Merge branch 'master' of https://github.com/tingleshao/eulerMKII

problem111to120/problem112.py

@@ -0,0 +1,43 @@
+# problem 112 
+# boundcy numbers
+def isDECorINC(n):
+	n_lst = map(int, list(str(n)))
+	if len(n_lst) <= 2:
+		return True
+	if n_lst[0] < n_lst[1]:
+		return isINC(n_lst[1:])
+	if n_lst[0] > n_lst[1]:
+		return isDEC(n_lst[1:])
+	return isDECorINC(int("".join(map(str,n_lst[1:]))))
+
+
+
+
+
+def isDEC(n_lst):
+	if len(n_lst) == 1:
+		return True
+	if n_lst[0] < n_lst[1]:
+		return False
+	return isDEC(n_lst[1:])
+
+def isINC(n_lst):
+	if len(n_lst)== 1:
+		return True
+	if n_lst[0] > n_lst[1]:
+		return False
+	return isINC(n_lst[1:])
+
+bouncy_count = 0  
+for i in range(1,2000001):
+	if not isDECorINC(i):
+		print str(i) + " is bouncy "
+		bouncy_count += 1
+	else:
+		print str(i) + ' is not bouncy'
+	if i > 1500000:
+		if bouncy_count / float(i) == 0.99:
+			print i 
+			break
+
+print bouncy_count / 2000000.0

problem161to170/problem166.py

@@ -0,0 +1,21 @@
+# problem 166
+
+def get_new_grid():
+	grid = []
+	for j in range(4):
+		row = []
+		for k in range(4):
+			row.append(0)
+		grid.append(row)
+	return grid
+
+for i in range(37):
+	sum_ = i
+	grid = get_new_grid()
+	for row in grid:
+		for ele in row:
+			for j in range(10):
+				grid[row] = j
+
+
+

problem201to210/problem206.py

@@ -0,0 +1,25 @@
+# problem 206
+i = 1009950493
+while True:
+
+	print i 
+	isq = str(i ** 2)
+	if len(isq) == 19:
+		if isq[0] == '1':
+			if isq[2] == '2':
+				if isq[4] == '3':
+					if isq[6] == '4':
+						if isq[8] == '5':
+							if isq[10] == '6':
+								if isq[12] == '7':
+									if isq[14] == '8':
+										if isq[16] == '9':
+											if isq[18] == '0':
+												print "-----------"
+												print i
+												print isq
+												break
+	i += 1
+	if i == 1389026623:
+		break
+

problem211to220/problem213.py

@@ -0,0 +1,146 @@
+# problem 213
+# http://projecteuler.net/thread=213
+#First? I just calculated the probability of each flee being in each square after 50 rounds, and #summed the probability of each square being empty based on those probabilities. Runs in a little #under 4 seconds on my machine.
+'''import random
+
+trials = 10001
+totalcount = 0
+for k in range(trials):
+	
+	grid = []
+	for i in range(30):
+		row = []
+		for j in range(30):
+			row.append(1)
+		grid.append(row)
+	bells = 50
+	for i in range(bells):
+		for row in range(30):
+			for col in range(30):
+				ran = random.random()
+				grid[row][col] -=1
+				if row == 0:
+					if col == 0:
+						if ran < 1.0 / 2:
+							grid[row+1][col] += 1
+						else:
+							grid[row][col+1] += 1
+					if col == 29:
+						if ran < 1.0 / 2:
+							grid[row+1][col] += 1
+						else:
+							grid[row][col-1] += 1
+					else:
+						if ran < 1.0 / 3:
+							grid[row][col+1] += 1
+						elif ran < 2.0 /3:
+							grid[row][col-1] += 1	
+						else:
+							grid[row+1][col] += 1
+				elif row == 29:
+					if col == 0:
+						if ran < 1.0 / 2:
+							grid[row-1][col] += 1
+						else:
+							grid[row][col+1] += 1
+					if col == 29:
+						if ran < 1.0 / 2:
+							grid[row-1][col] += 1
+						else:
+							grid[row][col-1] += 1
+					else:
+						if ran < 1.0 / 3:
+							grid[row][col-1] += 1
+						elif ran < 2.0 /3:
+							grid[row][col+1] += 1	
+						else:
+							grid[row-1][col] += 1
+				else:
+					if col == 0:
+						if ran < 1.0 / 3:
+							grid[row-1][col] += 1
+						elif ran < 2.0 / 3:
+							grid[row][col+1] += 1
+						else: 
+							grid[row+1][col] += 1
+					if col == 29:
+						if ran < 1.0 / 3:
+							grid[row-1][col] += 1
+						elif ran < 2.0 / 3:
+							grid[row][col-1] += 1
+						else: 
+							grid[row+1][col] += 1
+					else:
+						if ran < 1.0 / 4:
+							grid[row][col-1] += 1
+						elif ran < 2.0 /4:
+							grid[row-1][col] += 1	
+						elif ran < 3.0 /4:
+							grid[row][col+1] += 1
+						else:	
+							grid[row+1][col] += 1
+	count = 0
+
+	for i in range(30):
+		for j in range(30):
+			if grid[i][j] == 0:
+				count += 1
+
+	print count
+	totalcount += count
+print float(totalcount ) / trials'''
+
+# ---
+grid = []
+dx = [-1,1,0,0]
+dy = [0,0,1,-1]
+for i in range(900):
+	mat0 = []
+	mat1 = []
+	for j in range(30):
+		row0 = []
+		row1 = []
+		for k in range(30):
+			row0.append(0.0)
+			row1.append(0.0)
+		mat0.append(row0)
+		mat1.append(row1)
+	grid.append([mat0,mat1])
+for f in range(900):
+	print f
+	grid[f][0][f%30][f/30] = 1.0;
+	for r in range(1,51):
+		cur = r % 2
+		prev = 1 - cur
+		newmat = []
+		for j in range(30):
+			row = []
+			for k in range(30):
+				row.append(0.0)
+			newmat.append(row)
+      		grid[f][cur] = newmat
+		for x in range(30):
+			for y in range(30):
+				tot = 4
+				if x == 0 or x == 29:
+					tot -= 1
+				if y == 0 or y == 29:
+					tot -= 1 
+				for d in range(4):
+					nx = x + dx[d]
+					ny = y + dy[d]
+					if nx < 0 or ny < 0 or nx >= 30 or ny >= 30:
+						continue
+					#print grid[f][prev][x][y] / float(tot)
+					grid[f][cur][nx][ny]  += grid[f][prev][x][y] / float(tot)
+ret = 0.0
+for x in range(30):
+	for y in range(30):
+		p = 1.0
+		for f in range(900):
+			p *= 1 - grid[f][0][x][y]
+		print p
+		ret += p
+
+
+print ret

problem241to250/problem243.py

@@ -0,0 +1,16 @@
+# problem 243
+#http://blog.dreamshire.com/2012/12/19/project-euler-problem-243-solution/
+primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
+ratio = 15499/94744.0
+
+def denom(ratio):
+  d, s = 1, 1
+  for p in primes:
+    d *= p
+    s *= p-1
+    for i in range(2, p):
+      if s*i / (d*i-1.) < ratio:
+        return d*i
+  return "Please buy more primes!"
+
+print 'Answer to PE243 = ',denom(ratio)

problem61to70/problem64.py

@@ -0,0 +1,35 @@
+# problem 64
+# http://www.mathblog.dk/project-euler-continued-fractions-odd-period
+import math
+
+def loop_length(n):
+	m = 0.0
+	d = 1.0
+	a = math.floor(math.sqrt(n))
+	S = float(n)
+	param_lst = [[m,d,a]]
+	loop_len = 0
+	for i in range(1000):
+		m1 = d * a - m 
+	#	print "m: " + str(m1)
+		d1 = (S - m1 ** 2) / d 
+	#	print "d: " + str(d1)
+		a1 = math.floor( (math.sqrt(S) + m1) / float(d1) )
+	#	print "a: " + str(a1)
+		if [m1,d1,a1] in param_lst:
+		# why we can instread check a1 == 2 * a0 here? 
+			return len(param_lst) - param_lst.index([m1,d1,a1])
+		d = d1
+		a = a1
+		m = m1
+		param_lst.append([m,d,a])
+
+count= 0
+
+for i in range(2,10001):
+	if math.sqrt(i) % 1 != 0:
+		#print "i: " + str(i)
+		lop_len = loop_length(i)		
+		if lop_len % 2 == 1:
+			count += 1
+print count

problem61to70/problem70.py

@@ -0,0 +1,41 @@
+# problem 70
+# http://www.mathblog.dk/project-euler-70-investigate-values-of-n-for-which-%CF%86n-is-a-permutation-of-n/
+
+phi_best = 1
+best = 1
+best_ratio = 100000000
+
+
+def is_prime(n):
+	for i in range(2,n):
+		if n % i == 0:
+			return False
+	return True
+
+limit = 10000000
+prime_lst = []
+for n in range(2000,5001):
+	if is_prime(n):
+		prime_lst.append(n)
+
+for i in prime_lst:
+	for j in prime_lst:
+		n = i * j 
+		if n > limit:
+			break
+		phi = (i - 1) * (j-1)
+		ratio = float(n) / phi
+		n_sort = list(str(n))
+		n_sort.sort()
+		phi_sort = list(str(phi))
+		phi_sort.sort()
+		if phi_sort == n_sort and best_ratio > ratio:
+			best = n
+			phi_best = phi
+			best_ratio = ratio
+
+
+print "best: "+ str(best)
+print "phi_best: " + str(phi_best)
+print "best_ratio: " + str(best_ratio)
+

problem71to80/problem73.py

@@ -12,7 +12,7 @@ def gcd(a,b):
 #count = 0
 for d in range(1,12001):
 	print d
-	for n in range(1,d):
+	for n in range((d-1)/3,(d+1)/2):
 		fn = float(n)
 		flag = True
 		if fn / d >= 1.0 / 2:

problem71to80/problem74.py

@@ -0,0 +1,52 @@
+# problem 74
+def factorial(n):
+	if n == 0:
+		return 1
+	elif n == 1:
+		return 1
+	elif n == 2:
+		return 2
+	elif n == 3:
+		return 6
+	elif n == 4:
+		return 24
+	elif n == 5:
+		return 120
+	elif n == 6:
+		return 720 
+	elif n == 7:
+		return 5040
+	elif n == 8:
+		return 40320
+	elif n == 9:
+		return 362880
+#len_lst = []
+total_count = 0
+for i in range(1,1000000):
+	print "-----------"
+	print i
+	dd = i
+	sum_ = 0
+	lst = []
+	while True:
+		sum_ = 0
+		for d in str(dd):
+			sum_ = sum_ + factorial(int(d))
+		if sum_  in lst:
+			#len_lst.append(len(lst))
+			if i == 78:
+				print "--------"
+				print lst
+				print "88888"
+			if len(lst) == 59:
+				total_count += 1
+				print "-->>>>>" + str(i)
+			break
+		lst.append(sum_)
+		dd = sum_
+print total_count
+
+#print "max: " +str( max(len_lst)	)
+
+
+