Merge pull request #525 from Krishna200608/feature/issue-523-removal-sequence

Solved Issue #523: Removal of a Sequence (Binary Search)

Author: Dheeraj-06

Problems/Binary-Search/Day-10/sol/Krishna200608/Solution1.cpp

@@ -0,0 +1,87 @@
+/*
+Submission Link:
+https://codeforces.com/contest/2169/submission/356454662
+*/
+
+/*
+Problem: Removal of a Sequence (Easy Version)
+Link: https://codeforces.com/contest/2169/problem/D1
+Author: Krishna200608
+
+Short Problem Statement:
+Find min integer n such that after x operations (v -= v/y), the result is >= k.
+
+Approach:
+     Binary Search on Answer. The function is monotonic.
+     Simulate the process for a given start value to check validity.
+     Search range [1, 10^12].
+
+Time Complexity: O(T *x *log(N))
+Space : O(1)
+*/
+
+#include<bits/stdc++.h>
+using namespace std;
+#define MOD 1000000007
+const int M = 1e9+7;
+const double PI = acos(-1.0);
+#define INF 1e18
+#define pb push_back
+#define ppb pop_back
+#define ll long long
+#define no cout << "NO" << endl;
+#define yes cout << "YES" << endl;
+#define ff first
+#define ss second
+#define inn(x) int x; std::cin >> x;
+#define ill(x) ll x; std::cin >> x;
+#define all(x) x.begin(),x.end()
+#define in(a) for(int i = 0; i<a.size(); i++) cin>>a[i];
+#define out(a) for(int i = 0; i<a.size(); i++) cout<<a[i]<< " " ;
+typedef vector<int> vi;
+typedef vector<ll> vll;
+
+ll survivors_after_x(ll v, int x, ll y){
+    ll s = v;
+    for(int i=0;i<x && s>0;i++){
+        s -= s / y;
+    }
+    return s;
+}
+
+void solve(){
+    int T;
+    if(!(cin>>T)) return;
+    const ll NMAX = 1000000000000LL;
+    while(T--){
+        int x;
+        ll y, k;
+        cin >> x >> y >> k;
+        
+        // Optimization: check upper bound first
+        if(survivors_after_x(NMAX, x, y) < k){
+            cout << -1 << '\n';
+            continue;
+        }
+        
+        ll lo = 1, hi = NMAX;
+        while(lo < hi){
+            ll mid = lo + (hi - lo) / 2;
+            if(survivors_after_x(mid, x, y) >= k) hi = mid;
+            else lo = mid + 1;
+        }
+        cout << lo << '\n';
+    }
+}
+
+signed main(){
+    ios_base::sync_with_stdio(false);cin.tie(nullptr);cout.tie(nullptr);
+    auto begin = std::chrono::high_resolution_clock::now();
+    
+    solve(); // solve handles the test cases loop internally as per your code
+    
+    auto end = std::chrono::high_resolution_clock::now();
+    auto elapsed = std::chrono::duration_cast<std::chrono::nanoseconds>(end - begin);
+    cerr << "Time measured: " << elapsed.count() * 1e-6 << "ms";
+    return 0;
+}