Merge pull request #426 from Aiyaan-Mahajan/day6-q1

day 6 Q1

Author: zonedoutdg

Problems/Binary-Search/Day-06/sol/Aiyaan_Mahajan/Q1sol.cpp

@@ -0,0 +1,66 @@
+/*
+DAY 6
+Q1 Robin hood in the town
+.*/
+/*
+We need more than half the people to have wealth
+< half of the new average.
+
+Adding gold only increases the average, so poor people become “unhappy” first.
+
+So we find the smallest 
+𝑥
+x such that the poorest majority are still below:
+half-average= (S + x)/2*n
+
+Solve for 
+x, and if it’s negative → answer is 0.
+If 𝑛≤2
+ it’s impossible → -1.
+
+That’s it.
+
+*/
+
+#include <bits/stdc++.h>
+using namespace std;
+
+int main() {
+  
+    int t;
+    cin >> t;
+    while (t--) {
+        int n;
+        cin >> n;
+        vector<long long> a(n);
+        long long S = 0;
+        for (auto &x : a) {
+            cin >> x;
+            S += x;
+        }
+
+        if (n <= 2) {
+            cout << -1 << '\n';
+            continue;
+        }
+
+        sort(a.begin(), a.end());
+        int m = n / 2 + 1;
+        long long v = a[m - 1];
+
+        long long x = 2LL * n * v - S + 1;
+        if (x < 0) x = 0;
+
+        cout << x << '\n';
+    }
+    return 0;
+}
+
+
+
+
+
+//TC =O(Nlog(N)) and SC = O(N)
+/*
+My submission : https://codeforces.com/contest/2014/submission/356052582
+*/