Linear & Binary Search

8. Practice Problems

Try first, then click to reveal the runnable solution.

1. Find the first occurrence of a target in a sorted array with duplicates.
   duplicate-সহ sorted array-এ target-এর প্রথম occurrence বের করুন।
   ✨ Show Answer (উত্তর দেখুন)

   first_occ.cpp

   #include <bits/stdc++.h>
   using namespace std;
   int firstOcc(vector<int>& a, int x){
       int lo=0, hi=a.size(), ans=-1;
       while(lo<hi){
           int m=lo+(hi-lo)/2;
           if(a[m]==x){ ans=m; hi=m; }
           else if(a[m]<x) lo=m+1;
           else hi=m;
       }
       return ans;
   }
   int main(){
       vector<int> a={1,2,2,2,3,5};
       cout << firstOcc(a,2) << "\n";
   }

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2. Find the last occurrence of a target.
   target-এর সর্বশেষ occurrence বের করুন।
   ✨ Show Answer (উত্তর দেখুন)

   last_occ.cpp

   #include <bits/stdc++.h>
   using namespace std;
   int lastOcc(vector<int>& a, int x){
       int lo=0, hi=a.size()-1, ans=-1;
       while(lo<=hi){
           int m=lo+(hi-lo)/2;
           if(a[m]==x){ ans=m; lo=m+1; }
           else if(a[m]<x) lo=m+1;
           else hi=m-1;
       }
       return ans;
   }
   int main(){
       vector<int> a={1,2,2,2,3,5};
       cout << lastOcc(a,2) << "\n";
   }

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3. Count occurrences of x in a sorted array in O(log n).
   sorted array-এ x-এর সংখ্যা O(log n)-এ গণনা করুন।
   ✨ Show Answer (উত্তর দেখুন)

   count.cpp

   #include <bits/stdc++.h>
   using namespace std;
   int main(){
       vector<int> a={1,2,2,2,3,5};
       int x=2;
       auto lo = lower_bound(a.begin(),a.end(),x);
       auto hi = upper_bound(a.begin(),a.end(),x);
       cout << (hi - lo) << "\n";
   }

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4. Compute integer sqrt(n) using binary search (no cmath).
   binary search ব্যবহার করে integer sqrt(n) বের করুন।
   ✨ Show Answer (উত্তর দেখুন)

   isqrt.cpp

   #include <bits/stdc++.h>
   using namespace std;
   long long isqrt(long long n){
       long long lo=0, hi=n, ans=0;
       while(lo<=hi){
           long long m=lo+(hi-lo)/2;
           if(m*m<=n){ ans=m; lo=m+1; }
           else hi=m-1;
       }
       return ans;
   }
   int main(){ cout << isqrt(2025) << "\n"; }

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5. Find a peak in a mountain array (strictly increases then strictly decreases).
   mountain array-এ peak খুঁজে বের করুন।
   ✨ Show Answer (উত্তর দেখুন)

   peak.cpp

   #include <bits/stdc++.h>
   using namespace std;
   int peak(vector<int>& a){
       int lo=0, hi=a.size()-1;
       while(lo<hi){
           int m=lo+(hi-lo)/2;
           if(a[m]<a[m+1]) lo=m+1;
           else hi=m;
       }
       return lo;
   }
   int main(){
       vector<int> a={1,3,7,12,9,4};
       cout << peak(a) << " -> " << a[peak(a)] << "\n";
   }

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6. Search in a rotated sorted array (no duplicates).
   rotated sorted array-এ search করুন।
   ✨ Show Answer (উত্তর দেখুন)

   rotated.cpp

   #include <bits/stdc++.h>
   using namespace std;
   int rotSearch(vector<int>& a, int x){
       int lo=0, hi=a.size()-1;
       while(lo<=hi){
           int m=lo+(hi-lo)/2;
           if(a[m]==x) return m;
           if(a[lo]<=a[m]){
               if(a[lo]<=x && x<a[m]) hi=m-1; else lo=m+1;
           } else {
               if(a[m]<x && x<=a[hi]) lo=m+1; else hi=m-1;
           }
       }
       return -1;
   }
   int main(){
       vector<int> a={7,9,12,1,3,5};
       cout << rotSearch(a,3) << "\n";
   }

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7. Painter partition: distribute boards among k painters minimizing max paint time.
   painter partition: k জন painter-এর মধ্যে boards বিতরণ করুন যাতে সর্বাধিক সময় সর্বনিম্ন হয়।
   ✨ Show Answer (উত্তর দেখুন)

   painter.cpp

   #include <bits/stdc++.h>
   using namespace std;
   bool ok(vector<int>& b, int k, long long cap){
       long long sum=0; int cnt=1;
       for(int x:b){ if(x>cap) return false;
           if(sum+x>cap){cnt++;sum=x;} else sum+=x; }
       return cnt<=k;
   }
   int main(){
       vector<int> b={10,20,30,40}; int k=2;
       long long lo=*max_element(b.begin(),b.end());
       long long hi=accumulate(b.begin(),b.end(),0LL);
       while(lo<hi){ long long m=lo+(hi-lo)/2;
           if(ok(b,k,m)) hi=m; else lo=m+1; }
       cout << lo << "\n";
   }

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8. Find the smallest element in a rotated sorted array.
   rotated sorted array-এর সর্বনিম্ন element বের করুন।
   ✨ Show Answer (উত্তর দেখুন)

   min_rot.cpp

   #include <bits/stdc++.h>
   using namespace std;
   int findMin(vector<int>& a){
       int lo=0, hi=a.size()-1;
       while(lo<hi){
           int m=lo+(hi-lo)/2;
           if(a[m]>a[hi]) lo=m+1;
           else hi=m;
       }
       return a[lo];
   }
   int main(){
       vector<int> a={15,18,2,3,6,12};
       cout << findMin(a) << "\n";
   }

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