1857E. Power of Points · znzryb

## 思路讲解

题目说了一堆花里胡哨的，其实意思很简单，就是把你这个点，和所有点（包括你这个点）组成的线段的长度总和就是答案。

那么想要知道这个，我就想到了前缀和。但前缀和的话短的-长的是负值怎么办？可以对前缀和进行分段，具体的，其实就是这段代码。

```cpp
	for(int i=1;i<=N;++i){
		ll idx=upper_bound(X+1,X+1+N,(arr){X[i][0],INF,INF})-X;
		ll lsum=sum[idx-1],rsum=sum[N]-sum[idx-1];
		X[i][2]=(X[i][0]+1)*(idx-1)-lsum+rsum+N-idx+1-X[i][0]*(N-idx+1);
	}
```

## AC代码

[https://codeforces.com/problemset/submission/1857/309735803](https://codeforces.com/problemset/submission/1857/309735803)

```cpp
// Problem: E. Power of Points
// Contest: Codeforces - Codeforces Round 891 (Div. 3)
// URL: https://codeforces.com/problemset/problem/1857/E
// Memory Limit: 256 MB
// Time Limit: 2000 ms
// by znzryb
// 
// Powered by CP Editor (https://cpeditor.org)

#include <bits/stdc++.h>
#define FOR(i, a, b) for (long long i = (a); i <= (b); ++i)
#define ROF(i, a, b) for (long long i = (a); i >= (b); --i)
#define all(x) x.begin(),x.end()
#define CLR(i,a) memset(i,a,sizeof(i))
#define fi first
#define se second
#define pb push_back
#define SZ(a) ((int) a.size())

using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll,ll> pll;
typedef array<ll,3> arr;
typedef double DB;
typedef pair<DB,DB> pdd;
constexpr ll MAXN=static_cast<ll>(2e5)+10,INF=static_cast<ll>(5e18)+3;

ll N,M,T;
arr X[MAXN];
ll	sum[MAXN];

inline bool cmpi(const arr &a,const arr &b){
	return a[1]<b[1];
}

inline void solve(){
	cin>>N;
	for(int i=1;i<=N;++i){
		cin>>X[i][0];
		X[i][1]=i;
	}
	sort(X+1,X+1+N);
	sum[0]=0;
	for(int i=1;i<=N;++i){
		sum[i]=X[i][0]+sum[i-1];
	}
	for(int i=1;i<=N;++i){
		ll idx=upper_bound(X+1,X+1+N,(arr){X[i][0],INF,INF})-X;
		ll lsum=sum[idx-1],rsum=sum[N]-sum[idx-1];
		X[i][2]=(X[i][0]+1)*(idx-1)-lsum+rsum+N-idx+1-X[i][0]*(N-idx+1);
	}
	// 输出答案阶段
	sort(X+1,X+1+N,cmpi);
	for(int i=1;i<=N;++i){
		cout<<X[i][2]<<" ";
	}
	cout<<"\n";
}

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(0);cout.tie(0);
	cin>>T;
	while(T--){
		solve();
	}
	return 0;
}
/*
AC
https://codeforces.com/problemset/submission/1857/309735803
*/
```

## 心路历程（WA，TLE，MLE……）