Gym 100960G （set+树状数组）

Posted 2020-08-05 rpSebastian

Problem Youngling Tournament

题目大意

　　给一个序列a[i]，每次操作可以更改一个数，每次询问 将序列排序后有多少个数a[i]>=sum[i-1]。

　　n<=10^5,q<=5*10^4，a[i]<=10^12

解题分析

　　可以发现，在最优情况下，该序列长度最多为logn。

　　将询问离线后，用multiset来维护a[i],用树状数组来维护sum[i]。树状数组所存下标为离散化后的a[i]。

　　每次查询时跳跃式地在set中查找。

　　时间复杂度 O((n+m)log(n+m)+mlognlogn)

参考程序

  1 #include <map>
  2 #include <set>
  3 #include <stack>
  4 #include <queue>
  5 #include <cmath>
  6 #include <ctime>
  7 #include <string>
  8 #include <vector>
  9 #include <cstdio>
 10 #include <cstdlib>
 11 #include <cstring>
 12 #include <cassert>
 13 #include <iostream>
 14 #include <algorithm>
 15 #pragma comment(linker,"/STACK:102400000,102400000")
 16 using namespace std;
 17 
 18 #define N 100008             
 19 #define M 50008    
 20 #define LL long long
 21 #define lson l,m,rt<<1
 22 #define rson m+1,r,rt<<1|1 
 23 #define clr(x,v) memset(x,v,sizeof(x));
 24 #define bitcnt(x) __builtin_popcount(x)
 25 #define rep(x,y,z) for (int x=y;x<=z;x++)
 26 #define repd(x,y,z) for (int x=y;x>=z;x--)
 27 const int mo  = 1000000007;
 28 const int inf = 0x3f3f3f3f;
 29 const int INF = 2000000000;
 30 /**************************************************************************/ 
 31 
 32 int n,m,tot,flag;
 33 LL a[N],c[N],x[N*2];
 34 int b[N];
 35 multiset<long long> S;
 36 struct Binary_Indexed_Tree{
 37     LL a[N*3];
 38     void clear(){
 39         clr(a,0);
 40     }
 41     void insert(int x,LL val){
 42         for (int i=x;i<=N<<1;i+=i & (-i))
 43             a[i]+=val;
 44     }
 45     LL sigma(int x){
 46         LL res=0;
 47         for (int i=x;i>0;i-=i & (-i))
 48             res+=a[i];
 49         return res;
 50     }
 51     LL query(int x,int y){
 52         return sigma(y)-sigma(x-1);
 53     }
 54 }T;
 55 int id(LL xy){
 56     return lower_bound(x+1,x+tot+1,xy)-x;
 57 }
 58 set <long long> :: iterator it,it1;
 59 void query(){
 60     int ans=1; LL tmp;
 61     it = S.begin(); 
 62     it1 = it ; it1++; 
 63     if (*it==*it1) ans++;
 64     tmp=T.sigma(id(*it));
 65     while (1){
 66         it = S.lower_bound(tmp);
 67         if (it==S.begin()) it++;
 68         if (it==S.end()) break;
 69         it1 = it; it1--;
 70         tmp=T.sigma(id(*it1));
 71         if (*it>=tmp) ans++;
 72         tmp=T.sigma(id(*it));
 73     }
 74     printf("%d\\n",ans);
 75 
 76 }
 77 
 78 int main(){
 79     scanf("%d",&n);
 80     rep(i,1,n){
 81         scanf("%lld",&a[i]);
 82         x[++tot]=a[i];
 83     }
 84     scanf("%d",&m);
 85     rep(i,1,m){
 86         scanf("%d%lld",&b[i],&c[i]);
 87         x[++tot]=c[i];
 88     }
 89     sort(x+1,x+tot+1);
 90     tot=unique(x+1,x+tot+1)-x;
 91     T.clear();
 92     rep(i,1,n){
 93         T.insert(id(a[i]),a[i]);
 94         S.insert(a[i]);
 95     }
 96     query();
 97     rep(i,1,m){
 98         S.erase(S.find(a[b[i]]));
 99         T.insert(id(a[b[i]]),-a[b[i]]);
100         S.insert(c[i]);
101         T.insert(id(c[i]),c[i]);
102         a[b[i]]=c[i];
103         query();
104     }
105 
106 }

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