Merge pull request #497 from Abh-igyan/patch-2

Create Solution2.cpp

Author: Dheeraj-06

Problems/Binary-Search/Day-07/sol/Abhigyan/Solution2.cpp

@@ -0,0 +1,75 @@
+// submission: https://codeforces.com/contest/1777/submission/356260631
+
+/* Given n students of a school and m topics 1,2,3,…,m from which the quiz questions will be formed. 
+The i-th student is considered proficient in a topic T if (ai%T)=0.
+Otherwise, he is a rookie in that topic. We are asked to find the team formation of any no. of students 
+such that for every topic there is a member of the team proficient in this topic. Whilst minimizing the 
+maximum difference between the smartness of any two students and output this difference */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+using ll = long long;
+#define all(x) (x).begin(), (x).end()
+
+const int MOD = 1e9 + 7; // 998244353
+const ll INF = 1e18;
+const int maxval=100005;
+vector<int> divisors[maxval];
+
+void precompute(){
+    for(int i=1;i<maxval;i++){
+        for(int j=i;j<maxval;j+=i) divisors[j].push_back(i);
+    }
+}
+
+void solve() {
+    int n,m;
+    cin>>n>>m;
+    vector<int> a(n);
+    for(auto &x: a) cin>>x;
+    sort(all(a));
+    int cov_topics=0, min_dif=INT_MAX, l=0;//left
+    vector<int> cnt(m+1,0);
+
+    //we take 2 pointers left and right
+    for(int r=0;r<n;r++){
+        // Add current student's topics to the window
+        for(int topic: divisors[a[r]]){
+            if(topic>m) break; //since divisors[] also keeps sorted divisors, if one is greater than m, then all subsequent will be so
+            if(cnt[topic]==0) cov_topics++; //increment cov_topics for every unique topic
+            cnt[topic]++;
+        }
+
+        /* While covered_topics == m (i.e., the team is valid): 
+            Update the minimum difference: ans = min(ans, a[right] - a[left]).
+            Move the left pointer forward to try and shrink the window. 
+            Remove the left student's factors from the count.*/
+        while(cov_topics==m){
+            min_dif=min(min_dif,a[r]-a[l]);
+            for(int topic: divisors[a[l]]){
+                if(topic>m) break;
+                cnt[topic]--;
+                if(cnt[topic]==0) cov_topics--;
+            }
+            l++;
+        }
+    }
+    if(min_dif==INT_MAX) cout<<-1<<endl; //means no team can cover all the m topics
+    else cout<<min_dif<<endl;
+
+}
+
+int main() {
+    // Fast I/O
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+    precompute();
+    int t;
+    cin >> t;
+    while (t--) {
+        solve();
+    }
+    
+    return 0;
+}