update pe and spoj

Author: coderxiang

ProjectEuler/Note~

@@ -0,0 +1,3 @@
+64: finding the period of convergent of sqrt (n).
+65: convergent continued fractions.
+66: pell equation.

ProjectEuler/p002.py

@@ -0,0 +1,8 @@
+import sys
+s , x, x1, x2= [0, 0, 1, 0];
+while x <= 4000000:
+	x = x1 + x2;
+	if x <= 4000000 and x % 2 == 0:
+		s += x;
+	x2 = x1; x1 = x; 
+print (s);

ProjectEuler/p003.py

@@ -0,0 +1,30 @@
+import sys;
+
+pm = [];
+st = [True]*1000001;
+
+pm.append (2);
+for i in xrange (4, 1000001, 2):
+	st[i] = False;
+for i in xrange (3, 1000001, 2):
+	if st[i] == True:
+		pm.append (i);
+		for j in range (long(i * i), 1000001L, i):
+			st[j] = False;
+
+while True:
+	n = input ();
+	ans = 2;
+	for x in pm:
+		while n % x == 0:
+			n /= x;
+			ans = x;
+	if n != 1:
+		ans = n;
+	print ans;
+	
+
+	
+
+
+	

ProjectEuler/p004.py

@@ -0,0 +1,11 @@
+ans = -1;
+for i in range (999, 99, -1):
+	for j in range (999, 99, -1):
+		t = i * j;
+		s = str(t);
+		if s == s[::-1] and t > ans:
+			ans = t;
+print (ans);
+
+	
+

ProjectEuler/p005.py

@@ -0,0 +1,13 @@
+def gcd (x, y):
+	r = x % y;
+	while r != 0:
+		x = y;
+		y = r;
+		r = x % y;
+	return y
+
+ans = 1;
+for i in range (2, 21):
+	ans = i * ans / gcd (i, ans);
+	
+print (ans);

ProjectEuler/p006.py

@@ -0,0 +1,5 @@
+a = 0; b = 0;
+for i in range (101):
+	a += i**2;
+	b += i;
+print (b**2 - a);

ProjectEuler/p048.py

@@ -0,0 +1,5 @@
+md = 10000000000;
+ans = 0;
+for i in range (1, 1001):
+	ans += i ** i;
+print (ans % md);

ProjectEuler/p052.py

@@ -0,0 +1,19 @@
+def chk (x) :
+	lst = [];
+	for i in xrange (2, 7):
+		lst.append (''.join(sorted (str (i * x))))
+	ans = True;
+	
+	for i in xrange (0, 5):
+		if i < 4 and lst[i] != lst[i+1]:
+			ans = False;
+			break
+	return ans;
+	
+for i in xrange (1, 10000000000):
+	if chk (i):
+		ans = i;
+		break
+
+print ans;
+

ProjectEuler/p064.py

@@ -0,0 +1,98 @@
+import math
+def Pell (n, a0):
+
+	p0, p1, q0, q1 = 0, 1, 1, 0;
+	g, h = 0, 1;
+	a = a0;
+	while True:
+		p = a * p1 + p0;
+		q = a * q1 + q0;
+		if p * p - n * q * q == 1:
+			return p, q
+
+		p0 = p1; p1 = p;
+		q0 = q1; q1 = q;
+		
+		g = -g + a * h;
+		h = (n - g * g) / h;
+		a = (g + a0) // h;
+
+# calculate the period of the continued fractions of sqrt (n)
+def CalCFPeriod (n):
+	rt = math.sqrt (n);
+	a0 = int (rt);
+	p0, p1, q0, q1 = 0, 1, 1, 0;
+	g, h = 0, 1;
+	a, cnt = a0, 0;
+	
+	while True:
+		p, q = a * p1 + p0, a * q1 + q0;
+		p0 = p1; p1 = p; q0 = q1; q1 = q;
+		g = a * h - g; h = (n - g * g) / h;
+		cnt += 1;
+		a = (g + a0) // h;
+		t = (g + rt) / h;
+		if cnt == 1:
+			num = t * t;
+		elif t * t == num:
+			return cnt - 1
+		
+# How to compute CF for any irrational number to arbitrary precision ?
+
+def ProjectEuler66 ():
+	ma = -1; ans = -1;
+	for n in xrange (1, 1001):
+		a0 = int  (math.floor (math.sqrt (n)));
+		if a0 * a0 == n:
+			continue
+		
+		x, y = Pell (n, a0);
+		print n, x;
+		if x > ma:
+			ma = x;
+			ans = n;
+			
+	print ans;
+
+def ProjectEuler65 ():
+	v = math.e
+	a0 = int (v);
+
+	p0, p1, q0, q1 = 1, a0, 0, 1;
+	k = 0;
+	for i in xrange (1, 100):
+		a = 1;
+		if i % 3 == 2:
+			k += 2;
+			a = k;
+
+		p , q = a * p1 + p0, a * q1 + q0;
+		p0 = p1; p1 = p; q0 = q1; q1 = q;
+		
+	k = 0; x = int (p);
+	while x != 0:
+		k += x % 10;
+		x //= 10;
+	print k
+
+
+	
+def ProjectEuler64 ():
+	ans = 0;
+	for i in xrange (1, 10001):
+		rt = int (math.sqrt (i));
+		if rt * rt == i:
+			continue
+		x = CalCFPeriod (i);
+		if x & 1:
+			ans += 1
+	print ans
+
+if __name__ == "__main__":
+	ProjectEuler64 ();
+
+		
+
+
+
+

ProjectEuler/p065.py

@@ -0,0 +1,66 @@
+import math
+def Pell (n, a0):
+
+	p0, p1, q0, q1 = 0, 1, 1, 0;
+	g, h = 0, 1;
+	a = a0;
+	while True:
+		p = a * p1 + p0;
+		q = a * q1 + q0;
+		if p * p - n * q * q == 1:
+			return p, q
+
+		p0 = p1; p1 = p;
+		q0 = q1; q1 = q;
+		
+		g = -g + a * h;
+		h = (n - g * g) / h;
+		a = (g + a0) // h;
+
+
+# How to compute CF for any irrational number to arbitrary precision ?
+
+def ProjectEuler66 ():
+	ma = -1; ans = -1;
+	for n in xrange (1, 1001):
+		a0 = int  (math.floor (math.sqrt (n)));
+		if a0 * a0 == n:
+			continue
+		
+		x, y = Pell (n, a0);
+		print n, x;
+		if x > ma:
+			ma = x;
+			ans = n;
+			
+	print ans;
+
+def ProjectEuler65 ():
+	v = math.e
+	a0 = int (v);
+
+	p0, p1, q0, q1 = 1, a0, 0, 1;
+	k = 0;
+	for i in xrange (1, 100):
+		a = 1;
+		if i % 3 == 2:
+			k += 2;
+			a = k;
+
+		p , q = a * p1 + p0, a * q1 + q0;
+		p0 = p1; p1 = p; q0 = q1; q1 = q;
+		
+	k = 0; x = int (p);
+	while x != 0:
+		k += x % 10;
+		x //= 10;
+	print k
+
+if __name__ == "__main__":
+	ProjectEuler65 ();
+
+		
+
+
+
+

ProjectEuler/p066.py

@@ -0,0 +1,66 @@
+import math
+def Pell (n, a0):
+
+	p0, p1, q0, q1 = 0, 1, 1, 0;
+	g, h = 0, 1;
+	a = a0;
+	while True:
+		p = a * p1 + p0;
+		q = a * q1 + q0;
+		if p * p - n * q * q == 1:
+			return p, q
+
+		p0 = p1; p1 = p;
+		q0 = q1; q1 = q;
+		
+		g = -g + a * h;
+		h = (n - g * g) / h;
+		a = (g + a0) // h;
+
+
+# How to compute CF for any irrational number to arbitrary precision ?
+
+def ProjectEuler66 ():
+	ma = -1; ans = -1;
+	for n in xrange (1, 1001):
+		a0 = int  (math.floor (math.sqrt (n)));
+		if a0 * a0 == n:
+			continue
+		
+		x, y = Pell (n, a0);
+		print n, x;
+		if x > ma:
+			ma = x;
+			ans = n;
+			
+	print ans;
+
+def ProjectEuler65 ():
+	v = math.e
+	a0 = int (v);
+
+	p0, p1, q0, q1 = 1, a0, 0, 1;
+	k = 0;
+	for i in xrange (1, 100):
+		a = 1;
+		if i % 3 == 2:
+			k += 2;
+			a = k;
+
+		p , q = a * p1 + p0, a * q1 + q0;
+		p0 = p1; p1 = p; q0 = q1; q1 = q;
+		
+	k = 0; x = int (p);
+	while x != 0:
+		k += x % 10;
+		x //= 10;
+	print k
+
+if __name__ == "__main__":
+	ProjectEuler65 ();
+
+		
+
+
+
+

ProjectEuler/p081.py

@@ -0,0 +1,14 @@
+import urllib
+
+fin = urllib.urlopen ('http://projecteuler.net/project/matrix.txt');
+a = [];
+for cnt in xrange (80):
+	a.append (map (int, fin.readline().split (',')))
+
+d = [ [100000000000000 for i in xrange (81)] for j in xrange (81)];
+d[0][1] = 0;
+for i in xrange (1, 81):
+	for j in xrange (1, 81):
+		d[i][j] = min (d[i][j - 1], d[i - 1][j]) + a[i-1][j-1];
+print d[80][80];
+