first 10 problem of project-eulers

problem001.py

@@ -0,0 +1,11 @@
+# coding: utf-8
+s = 0
+for i in range(1000):
+    #print i,
+    if (i % 3 == 0):
+        s = s + i
+    if (i % 5 == 0):
+        s = s + i
+    if (i % 15 == 0):
+        s = s - i
+print s

problem002.py

@@ -0,0 +1,16 @@
+#coding: utf-8
+
+c = [1]
+a,b = 1,2
+s = 0
+while b <4000000:
+    a,b = b, a+b
+    c.append(a)
+print c
+print len(c)
+for i in range(len(c)):
+    if c[i] % 2 == 0:
+        s = s + c[i]
+print s
+
+

problem003.py

@@ -0,0 +1,16 @@
+#coding: utf-8
+
+import math
+
+
+def prime_factors(n):
+    factors = []
+    d = 2
+    while n > 1:
+        while n % d == 0:
+            factors.append(d)
+            n /= d
+        d += 1
+    return factors
+print prime_factors(600851475143)
+print max(prime_factors(600851475143))

problem004.py

@@ -0,0 +1,10 @@
+# coding: utf-8
+c = []
+for i in range(999):
+    for j in range(999):
+        a = i * j
+        b = a % 1000
+        d = a / 1000
+        if (str(d) == str(b)[::-1]):
+            c.append(a)
+print max(c)

problem005.py

@@ -0,0 +1,23 @@
+#coding: utf-8
+
+def ucln(a, b):
+    while b:
+        r = a % b
+        a, b = b, r
+    return a
+def bcnn(a, b):
+    bcnn1 = a * b / ucln(a, b)
+    return bcnn1
+
+lists = list(range(2,21))
+
+bcnn1 = bcnn(lists[0], lists[1])
+
+for i in range(2,len(lists)):
+    bcnn1 = bcnn(bcnn1, lists[i])
+
+print bcnn1
+
+
+
+

problem006.py

@@ -0,0 +1,8 @@
+#coding: utf-8
+
+SOQ = 0
+QOS = 0
+for i in range(101):
+    SOQ = SOQ + i*i
+    QOS = QOS + i
+print QOS*QOS-SOQ

problem007.py

@@ -0,0 +1,24 @@
+#coding: utf-8
+
+import time
+
+def fast_nth_prime(n, limit = 125000):
+      if limit % 2 != 0:
+            limit += 1
+      primes = [True] * limit
+      primes[0],primes[1] = [None, None]
+      count = 0
+      for ind,val in enumerate(primes):
+            if val:
+                  primes[ind*2::ind] = [False] * ((limit -1)//ind - 1)
+                  count += 1
+            if count == n:
+                  return ind
+      return False
+
+
+start = time.time()
+prime = fast_nth_prime(10001)
+elapsed = (time.time() - start)
+
+print "found %s in %s seconds." % (prime,elapsed)

problem008.py

@@ -0,0 +1,23 @@
+#coding: utf-8
+
+import time
+start = time.time()
+s = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450"
+
+P = []
+
+for i in range(0, len(s) - 13):
+
+    product = 1
+
+    for j in range(i, i + 13):
+        product *= int(s[j])
+        P.append(product)
+
+elapsed = (time.time() - start)
+print max(P)
+print elapsed
+
+
+
+

problem009.py

@@ -0,0 +1,13 @@
+#coding: utf-8
+
+from math import sqrt
+import time
+start = time.time()
+
+for b in range(500):
+    for a in range(b):
+        c = sqrt(a*a + b*b)
+        if a + b + c == 1000:
+            print a*b*c
+            break
+print time.time() - start

problem010.py

@@ -0,0 +1,21 @@
+#coding: utf-8
+
+import time
+start = time.time()
+
+def prime(limit):
+    prime_num = []
+    primes = [True] * limit
+    primes[0],primes[1] = [None, None]
+    for ind,val in enumerate(primes):
+        if val:
+            primes[ind*2::ind] = [False] * ((limit -1)//ind - 1)
+            prime_num.append(ind)
+    return prime_num
+
+a = prime(2000000)
+s = 0
+for i in a:
+    s += i
+print s, time.time()-start
+