Create day06sol02.cpp

Author: suzzzal

Problems/Binary-Search/Day-06/sol/suzzzal/day06sol02.cpp

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+//submission- https://codeforces.com/contest/1846/submission/356011684
+
+/*
+Approach:
+- Precompute all valid snowflake sizes of the form:
+  1 + k + k^2 + k^3 + ... (k > 1, at least 3 terms)
+- Use __int128 to safely handle values up to 10^18
+- Store all generated values in a set for fast lookup
+- For large x, additionally check the special case:
+  x = 1 + k + k^2 using quadratic formula
+- Answer YES if x matches any valid construction
+
+Complexity:
+Precomputation: ~O(K * log n)
+Query: O(log n)
+Space: O(N)
+*/
+
+#include <bits/stdc++.h>
+using namespace std;
+ 
+set <__int128> s;
+ 
+const __int128 INF = 1000000000000000000ll;
+ 
+int main()	{
+	for(long long i = 2; i <= 1000000; ++i)	{
+		__int128 j = i + 1;
+		__int128 l = i * i;
+		while(j + l <= INF)	{
+			j += l;
+			l *= i;
+			s.insert(j);
+		}
+  }
+	int tt;
+	cin >> tt;
+	while(tt--)	{
+		long long x;
+		cin >> x;
+		if(s.count(x))	{
+			cout << "YES" << endl;
+		}
+		else if(x >= 1000000000000ll){
+			long long delta = 1 - 4 * (1 - x);
+			long long x1 = 0.5 * (-1 + sqrt(delta));
+			if(x1 * x1 + x1 + 1 == x)	{
+				cout << "YES" << endl;
+			}
+			else	{
+				cout << "NO" << endl;
+			}
+		}
+		else	{
+			cout << "NO" << endl;
+		}
+	}
+}