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 << "]" << "\n";
     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, , BUF, stdin);
     return *bg++;
 } 
 
 inline int ri(){
     int x = , f = , c = gc();
     for(; c<||c>; f = c=='-'?-:f, c=gc());
     for(; c>&&c<; x = x* + c - , 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-;
 const LL inf = 0x7fffffff;
 const LL infLL = 0x7fffffffffffffffLL;
 const LL mod = 1e9 + ;
 const int maxN = 2e5 + ;
 const LL ONE = ;
 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 == ) {
             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 ;
 }