Merge pull request #122 from ashishtheman/master

Add three new codes

misc/Collatz.c

@@ -0,0 +1,26 @@
+/*
+collatz conjecture: a series for a number n in which if n even then the next number is n/2 ,but if n is odd then the next number is 3n+1.
+this series continues till it reaches 1*/
+
+#include<stdio.h>
+int main()
+{
+    int n,curr_no;   
+    scanf("%d",&n);     //input number 
+    curr_no=n;        //curr_no stores input number n   
+    while(curr_no!=1)     //loop till series reaches 1
+    {
+        if(curr_no%2==0)      //condition   for even number
+        {
+            curr_no=curr_no/2;
+            printf("%d->",curr_no);
+        }    
+        else 
+        {
+            curr_no=(curr_no*3)+1;      //condition for odd number
+            printf("%d->",curr_no);
+        }
+    }
+    printf("1");
+    return 0;
+}

misc/catalan.c

@@ -0,0 +1,28 @@
+/*
+code for computing nth catalan number
+*/
+#include<stdio.h>
+long int factorial(int x)    //long int for more than 10 factorial
+{
+     int i;
+     long int fac;   //fac stores x factorial  
+     fac=x;
+     for(i=1;i<x;i++)    //loop to calculate x factorial
+     {
+        fac=fac*(x-i);
+     }
+     return fac;   //returning x factorial
+}
+int main()
+{
+    long int f1,f2,f3;  //long int for more than 10 factorial
+    int n;
+    float C;    //C is catalan number for n;
+    scanf("%d",&n);
+    f1=factorial(2*n);
+    f2=factorial(n+1);
+    f3=factorial(n);
+    C=f1/(f2*f3);   //formula for catalan number for n
+    printf("%0.2f",C);
+    return 0;
+}

misc/factorial_trailing_zeroes.c

@@ -0,0 +1,25 @@
+/*
+programme for computing number of zeroes at the end of factorial of a given number n
+*/
+#include<stdio.h>
+#include<math.h>        //including math.h header file to use pow function
+int main()
+{
+    int i,n,test=0,count=0;
+    //taking input number n
+    scanf("%d",&n);
+    
+    //looping from 1 till loop break
+    for(i=1;;i++)
+    {
+        test=n/pow(5,i);//division of n by ith power of 5(storing in integer form)
+        if(test!=0)     //condition for zeroes at end corresponding individual ith case
+        {
+            count=count+test;  
+        }
+        else 
+            break;      //break the loop for if test=0
+    }
+    printf("%d\n",count);         
+    return 0;
+}