CHFMIST-Editorial

Setter: Akash Sharma
Tester: Aryan, Satyam
Editorialist: Devendra Singh

NA

PREREQUISITES:

Mean of N values : \displaystyle\frac{Sum\: of\: all\: values}{N}

PROBLEM:

Akash goes to class everyday. His classes are held on the 9^{th} floor so he uses a lift. One day N people get on the lift. However, since the lift can carry at most N-2 people, 2 of them need to get off.

Given an array A of the weights of the N people, help Akash find the number of pairs of people such that the mean of weights of the N-2 people remaining in the lift excluding them is the same as the mean of weights of all the N people who were initially in the lift.

EXPLANATION:

Let sum denote the sum of weights of N people. Then the mean of these weights is \displaystyle\frac{sum}{N}. Let x be the sum of weights of the pair of people removed such that the mean of the weights of N-2 people is still same. Then by the definition of mean (sum-x)/(N-2)=sum/N \\x=sum-\displaystyle\frac{sum*(N-2)}{N}
x=\displaystyle\frac{2*sum}{N}
This problem is reduced to finding the number of pairs of people such that the sum of their weights is \displaystyle\frac{2*sum}{N}. This can easily be done using a Map.

TIME COMPLEXITY:

O(Nlog(N)) for each test case.

SOLUTION:

Setter's Solution
#include <bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
#define debug(x) cerr<<#x<<" "; _print(x); cerr<<nline;
#else
#define debug(x);
#endif

/*
------------------------Input Checker----------------------------------
*/

long long readInt(long long l,long long r,char endd){
long long x=0;
int cnt=0;
int fi=-1;
bool is_neg=false;
while(true){
char g=getchar();
if(g=='-'){
assert(fi==-1);
is_neg=true;
continue;
}
if('0'<=g && g<='9'){
x*=10;
x+=g-'0';
if(cnt==0){
fi=g-'0';
}
cnt++;
assert(fi!=0 || cnt==1);
assert(fi!=0 || is_neg==false);

assert(!(cnt>19 || ( cnt==19 && fi>1) ));
} else if(g==endd){
if(is_neg){
x= -x;
}

if(!(l <= x && x <= r))
{
cerr << l << ' ' << r << ' ' << x << '\n';
assert(1 == 0);
}

return x;
} else {
assert(false);
}
}
}
string readString(int l,int r,char endd){
string ret="";
int cnt=0;
while(true){
char g=getchar();
assert(g!=-1);
if(g==endd){
break;
}
cnt++;
ret+=g;
}
assert(l<=cnt && cnt<=r);
return ret;
}
long long readIntSp(long long l,long long r){
}
long long readIntLn(long long l,long long r){
}
string readStringLn(int l,int r){
}
string readStringSp(int l,int r){
}

/*
------------------------Main code starts here----------------------------------
*/
int MAX=100000;
int tes_sum=0;
void solve(){
long long sum=0,x;
tes_sum+=n;
vector<long long> a;
for(int i=1;i<n;i++){
a.push_back(x);
sum+=x;
}
a.push_back(x); sum+=x;
long long g=__gcd(sum,n);
sum/=g; n/=g;
if(n>2){
cout<<"0\n";
return;
}
long long target=(2*sum)/n;
map<long long,long long> freq;
long long ans=0;
for(auto it:a){
ans+=freq[target-it];
freq[it]++;
}
cout<<ans<<"\n";
return;
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
#ifndef ONLINE_JUDGE
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
freopen("error.txt", "w", stderr);
#endif
while(test_cases--){
solve();
}
assert(getchar()==-1);
assert(tes_sum<=200000);
return 0;
}


Tester-1's Solution
/* in the name of Anton */

/*
Compete against Yourself.
Author - Aryan (@aryanc403)
Atcoder library - https://atcoder.github.io/ac-library/production/document_en/
*/

#ifdef ARYANC403
#else
#pragma GCC optimize ("Ofast")
#pragma GCC target ("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
//#pragma GCC optimize ("-ffloat-store")
#include<bits/stdc++.h>
#define dbg(args...) 42;
#endif

// y_combinator from @neal template https://codeforces.com/contest/1553/submission/123849801
// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2016/p0200r0.html
template<class Fun> class y_combinator_result {
Fun fun_;
public:
template<class T> explicit y_combinator_result(T &&fun): fun_(std::forward<T>(fun)) {}
template<class ...Args> decltype(auto) operator()(Args &&...args) { return fun_(std::ref(*this), std::forward<Args>(args)...); }
};
template<class Fun> decltype(auto) y_combinator(Fun &&fun) { return y_combinator_result<std::decay_t<Fun>>(std::forward<Fun>(fun)); }

using namespace std;
#define fo(i,n)   for(i=0;i<(n);++i)
#define repA(i,j,n)   for(i=(j);i<=(n);++i)
#define repD(i,j,n)   for(i=(j);i>=(n);--i)
#define all(x) begin(x), end(x)
#define sz(x) ((lli)(x).size())
#define pb push_back
#define mp make_pair
#define X first
#define Y second
#define endl "\n"

typedef long long int lli;
typedef long double mytype;
typedef pair<lli,lli> ii;
typedef vector<ii> vii;
typedef vector<lli> vi;

const auto start_time = std::chrono::high_resolution_clock::now();
void aryanc403()
{
#ifdef ARYANC403
auto end_time = std::chrono::high_resolution_clock::now();
std::chrono::duration<double> diff = end_time-start_time;
cerr<<"Time Taken : "<<diff.count()<<"\n";
#endif
}

long long readInt(long long l, long long r, char endd) {
long long x=0;
int cnt=0;
int fi=-1;
bool is_neg=false;
while(true) {
char g=getchar();
if(g=='-') {
assert(fi==-1);
is_neg=true;
continue;
}
if('0'<=g&&g<='9') {
x*=10;
x+=g-'0';
if(cnt==0) {
fi=g-'0';
}
cnt++;
assert(fi!=0 || cnt==1);
assert(fi!=0 || is_neg==false);

assert(!(cnt>19 || ( cnt==19 && fi>1) ));
} else if(g==endd) {
if(is_neg) {
x=-x;
}
assert(l<=x&&x<=r);
return x;
} else {
assert(false);
}
}
}
string readString(int l, int r, char endd) {
string ret="";
int cnt=0;
while(true) {
char g=getchar();
assert(g!=-1);
if(g==endd) {
break;
}
cnt++;
ret+=g;
}
assert(l<=cnt&&cnt<=r);
return ret;
}
long long readIntSp(long long l, long long r) {
}
long long readIntLn(long long l, long long r) {
}
string readStringLn(int l, int r) {
}
string readStringSp(int l, int r) {
}

assert(getchar()==EOF);
}

vi readVectorInt(int n,lli l,lli r){
vi a(n);
for(int i=0;i<n-1;++i)
return a;
}

bool isBinaryString(const string s){
for(auto x:s){
if('0'<=x&&x<='1')
continue;
return false;
}
return true;
}

// #include<atcoder/dsu>
// vector<vi> readTree(const int n){
//     vector<vi> e(n);
//     atcoder::dsu d(n);
//     for(lli i=1;i<n;++i){
//         const lli u=readIntSp(1,n)-1;
//         const lli v=readIntLn(1,n)-1;
//         e[u].pb(v);
//         e[v].pb(u);
//         d.merge(u,v);
//     }
//     assert(d.size(0)==n);
//     return e;
// }

const lli INF = 0xFFFFFFFFFFFFFFFL;

lli seed;
inline lli rnd(lli l=0,lli r=INF)
{return uniform_int_distribution<lli>(l,r)(rng);}

class CMP
{public:
bool operator()(ii a , ii b) //For min priority_queue .
{    return ! ( a.X < b.X || ( a.X==b.X && a.Y <= b.Y ));   }};

void add( map<lli,lli> &m, lli x,lli cnt=1)
{
auto jt=m.find(x);
if(jt==m.end())         m.insert({x,cnt});
else                    jt->Y+=cnt;
}

void del( map<lli,lli> &m, lli x,lli cnt=1)
{
auto jt=m.find(x);
if(jt->Y<=cnt)            m.erase(jt);
else                      jt->Y-=cnt;
}

bool cmp(const ii &a,const ii &b)
{
return a.X<b.X||(a.X==b.X&&a.Y<b.Y);
}

const lli mod = 1000000007L;
// const lli maxN = 1000000007L;

lli T,n,i,j,k,in,cnt,l,r,u,v,x,y;
lli m;
string s;
vi a;
//priority_queue < ii , vector < ii > , CMP > pq;// min priority_queue .

int main(void) {
ios_base::sync_with_stdio(false);cin.tie(NULL);
// freopen("txt.in", "r", stdin);
// freopen("txt.out", "w", stdout);
// cout<<std::fixed<<std::setprecision(35);
lli sumN = 2e5;
while(T--)
{

sumN-=n;
lli sum=0;
for(auto x:a)
sum+=x;
sum*=2;
if(sum%n){
cout<<0<<endl;
continue;
}
sum/=n;
map<lli,lli> b;
lli ans=0;
for(auto x:a){
ans+=b[sum-x];
b[x]++;
}
cout<<ans<<endl;
}   aryanc403();
return 0;
}


Tester-2's Solution
#include <bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
#define debug(x) cerr<<#x<<" "; _print(x); cerr<<nline;
#else
#define debug(x);
#endif
#define ll long long

/*
------------------------Input Checker----------------------------------
*/

long long readInt(long long l,long long r,char endd){
long long x=0;
int cnt=0;
int fi=-1;
bool is_neg=false;
while(true){
char g=getchar();
if(g=='-'){
assert(fi==-1);
is_neg=true;
continue;
}
if('0'<=g && g<='9'){
x*=10;
x+=g-'0';
if(cnt==0){
fi=g-'0';
}
cnt++;
assert(fi!=0 || cnt==1);
assert(fi!=0 || is_neg==false);

assert(!(cnt>19 || ( cnt==19 && fi>1) ));
} else if(g==endd){
if(is_neg){
x= -x;
}

if(!(l <= x && x <= r))
{
cerr << l << ' ' << r << ' ' << x << '\n';
assert(1 == 0);
}

return x;
} else {
assert(false);
}
}
}
string readString(int l,int r,char endd){
string ret="";
int cnt=0;
while(true){
char g=getchar();
assert(g!=-1);
if(g==endd){
break;
}
cnt++;
ret+=g;
}
assert(l<=cnt && cnt<=r);
return ret;
}
long long readIntSp(long long l,long long r){
}
long long readIntLn(long long l,long long r){
}
string readStringLn(int l,int r){
}
string readStringSp(int l,int r){
}

/*
------------------------Main code starts here----------------------------------
*/
ll MAX=100000;
ll tes_sum=0;
void solve(){
ll sum=0,x;
tes_sum+=n;
vector<ll> a;
for(ll i=1;i<n;i++){
a.push_back(x);
sum+=x;
}
a.push_back(x); sum+=x;
ll g=__gcd(sum,n);
sum/=g; n/=g;
if(n>2){
cout<<"0\n";
return;
}
ll target=(2*sum)/n;
map<ll,ll> freq;
ll ans=0;
for(auto it:a){
ans+=freq[target-it];
freq[it]++;
}
cout<<ans<<"\n";
return;
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
#ifndef ONLINE_JUDGE
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
freopen("error.txt", "w", stderr);
#endif
while(test_cases--){
solve();
}
assert(getchar()==-1);
assert(tes_sum<=200000);
return 0;
}


Editorialist's Solution
#include "bits/stdc++.h"
using namespace std;
#define ll long long
#define pb push_back
#define all(_obj) _obj.begin(),_obj.end()
#define F first
#define S second
#define pll pair<ll, ll>
#define vll vector<ll>
const int N=1e5+11,mod=1e9+7;
ll max(ll a,ll b) {return ((a>b)?a:b);}
ll min(ll a,ll b) {return ((a>b)?b:a);}
void sol(void)
{
ll n,ans=0;
unsigned ll sum=0;
map<ll, ll> cnt;
cin>>n;
vll v(n);
for(int i=0;i<n;i++)
cin>>v[i],sum+=v[i];
unsigned ll needed=sum*(n-2);
if(needed%n)
{
cout<<0<<'\n';
return ;
}
needed/=n;
unsigned ll pairsum=sum-needed;
for(int i=0;i<n;i++)
{
ans+=cnt[pairsum-v[i]];
cnt[v[i]]++;
}
cout<<ans<<'\n';
return ;
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL),cout.tie(NULL);
int test=1;
cin>>test;
while(test--) sol();
}


My code failed the last TC. Any idea why?

cook your dish here

T = int(input())
for _ in range(T):
n = int(input())
A = list(map(int,input().split()))
mean = sum(A)/n
given_sum = mean*2
hmap = {}
count = 0
for i in range(n):
if A[i] in hmap:
count += hmap[A[i]]
hmap[A[i]] += 1
else:
hmap[given_sum-A[i]] = 1
print(count)

My 3rd test case is failing, where am i wrong , help me please…

#include<bits/stdc++.h>
#define ll long long
#define ld double
using namespace std;
int main(){
ll t,n,i,j;
cin>>t;
while(t–){
cin>>n;
vectorv(n);
ll s1=0;
map<ll,ll>m;
for(i=0; i<n; i++){
cin>>v[i];
s1+=v[i];
m[v[i]]++;
}
ld d1 = (s1/(n*1.0));
ld R = d1 * 2.0000;

    ll sum1=0,sum2=0;
for(auto pr : m){

ld k = (R - pr.first)*1.0000000000;

if(k==pr.first){
ll h = pr.second;
sum1 += ( h*(h-1) ) / 2;
}

else{
auto it = m.find(k);
if(it==m.end()){continue;}
else{
ll j = it->second;
sum2 += pr.second*j;
}
}

}

cout<<sum1 + sum2/2<<"\n";
}


}