这个问题的本质就是让你动态找中位数，维护中位数可以用双堆。

代码如下

#include <bits/stdc++.h>
using namespace std;
 
#define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define Rep(i,n) for (int i = 0; i < (n); ++i)
#define For(i,s,t) for (int i = (s); i <= (t); ++i)
#define rFor(i,t,s) for (int i = (t); i >= (s); --i)
#define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)
#define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)
#define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)
#define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)
 
#define pr(x) cout << #x << " = " << x << "  "
#define prln(x) cout << #x << " = " << x << endl
 
#define LOWBIT(x) ((x)&(-x))
 
#define ALL(x) x.begin(),x.end()
#define INS(x) inserter(x,x.begin())
 
#define ms0(a) memset(a,0,sizeof(a))
#define msI(a) memset(a,inf,sizeof(a))
#define msM(a) memset(a,-1,sizeof(a))

#define MP make_pair
#define PB push_back
#define ft first
#define sd second
 
template<typename T1, typename T2>
istream &operator>>(istream &in, pair<T1, T2> &p) {
    in >> p.first >> p.second;
    return in;
}
 
template<typename T>
istream &operator>>(istream &in, vector<T> &v) {
    for (auto &x: v)
        in >> x;
    return in;
}
 
template<typename T1, typename T2>
ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
    out << "[" << p.first << ", " << p.second << "]" << "
";
    return out;
}

inline int gc(){
    static const int BUF = 1e7;
    static char buf[BUF], *bg = buf + BUF, *ed = bg;
    
    if(bg == ed) fread(bg = buf, 1, BUF, stdin);
    return *bg++;
} 

inline int ri(){
    int x = 0, f = 1, c = gc();
    for(; c<48||c>57; f = c=='-'?-1:f, c=gc());
    for(; c>47&&c<58; x = x*10 + c - 48, c=gc());
    return x*f;
}
 
typedef long long LL;
typedef unsigned long long uLL;
typedef pair< double, double > PDD;
typedef pair< int, int > PII;
typedef pair< string, int > PSI;
typedef set< int > SI;
typedef vector< int > VI;
typedef vector< PII > VPII;
typedef map< int, int > MII;
typedef pair< LL, LL > PLL;
typedef vector< LL > VL;
typedef vector< VL > VVL;
typedef priority_queue< int > PQIMax;
typedef priority_queue< int, VI, greater< int > > PQIMin;
const double EPS = 1e-10;
const LL inf = 0x7fffffff;
const LL infLL = 0x7fffffffffffffffLL;
const LL mod = 1e9 + 7;
const int maxN = 2e5 + 7;
const LL ONE = 1;
const LL evenBits = 0xaaaaaaaaaaaaaaaa;
const LL oddBits = 0x5555555555555555;


int Q;
PQIMax maxH;
PQIMin minH;
LL sumB, sumLA, sumRA, ans;

int main(){
    INIT(); 
    cin >> Q;
    while(Q--) {
        int x, a, b;
        cin >> x;
        if(x == 1) {
            cin >> a >> b;
            sumB += b;
            if(maxH.size() == minH.size()) {
                if(maxH.empty()) {
                    maxH.push(a);
                    sumLA += a;
                }
                else if(a >= maxH.top()) {
                    minH.push(a);
                    sumRA += a;
                }
                else {
                    maxH.push(a);
                    sumLA += a;
                }
            }
            else if(maxH.size() > minH.size()) {
                if(a >= maxH.top()) {
                    minH.push(a);
                    sumRA += a;
                }
                else {
                    maxH.push(a);
                    sumLA += a;
                    sumLA -= maxH.top();
                    minH.push(maxH.top());
                    sumRA += maxH.top();
                    maxH.pop();
                }
            }
            else {
                if(a < minH.top()) {
                    maxH.push(a);
                    sumLA += a;
                }
                else {
                    minH.push(a);
                    sumRA += a;
                    sumRA -= minH.top();
                    maxH.push(minH.top());
                    sumLA += minH.top();
                    minH.pop();
                }
            }
        }
        else {
            int x = maxH.top();
            ans = sumRA - sumLA + sumB;
            if(maxH.size() > minH.size()) ans += maxH.top();
            else if(maxH.size() < minH.size()) {
                ans -= minH.top();
                x = minH.top();
            }
            cout << x << " " << ans << endl;
        }
    }
    return 0;
}