CHFMIST-Editorial

PROBLEM LINK:

Contest Division 1
Contest Division 2
Contest Division 3
Contest Division 4

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

DIFFICULTY:

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){
    return readInt(l,r,' ');
}
long long readIntLn(long long l,long long r){
    return readInt(l,r,'\n');
}
string readStringLn(int l,int r){
    return readString(l,r,'\n');
}
string readStringSp(int l,int r){
    return readString(l,r,' ');
}
 
 
/*
------------------------Main code starts here----------------------------------
*/
int MAX=100000;
int tes_sum=0;
void solve(){  
    long long n=readIntLn(3,MAX);
    long long sum=0,x;
    tes_sum+=n;
    vector<long long> a;
    for(int i=1;i<n;i++){  
        x=readIntSp(1,1000000000);
        a.push_back(x);
        sum+=x;
    }
    x=readIntLn(1,1000000000);
    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         
    int test_cases=readIntLn(1,1000); 
    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
    #include <header.h>
#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) {
    return readInt(l,r,' ');
}
long long readIntLn(long long l, long long r) {
    return readInt(l,r,'\n');
}
string readStringLn(int l, int r) {
    return readString(l,r,'\n');
}
string readStringSp(int l, int r) {
    return readString(l,r,' ');
}

void readEOF(){
    assert(getchar()==EOF);
}

vi readVectorInt(int n,lli l,lli r){
    vi a(n);
    for(int i=0;i<n-1;++i)
        a[i]=readIntSp(l,r);
    a[n-1]=readIntLn(l,r);
    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;
mt19937 rng(seed=chrono::steady_clock::now().time_since_epoch().count());
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);
T=readIntLn(1,1e3);
lli sumN = 2e5;
while(T--)
{

    n=readIntLn(3,min(sumN,100000LL));
    sumN-=n;
    a=readVectorInt(n,1,1e9);
    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();
    readEOF();
    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){
    return readInt(l,r,' ');
}
long long readIntLn(long long l,long long r){
    return readInt(l,r,'\n');
}
string readStringLn(int l,int r){
    return readString(l,r,'\n');
}
string readStringSp(int l,int r){
    return readString(l,r,' ');
}
 
 
/*
------------------------Main code starts here----------------------------------
*/
ll MAX=100000;
ll tes_sum=0;
void solve(){  
    ll n=readIntLn(3,MAX);
    ll sum=0,x;
    tes_sum+=n;
    vector<ll> a;
    for(ll i=1;i<n;i++){  
        x=readIntSp(1,1000000000);
        a.push_back(x);
        sum+=x;  
    }
    x=readIntLn(1,1000000000);
    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         
    int test_cases=readIntLn(1,1000); 
    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);}
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
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";
}

}