From 61ac578636f98c03b5b17ca8004e34e6141ffe3d Mon Sep 17 00:00:00 2001
From: "xw_y_am@rmbp" <xw_y_am@163.com>
Date: Tue, 15 Aug 2017 23:43:36 +0800
Subject: [PATCH] update 91, 92

---
 python/91.py            | 37 ++++++++--------
 python/92.py            | 98 ++++++++++++++++++++---------------------
 python/tools/algebra.py |  6 +++
 3 files changed, 71 insertions(+), 70 deletions(-)
 create mode 100644 python/tools/algebra.py

diff --git a/python/91.py b/python/91.py
index c111985..602a99b 100644
--- a/python/91.py
+++ b/python/91.py
@@ -1,25 +1,24 @@
-from sys import argv
 
-n = int(argv[1])
-total = 3 * n ** 2
+from tools import number_theory
 
-if n % 2 == 0:
-  total += n
+def cnt_side(limit):
+    return limit ** 2 * 3
 
-total += (n - 1) / 2 * n
+def cnt_cross(limit):
+    return (limit - 1) // 2 * limit + (1 - limit % 2) * limit
 
-def gcd(x, y):
-  if y == 0:
-    return x
-  return gcd(y, x % y)
+def cnt_inner(limit):
+    tale = 0
+    for y in range(1, limit - 1):
+        for x in range(y + 1, limit + 1):
+            d = number_theory.gcd(x, y)
+            dx = x // d
+            dy = y // d
+            tale += min((limit - x) // dy, y // dx)
+            tale += min((limit - y) // dx, x // dy)
+    return 2 * tale
 
-for i in xrange(1, n - 1):
-  for j in xrange(i + 1, n + 1):
-    d = gcd(i, j)
-    i_ = i / d
-    j_ = j / d
-    total += min((n - i) / j_, j / i_) * 2
-    total += min((n - j) / i_, i / j_) * 2
+def count(limit):
+    return cnt_side(limit) + cnt_cross(limit) + cnt_inner(limit)
 
-
-print total
+print(count(50))
diff --git a/python/92.py b/python/92.py
index e556835..e1b2c4c 100644
--- a/python/92.py
+++ b/python/92.py
@@ -1,58 +1,54 @@
-maxx = 7
+import time
+from functools import reduce
+from tools import algebra
 
-def make_iter(x, a, l, lis):
-  for i in xrange(a % 10, 10):
-    if l == x - 1:
-      lis.append(a * 10 + i)
+def jump(num):
+    if 9 > num % 10:
+        return 1
     else:
-      make_iter(x, a * 10 + i, l + 1, lis)
+        num += 1
+        offset = 0
+        while not num % 10:
+            num //= 10
+            offset += 1
+        return 1 + (10 ** offset - 1) // 9 * (num % 10)
 
-def make(x):
-  if x == 1:
-    return [1,2,3,4,5,6,7,8,9]
-  out = []
-  for i in xrange(1, 10):
-    make_iter(x - 1, i, 0, out)
-  return out
+def gen_pick(digit):
+    maxi = 10 ** (digit + 1) - 1
+    num = maxi // 9
+    while num < maxi:
+        yield num
+        num += jump(num)
+    yield maxi
 
-#print make(5)
+def judge(num):
+    while True:
+        a = 0
+        while num != 0:
+            a += (num % 10) ** 2
+            num //= 10
+        if a == 1:
+            return False
+        elif a == 89:
+            return True
+        else:
+            num = a
 
-def calc(x):
-  while 1:
-    a = 0
-    while x != 0:
-      a += (x % 10) ** 2
-      x /= 10
-    if a == 1 or a == 89:
-      return a
-    else:
-      x = a
+def count(limit, s_num):
+    total = 1
+    for i in range(len(s_num)):
+        total *= (limit - i)
+    for ch in set(list(s_num)):
+        total //= algebra.factorial(s_num.count(ch))
+    return total
 
-#print calc(44)
+def statistic(limit):
+    total = 0
+    for digit in range(limit):
+        for num in gen_pick(digit):
+            if judge(num):
+                total += count(limit, str(num))
+    return total
 
-def fac(x):
-  out = 1
-  for i in xrange(2, x + 1):
-    out *= i
-  return out
-
-def alanum(x):
-  x = str(x)
-  out = 1
-  for i in xrange(maxx, maxx - len(x), -1):
-    out *= i
-  for i in set('.'.join(x).split('.')):
-    tmp = x.count(i)
-    if tmp > 1:
-      out /= fac(tmp)
-  return out
-
-#print alanum(113)
-
-count = 0
-for length in xrange(1, maxx + 1):
-  tmp = make(length)
-  for xx in tmp:
-    if calc(xx) == 89:
-      count += alanum(xx)
-print count
+print(statistic(7))
+print(time.process_time())
diff --git a/python/tools/algebra.py b/python/tools/algebra.py
new file mode 100644
index 0000000..c2cc446
--- /dev/null
+++ b/python/tools/algebra.py
@@ -0,0 +1,6 @@
+
+def factorial(n, multi=1):
+    if 1 == n:
+        return multi
+    else:
+        return factorial(n - 1, multi * n)