题目传送门:http://oi.cyo.ng/wp-content/uploads/2016/10/test3_problem.pdf
官方题解:http://oi.cyo.ng/wp-content/uploads/2016/10/solution.pdf
这题被挖出是大原题了:http://www.51nod.com/onlineJudge/questionCode.html#!problemId=1711
另外™鬼畜出题人硬生生把NOIP搞成NOI Professional有意思吗?
std也是二分,然后搞归并排序
不过我有一种更自然的方法,复杂度一样,常数较大:
首先求出前缀和,记为ai
二分最后的答案记为x
不难发现,平均值大于x的需要满足一下条件:\(\frac{{{a_i} – {a_j}}}{{i – j}} \le x\)
然后化简一下得到:\({a_i} – x \cdot i \le {a_j} – x \cdot j\)
换一句话来说,把ai-x*i作为新序列求逆序对的个数就好啦!
结果被卡常了…..
管他的,51nod上能过
#include<bits/stdc++.h> #define LL long long using namespace std; const int N = 100000+9; const double EPS = 0.00001; LL arr[N],k; double tmp[N]; int n,Rank[N]; inline int read(){ char c=getchar(); int ret=0,f=1; while (c<'0'||c>'9') {if(c=='-')f=-1;c=getchar();} while (c<='9'&&c>='0') {ret=ret*10+c-'0';c=getchar();} return ret*f; } namespace Fenwick_Tree{ #define BIT Fenwick_Tree #define lowbit(x) ((x)&-(x)) int cnt[N],tot,lim; inline void init(int w){ memset(cnt,0,sizeof(cnt)); tot = 1; lim = n+1; for (int i=w;i<=lim;i+=lowbit(i)) { cnt[i]++; } } inline int query(int sta) { int ret = 0; for (int i=sta;i;i-=lowbit(i)) { ret += cnt[i]; } return tot - ret; } inline void insert(int w) { tot++; for (int i=w;i<=lim;i+=lowbit(i)) { cnt[i]++; } } }; bool judge(double sta) { for (register int i=1;i<=n;++i) { tmp[i] = arr[i] - sta*i; } tmp[n+1] = 0; sort(tmp+1,tmp+1+n+1); for (register int i=0;i<=n;++i) { Rank[i] = lower_bound(tmp+1,tmp+1+n+1,arr[i]-sta*i) - tmp; } LL ret = 0; BIT::init(Rank[0]); for (int i=1;i<=n;i++) { ret += BIT::query(Rank[i]); BIT::insert(Rank[i]); } return ret >= k; } int main(){ n = read(); cin>>k; k = (LL)n*(n+1) / 2 - k + 1; for (int i=1;i<=n;i++) { arr[i] = arr[i-1] + read(); } double L = 0, R = 1e9, mid; while (R - L > EPS) { mid = (L + R) / 2; if (judge(mid)) { R = mid; } else { L = mid; } } printf("%.4lf",(R+L)/2); return 0; }
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