Merge pull request #192 from sachinarora707/master

Project Euler Solutions Added.

Author: harshildarji

Diff for: Project Euler/Problem 01/sol1.py

@@ -0,0 +1,12 @@
+'''
+Problem Statement:
+If we list all the natural numbers below 10 that are multiples of 3 or 5,
+we get 3,5,6 and 9. The sum of these multiples is 23.
+Find the sum of all the multiples of 3 or 5 below N.
+'''
+n = int(raw_input().strip())
+sum=0;
+for a in range(3,n):
+    if(a%3==0 or a%5==0):
+        sum+=a
+print sum;

Diff for: Project Euler/Problem 01/sol2.py

@@ -0,0 +1,15 @@
+'''
+Problem Statement:
+If we list all the natural numbers below 10 that are multiples of 3 or 5,
+we get 3,5,6 and 9. The sum of these multiples is 23.
+Find the sum of all the multiples of 3 or 5 below N.
+'''
+n = int(raw_input().strip())
+sum = 0
+terms = (n-1)/3
+sum+= ((terms)*(6+(terms-1)*3))/2 #sum of an A.P.
+terms = (n-1)/5
+sum+= ((terms)*(10+(terms-1)*5))/2
+terms = (n-1)/15
+sum-= ((terms)*(30+(terms-1)*15))/2
+print sum

Diff for: Project Euler/Problem 01/sol3.py

@@ -0,0 +1,42 @@
+'''
+Problem Statement:
+If we list all the natural numbers below 10 that are multiples of 3 or 5,
+we get 3,5,6 and 9. The sum of these multiples is 23.
+Find the sum of all the multiples of 3 or 5 below N.
+'''
+'''
+This solution is based on the pattern that the successive numbers in the series follow: 0+3,+2,+1,+3,+1,+2,+3.
+'''
+n = int(raw_input().strip())
+sum=0;
+num=0;
+while(1):
+    num+=3
+    if(num>=n):
+        break
+    sum+=num
+    num+=2
+    if(num>=n):
+        break
+    sum+=num
+    num+=1
+    if(num>=n):
+        break
+    sum+=num
+    num+=3
+    if(num>=n):
+        break
+    sum+=num
+    num+=1
+    if(num>=n):
+        break
+    sum+=num
+    num+=2
+    if(num>=n):
+        break
+    sum+=num
+    num+=3
+    if(num>=n):
+        break
+    sum+=num
+print sum;

Diff for: Project Euler/Problem 02/sol1.py

@@ -0,0 +1,18 @@
+'''
+Problem:
+Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2,
+the first 10 terms will be:
+                1,2,3,5,8,13,21,34,55,89,..
+By considering the terms in the Fibonacci sequence whose values do not exceed n, find the sum of the even-valued terms.
+e.g. for n=10, we have {2,8}, sum is 10.
+'''
+
+n = int(raw_input().strip())
+i=1; j=2; sum=0
+while(j<=n):
+    if((j&1)==0): #can also use (j%2==0)
+        sum+=j
+    temp=i
+    i=j
+    j=temp+i
+print sum

Diff for: Project Euler/Problem 03/sol1.py

@@ -0,0 +1,38 @@
+'''
+Problem:
+The prime factors of 13195 are 5,7,13 and 29. What is the largest prime factor of a given number N?
+e.g. for 10, largest prime factor = 5. For 17, largest prime factor = 17.
+'''
+
+import math
+
+def isprime(no):
+    if(no==2):
+        return True
+    elif (no%2==0):
+        return False
+    sq = int(math.sqrt(no))+1
+    for i in range(3,sq,2):
+        if(no%i==0):
+            return False
+    return True
+
+max=0
+n=int(input())
+if(isprime(n)):
+    print n
+else:
+    while (n%2==0):
+        n=n/2
+    if(isprime(n)):
+        print n
+    else:
+        n1 = int(math.sqrt(n))+1
+        for i in range(3,n1,2):
+            if(n%i==0):
+                if(isprime(n/i)):
+                    max=n/i
+                    break
+                elif(isprime(i)):
+                    max=i
+        print max

Diff for: Project Euler/Problem 03/sol2.py

@@ -0,0 +1,16 @@
+'''
+Problem:
+The prime factors of 13195 are 5,7,13 and 29. What is the largest prime factor of a given number N?
+e.g. for 10, largest prime factor = 5. For 17, largest prime factor = 17.
+'''
+n=int(input())
+prime=1
+i=2
+while(i*i<=n):
+    while(n%i==0):
+        prime=i
+        n/=i
+    i+=1
+if(n>1):
+    prime=n
+print prime

Diff for: Project Euler/Problem 04/sol1.py

@@ -0,0 +1,15 @@
+'''
+Problem:
+A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 x 99.
+Find the largest palindrome made from the product of two 3-digit numbers which is less than N.
+'''
+n=int(input())
+for i in range(n-1,10000,-1):
+    temp=str(i)
+    if(temp==temp[::-1]):
+        j=999
+        while(j!=99):
+            if((i%j==0) and (len(str(i/j))==3)):
+                print i
+                exit(0)
+            j-=1

Diff for: Project Euler/Problem 04/sol2.py

@@ -0,0 +1,18 @@
+'''
+Problem:
+A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 x 99.
+Find the largest palindrome made from the product of two 3-digit numbers which is less than N.
+'''
+arr = []
+for i in range(999,100,-1):
+    for j in range(999,100,-1):
+        t = str(i*j)
+        if t == t[::-1]:
+            arr.append(i*j)
+arr.sort()
+
+n=int(input())
+for i in arr[::-1]:
+    if(i<n):
+        print i
+        exit(0)

Diff for: Project Euler/Problem 05/sol1.py

@@ -0,0 +1,20 @@
+'''
+Problem:
+2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
+What is the smallest positive number that is evenly divisible(divisible with no remainder) by all of the numbers from 1 to N?
+'''
+
+n = int(input())
+i = 0
+while 1:
+    i+=n*(n-1)
+    nfound=0
+    for j in range(2,n):
+        if (i%j != 0):
+            nfound=1
+            break
+    if(nfound==0):
+        if(i==0):
+            i=1
+        print i
+        break

Diff for: Project Euler/Problem 06/sol1.py

@@ -0,0 +1,19 @@
+# -*- coding: utf-8 -*-
+'''
+Problem:
+The sum of the squares of the first ten natural numbers is,
+            1^2 + 2^2 + ... + 10^2 = 385
+The square of the sum of the first ten natural numbers is,
+            (1 + 2 + ... + 10)^2 = 552 = 3025
+Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 − 385 = 2640.
+Find the difference between the sum of the squares of the first N natural numbers and the square of the sum.
+'''
+
+suma = 0
+sumb = 0
+n = int(input())
+for i in range(1,n+1):
+    suma += i**2
+    sumb += i
+sum = sumb**2 - suma
+print sum

Diff for: Project Euler/Problem 06/sol2.py

@@ -0,0 +1,15 @@
+# -*- coding: utf-8 -*-
+'''
+Problem:
+The sum of the squares of the first ten natural numbers is,
+            1^2 + 2^2 + ... + 10^2 = 385
+The square of the sum of the first ten natural numbers is,
+            (1 + 2 + ... + 10)^2 = 552 = 3025
+Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 − 385 = 2640.
+Find the difference between the sum of the squares of the first N natural numbers and the square of the sum.
+'''
+n = int(input())
+suma = n*(n+1)/2
+suma **= 2
+sumb = n*(n+1)*(2*n+1)/6
+print suma-sumb

Diff for: Project Euler/Problem 07/sol1.py

@@ -0,0 +1,29 @@
+'''
+By listing the first six prime numbers:
+2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
+What is the Nth prime number?
+'''
+from math import sqrt
+def isprime(n):
+    if (n==2):
+        return True
+    elif (n%2==0):
+        return False
+    else:
+        sq = int(sqrt(n))+1
+        for i in range(3,sq,2):
+            if(n%i==0):
+                return False
+    return True
+n = int(input())
+i=0
+j=1
+while(i!=n and j<3):
+    j+=1
+    if (isprime(j)):
+        i+=1
+while(i!=n):
+    j+=2
+    if(isprime(j)):
+        i+=1
+print j