Elementary Sorting: Bubble, Selection, Insertion

8. Practice Problems

Try first; reveal the runnable answer when you're stuck.

1. Sort the array and report the total number of swaps bubble sort performs.
   array sort করে bubble sort-এর মোট swap সংখ্যা বের করুন।
   ✨ Show Answer (উত্তর দেখুন)

   bubble_swaps.cpp

   #include <bits/stdc++.h>
   using namespace std;
   int main(){
       vector<int> a={5,2,8,1,4};
       long long sw=0;
       for(int i=0;i<(int)a.size()-1;i++)
           for(int j=0;j<(int)a.size()-1-i;j++)
               if(a[j]>a[j+1]){swap(a[j],a[j+1]);sw++;}
       cout<<"swaps = "<<sw<<"\n";
       for(int x:a) cout<<x<<" ";
       cout<<"\n";
   }

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2. Bubble sort with early termination: stop when a pass makes no swap.
   যদি কোনো pass-এ একটিও swap না হয়, bubble sort বন্ধ করুন।
   ✨ Show Answer (উত্তর দেখুন)

   bubble_early.cpp

   #include <bits/stdc++.h>
   using namespace std;
   int main(){
       vector<int> a={1,2,3,5,4};
       int n=a.size(), passes=0;
       for(int i=0;i<n-1;i++){
           bool moved=false; passes++;
           for(int j=0;j<n-1-i;j++)
               if(a[j]>a[j+1]){swap(a[j],a[j+1]);moved=true;}
           if(!moved) break;
       }
       cout<<"passes used = "<<passes<<"\n";
   }

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3. Sort an array where every element is at most k positions from its sorted location (use insertion sort).
   এমন array sort করুন যেখানে প্রতিটি element সর্বাধিক k পজিশন দূরে আছে।
   ✨ Show Answer (উত্তর দেখুন)

   k_sorted.cpp

   #include <bits/stdc++.h>
   using namespace std;
   int main(){
       vector<int> a={2,1,3,5,4,6}; // k = 1
       int n=a.size();
       for(int i=1;i<n;i++){
           int key=a[i], j=i-1;
           while(j>=0 && a[j]>key){a[j+1]=a[j];j--;}
           a[j+1]=key;
       }
       for(int x:a) cout<<x<<" ";
       cout<<"\n";
   }

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4. Stable sort a list of (name, age) first by name, then by age — using insertion sort twice.
   (name, age) list-কে আগে name, পরে age দিয়ে stable sort করুন।
   ✨ Show Answer (উত্তর দেখুন)

   multi_sort.cpp

   #include <bits/stdc++.h>
   using namespace std;
   using P = pair<string,int>;
   template<class Cmp>
   void isort(vector<P>& a, Cmp cmp){
       for(int i=1;i<(int)a.size();i++){
           P k=a[i]; int j=i-1;
           while(j>=0 && cmp(k,a[j])){a[j+1]=a[j];j--;}
           a[j+1]=k;
       }
   }
   int main(){
       vector<P> v={{"Karim",25},{"Anika",30},{"Karim",22},{"Anika",28}};
       isort(v, [](const P& a, const P& b){ return a.second < b.second; });
       isort(v, [](const P& a, const P& b){ return a.first  < b.first;  });
       for(auto& p:v) cout<<p.first<<" "<<p.second<<"\n";
   }

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5. Modify selection sort to find the min and max together — fewer comparisons.
   selection sort পরিবর্তন করুন যাতে min ও max একসাথে খুঁজে — কম comparison হয়।
   ✨ Show Answer (উত্তর দেখুন)

   double_select.cpp

   #include <bits/stdc++.h>
   using namespace std;
   int main(){
       vector<int> a={5,2,9,1,7,3};
       int lo=0, hi=a.size()-1;
       while(lo<hi){
           int mn=lo, mx=lo;
           for(int j=lo;j<=hi;j++){
               if(a[j]<a[mn]) mn=j;
               if(a[j]>a[mx]) mx=j;
           }
           swap(a[lo],a[mn]);
           if(mx==lo) mx=mn;     // the max moved!
           swap(a[hi],a[mx]);
           lo++; hi--;
       }
       for(int x:a) cout<<x<<" ";
       cout<<"\n";
   }

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6. Use insertion sort with binary search to find the insertion point (binary-insertion sort).
   insertion sort-এ insertion point খুঁজতে binary search ব্যবহার করুন।
   ✨ Show Answer (উত্তর দেখুন)

   bin_insert.cpp

   #include <bits/stdc++.h>
   using namespace std;
   int main(){
       vector<int> a={5,2,9,1,7,3};
       int n=a.size();
       for(int i=1;i<n;i++){
           int key=a[i];
           int pos = upper_bound(a.begin(), a.begin()+i, key) - a.begin();
           for(int j=i;j>pos;j--) a[j]=a[j-1];
           a[pos]=key;
       }
       for(int x:a) cout<<x<<" ";
       cout<<"\n";
   }

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