added soluiton for day6 problem 1

Author: aricthecoder

Problems/Binary-Search/Day-06/sol/aricthecoder/Solution1.cpp

@@ -0,0 +1,148 @@
+/*
+
+Problem : Robin Hood in Town 2014C
+
+Approach : Used binary search to find the minimum amount that needs to be added to 
+         the richest person’s wealth to make Robin Hood appear.
+         if(n<=2) not possible
+
+Time Complexity : O(nlogn)
+Space Complexity : O(1) if input is not considered
+
+Submission Link : https://codeforces.com/contest/2014/submission/355969335
+*/
+#include <bits/stdc++.h>
+#include <bits/stdc++.h>
+#include <ext/pb_ds/assoc_container.hpp>
+#include <ext/pb_ds/tree_policy.hpp>
+using namespace std;
+using namespace __gnu_pbds;
+
+#define fast_io ios::sync_with_stdio(false); cin.tie(nullptr);
+#define int long long
+#define ull unsigned long long
+#define ld long double
+#define vi vector<int>
+#define vb vector<bool>
+#define vs vector<string>
+#define pii pair<int,int>
+#define pll pair<long long,long long>
+#define vpi vector<pii>
+#define vpl vector<pll>
+#define vvi vector<vi>
+#define mii map<int,int>
+#define si set<int>
+#define osi ordered_set<int>
+#define loop(i,n) for (int i = 0; i < n; i++)
+#define rloop(i,n) for (int i = n - 1; i >= 0; i--)
+#define loop1(i,a,b) for (int i = a; i <= b; i++)
+#define rloop1(i,a,b) for (int i = a; i >= b; i--)
+#define pb push_back
+#define ppb pop_back
+#define mp make_pair
+#define F first
+#define S second
+#define lb lower_bound
+#define ub upper_bound
+#define all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+#define sz(x) ((int)(x).size())
+#define findbo(x) find_by_order(x) // returns iterator to the k-th largest element (0-based)
+#define orderbk(x) order_of_key(x) // returns number of items strictly smaller than x
+#define endl '\n'
+#define printy cout<<"YES"<<endl
+#define printn cout<<"NO"<<endl
+#define vout(a) for (int i = 0; i < a.size(); i++) cout << a[i] << ' '; cout << endl;
+#define vpout(a) loop(i,sz(a)) cout <<a[i].F<<' '<< a[i].S<< endl; cout << endl;
+#define rt(x){ cout<<x<<endl; return; }
+template<typename T>
+using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>; // less_equal<T> for multiset, greater<T> for decreasing order
+
+const int MOD = 1e9 + 7;
+const int INF = 1e9;
+
+#ifndef ONLINE_JUDGE
+#define debug(x) cerr<<#x<<" = "; _print(x); cerr<<endl;
+template<typename T> void _print(const T& x){ cerr<<x; }
+template<typename T,typename U> void _print(const pair<T,U>& p){ cerr<<"("; _print(p.first); cerr<<", "; _print(p.second); cerr<<")"; }
+template<typename T> void _print(const vector<T>& v){ cerr<<"["; for(size_t i=0;i<v.size();++i){ _print(v[i]); if(i+1!=v.size()) cerr<<", "; } cerr<<"]"; }
+template<typename T> void _print(const set<T>& s){ cerr<<"{"; for(auto it=s.begin(); it!=s.end(); ++it){ _print(*it); if(next(it)!=s.end()) cerr<<", "; } cerr<<"}"; }
+template<typename T,typename U> void _print(const map<T,U>& m){ cerr<<"{"; for(auto it=m.begin(); it!=m.end(); ++it){ _print(it->first); cerr<<": "; _print(it->second); if(next(it)!=m.end()) cerr<<", "; } cerr<<"}"; }
+#else
+#define debug(x)
+#endif
+
+#define sumV(a) accumulate(all(a), 0LL)
+#define minV(a) min_element(all(a))
+#define maxV(a) max_element(all(a))
+
+int log2f(long long n) {
+    if (n==0) return -1;
+    int res = 0;
+    while (n > 1){
+        n >>= 1;
+        res++;
+    }
+    return res;
+}
+
+int binpow(int a, int n) {
+    int result = 1;
+    a %= MOD;
+    while (n > 0) {
+        if (n & 1)
+            result = (result * a) % MOD;
+        a = (a * a) % MOD;
+        n >>= 1;
+    }
+    return result;
+}
+
+int check(int m, int sum, vi a){
+    int n = a.size(), ind, mx = -1;
+    loop(i,n){
+        if(a[i]>mx){
+            mx = a[i];
+            ind = i;
+        }
+    }
+    sum+=m;
+    int cnt = 0;
+    loop(i,n){
+        if(i!=ind && 2*n*a[i]<sum) cnt++;
+    }
+    return (cnt > n/2);
+}
+
+void solve(){
+    int n;
+    cin>>n;
+    vi a(n);
+    loop(i,n) cin>>a[i];
+    
+    int sum = accumulate(all(a),0LL);
+
+    if(n<3) {rt(-1)}
+
+    int l = 0, h = INT64_MAX, ans;
+    while(h-l>1){
+        int mid = (l+h)/2;
+        if(check(mid,sum,a)) h = mid;
+        else l = mid + 1;
+    }
+
+    if(check(l,sum,a)) ans = l;
+    else ans = h;
+
+    cout<<ans<<endl;
+}
+
+int32_t main(){ 
+    fast_io; 
+    int t=1;
+    cin>>t; 
+    while(t--){ 
+        solve(); 
+    } 
+    return 0;
+}