Merge pull request #419 from aricthecoder/day6sol2

Day6sol2

Author: Dheeraj-06

Problems/Binary-Search/Day-06/sol/aricthecoder/Solution2.cpp

@@ -0,0 +1,158 @@
+/*
+
+Problem : Rudolf and Snowflakes 1846E2
+
+Approach : sum = 1+k+k2+k3+...kd  : ki = k^i
+                so we need to find a pair of k,d for n such {sum = n}
+                2^60>1e18 so we can iterate for each d and using binary search we can also find k;
+
+Time Complexity : O(nlogn)
+Space Complexity : O(n)
+
+Submission Link : https://codeforces.com/problemset/submission/1846/356008118
+*/
+#include <bits/stdc++.h>
+using namespace std;
+ 
+#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 vll vector<long long>
+#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 vvll vector<vll>
+#define mii map<int, int>
+#define mll map<long long, long long>
+#define si set<int>
+#define sll set<long long>
+ 
+#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 all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+#define sz(x) ((int)(x).size())
+#define endl '\n'
+#define print1 cout<<"YES"<<endl
+#define print0 cout<<"NO"<<endl
+ 
+const int MOD = 1e18;
+const int INF = 1e18;
+ 
+#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 != v.size() - 1) 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
+ 
+ 
+int binpow(int a, int n) {
+    int result = 1;
+    a %= MOD;
+    while (n > 0) {
+        if (n & 1)
+            result = (result * a);
+        a = (a * a);
+        n >>= 1;
+    }
+    return result;
+}
+
+/*
+
+s(k) = [k^(d+1) - 1]/[k-1]
+
+*/
+
+int cal(int k, int d, int n){
+    int sum = 1, term = 1;
+    loop(i,d){
+        if(term>n/k || sum>n) return 2;
+        term *= k;
+        sum += term;
+    }
+    if(sum == n) return 0;
+    return 1;
+}
+ 
+void solve(){
+    int n;
+    cin>>n;
+ 
+    if(n<7) {print0; return;}
+
+    loop1(d,2,60){
+        int l = 2, h = n;
+        while (l <= h)
+        {
+            int k = l + (h-l)/2;
+            int res = cal(k,d,n);
+            if (res==0){
+                print1;
+                return;
+            }
+            else if (res==1) l = k + 1;
+            else h = k - 1;
+        }
+    }
+    print0;
+}
+ 
+int32_t main() {
+    fast_io;
+    int t = 1;
+    cin >> t;
+    while (t--) {
+        solve();
+    }
+    return 0;
+}