Week2

Week1/Swarnima_Shishodia/Que1.cpp

@@ -0,0 +1,14 @@
+#include<iostream>
+using namespace std;
+
+int main()
+{
+    long long int n;
+
+    cout<<"Enter a number ";
+    //Input a number
+    cin>>n;
+    //Output the square of a number
+    cout<<n*n;
+    return 0;
+}

Week1/Swarnima_Shishodia/Que10.cpp

@@ -0,0 +1,20 @@
+// To calculate gcd of a number
+#include<iostream>
+using namespace std;
+
+int gcd(int num1,int num2)
+{
+    if(num2==0)
+        return num1;
+    else
+     return gcd(num2,num1%num2);
+}
+int main()
+{
+    int num1,num2,result;
+    cin>>num1;
+    cin>>num2;
+    result=gcd(num1,num2);
+    cout<<result<<endl;
+    return 0;
+}

Week1/Swarnima_Shishodia/Que11.cpp

@@ -0,0 +1,36 @@
+
+#include <iostream>
+using namespace std;
+
+void sieve_of_erasthones(int a[])
+{
+int p=10000,i,q=2,j;
+for(i=0;i<=p;i++)//Mark all the array position as 1
+    a[i]=1;
+a[0]=0;
+a[1]=0;
+while(q*q<=p) //Mark the sieve positions as 0 which gets divided by q
+{
+    for(j=q*q;j<=p;j=j+q)
+    a[j]=0;
+    q=q+1;
+}
+//The numbers which are prime, 1 will be present
+}
+int main() {
+	int t,i,n,j;
+	cin>>t;
+	int a[10000];
+	sieve_of_erasthones(a); //Call the sieve function
+	for(i=0;i<t;i++)
+	{
+	   cin>>n;
+	   for(j=0;j<=n;j++)
+	   {
+	       if(a[j]==1)
+	       cout<<j<<" ";//Print the prime numbers
+	   }
+	   cout<<endl;
+	}
+	return 0;
+}

Week1/Swarnima_Shishodia/Que12.cpp

@@ -0,0 +1,62 @@
+//Segmented sieve is used when we need to print the prime in a given range because simple sieve is not memory efficient
+#include <bits/stdc++.h>
+using namespace std;
+void simpleSieve(int limit, vector<int> &prime)
+{
+    bool mark[limit+1];
+    memset(mark, true, sizeof(mark));
+    for (int p=2; p*p<limit; p++)
+    {
+        if (mark[p] == true)
+        {
+            for (int i=p*2; i<limit; i=i+p)
+                mark[i] = false;//Mark the composite number as false
+        }
+    }
+    for (int p=2; p<limit; p++)
+    {
+        if (mark[p] == true)
+        {
+            prime.push_back(p);
+            cout << p << " ";
+        }
+    }
+}
+
+void segmentedSieve(int n)
+{
+    int limit = floor(sqrt(n))+1;
+    vector<int> prime;
+    simpleSieve(limit, prime);
+    int low = limit;
+    int high = 2*limit;
+    while (low < n)
+    {
+        if (high >= n)
+           high = n;
+        bool mark[limit+1];
+        memset(mark, true, sizeof(mark));
+        for (int i = 0; i < prime.size(); i++)
+        {
+            int loLim = floor(low/prime[i]) * prime[i];
+            if (loLim < low)
+                loLim += prime[i];
+            for (int j=loLim; j<high; j+=prime[i])
+                mark[j-low] = false;
+        }
+        for (int i = low; i<high; i++)
+            if (mark[i - low] == true)
+                cout << i << " ";
+        low = low + limit;
+        high = high + limit;
+    }
+}
+
+int main()
+{
+    int n;
+    cout<<"Enter a number\n";
+    cin>>n;
+    segmentedSieve(n);
+    return 0;
+}

Week1/Swarnima_Shishodia/Que13.cpp

@@ -0,0 +1,42 @@
+//To calculate the power of a number
+#include<iostream>
+using namespace std;
+int power_(int base,int power)
+{
+    int result=1;
+    while(power!=0)
+    {
+        if(power%2==0)
+        {
+            base=base*base; //If power is even then take square of the base and divide the power by 2
+            power=power/2;
+        }
+        else
+        {
+            result=result*base; //If power is odd then multiply base by result
+            power=power-1; //and decrease the power by 1
+        }
+
+    }
+    return result;
+}
+int main()
+{
+    int base,power,m,y,i,p;
+    cin>>base;
+    cin>>power;
+    cin>>m;
+    p=power;
+    if(power%2==0)
+        power=power/2; //If power is even divide it by 2
+    else
+        power=power-1; // If power is odd subtract it by 1
+
+    y=power_(base,power);
+    if(p%2==0)
+        i=(((y%m)*(y%m))%m);//Using the properties
+    else
+        i=(((base%m)*(y%m))%m);
+    cout<<i;
+    return 0;
+}

Week1/Swarnima_Shishodia/Que14.cpp

@@ -0,0 +1,36 @@
+//To check whether n  is prime or not
+/*Logic- All prime numbers can be represented in the form of 6k+1 and 6k-1 except 2 and 3 and does not get divided by a number which is represented as 6k-1
+and 6k+1*/
+#include<iostream>
+using namespace std;
+int main()
+{
+    int t,i,j,n,flag;
+    cin>>t;
+    for(i=0;i<t;i++)
+    {
+        cin>>n;
+        if(n==1)
+            cout<<"No"<<endl;
+        else if(n==2 || n==3)
+            cout<<"Yes"<<endl; //To print 2 and 3
+        else if(n%2==0 && n%3==0)
+            cout<<"No"<<endl;
+        else
+        {
+            flag=0;
+            for(j=5;j<=n*n;j=j+6)
+             {
+            if(n%j==0 or n%(j+2)==0)
+            {
+              flag=1;
+              break;
+            }
+             }
+             if(flag==0)
+                cout<<"Yes"<<endl;
+             else
+                cout<<"No"<<endl;
+        }
+    }
+}

Week1/Swarnima_Shishodia/Que15.cpp

@@ -0,0 +1,40 @@
+//To print pair if primes
+#include<iostream>
+using namespace std;
+void sieve_of_erasthones(int a[]) //Use sieve to calculate prime number
+{
+  int p=2,i;
+  for(i=0;i<401;i++) //Mark all array index as 1
+        a[i]=1;
+a[0]=0;
+a[1]=0;
+  while(p*p<=400)
+  {
+      for(i=p*p;i<401;i=i+p)
+        a[i]=0; //The numbers which are not prime will be marked as 0
+      p=p+1;
+  }
+}
+int main()
+{
+    int t,i,j,n,k;
+    cin>>t;
+    int a[401];
+
+    sieve_of_erasthones(a); //Call the sieve function
+
+    for(i=0;i<t;i++)
+    {
+      cin>>n;
+      for(j=2;j<=n;j++)
+      {
+          for(k=2;k<=n;k++)
+          {
+              if(k*j<=n && a[k]==1 && a[j]==1) //To print the pairs
+                cout<<j<<" "<<k<<" ";
+          }
+      }
+      cout<<endl;
+    }
+    return 0;
+}

Week1/Swarnima_Shishodia/Que16.cpp

@@ -0,0 +1,24 @@
+//To check whether a number can be represented as power of 2 or not
+#include<iostream>
+using namespace std;
+int main()
+{
+    int t,i,j,a,b;
+    cin>>t;
+    uint64_t n;
+    if(n==0)
+    cout<<"NO";
+    else
+    {
+    for(i=0;i<t;i++)
+    {
+        cin>>n;
+        if((n&(n-1))==0) //If a number and with number-1 is 0, it means that it can be represented as power of 2
+            cout<<"YES"<<endl;
+        else
+        cout<<"NO"<<endl;
+
+    }
+    }
+return 0;
+}

Week1/Swarnima_Shishodia/Que2.cpp

@@ -0,0 +1,19 @@
+#To print the table of a number
+
+#include<iostream>
+using namespace std;
+int main()
+{
+    long long int n;
+    int i;
+
+    cout<<"Enter a number ";
+    cin>>n;
+
+    //Print the table
+    for(i=1;i<=10;i++)
+        cout<<n<<"*"<<i<<"="<<n*i<<endl;
+
+    return 0;
+}
+

Week1/Swarnima_Shishodia/Que3a.cpp

@@ -0,0 +1,22 @@
+//To print a upward Star Triangle
+
+#include<iostream>
+using namespace std;
+int main()
+{
+    int n,i,j;
+    cout<<"Enter a number ";
+    cin>>n;
+
+    //Run first loop till n and inside that print the number of star for each line which is always equal to the i
+
+    for(i=1;i<=n;i++)
+    {
+        for(j=1;j<=i;j++)
+            cout<<"*";
+        cout<<endl;
+    }
+
+    return 0;
+}
+

Week1/Swarnima_Shishodia/Que3b.cpp

@@ -0,0 +1,27 @@
+//To print Upward Centered Triangle
+#include <iostream>
+using namespace std;
+int main()
+{
+    int space, rows,i,k;
+    cout <<"Enter number of rows: ";
+    cin >> rows;
+    for(i=1;i<= rows;i++)
+    {
+        k=0;
+        //To print the space in left side
+        for(space=1;space<=rows-i;space++)
+        {
+            cout <<" ";
+        }
+
+         //To print the stars
+        while(k != i)
+        {
+            cout << "* ";
+            ++k;
+        }
+        cout << endl;
+    }
+    return 0;
+}

Week1/Swarnima_Shishodia/Que4.cpp

@@ -0,0 +1,20 @@
+//To print Downward Star Triangle
+
+#include<iostream>
+using namespace std;
+int main()
+{
+    int n,i,j;
+    cout<<"Enter a number ";
+    cin>>n;
+    //Run a loop from n to 1.Inside it run another loop which will print exactly i stars
+    for(i=n;i>=1;i--)
+    {
+        for(j=1;j<=i;j++)
+            cout<<"*";
+        cout<<endl;
+    }
+
+    return 0;
+}
+