solution to hotdate

Author: joshmcgrath08

solutions/joshmcgrath08/hotdate.py

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+#!/usr/bin/env python
+
+# Josh McGrath
+# Solution to http://puzzles.bostonpython.com/hotdate.html
+# Tested with: Python 2.7.6
+
+# Consider these base-10 digits: 123456789. If you insert spaces between them, you get various sequences of numbers:
+
+# 1 2 3 4 5 6 7 8 9
+# 12 3 4 5 67 8 9
+# 1 2 34 5 6 7 89
+# 12 34 56 78 9
+# 1 23456 78 9
+# 12345 6789
+# etc.
+
+from itertools import *
+
+# 1) Write a program that generates all possible combinations of those digits.
+
+digits = map (str, range (1, 10))
+
+# alternate the elements of two lists, until both lists exhausted
+def alternate (l1, l2):
+    len_l1 = len (l1)
+    len_l2 = len (l2)
+    l = []
+    for i in range (max (len_l1, len_l2)):
+        if i < len_l1:
+            l.append(l1[i])
+        if i < len_l2:
+            l.append(l2[i])
+    return l
+
+assert (alternate ([], []) == [])
+assert (alternate ([1, 2, 3], [4, 5]) == [1, 4, 2, 5, 3])
+assert (alternate ([4, 5], [1, 2, 3]) == [4, 1, 5, 2, 3])
+
+# given a list of strings and an iterator to strings, return
+# an iterator to strings where a value from the iterator arg is
+# inserted between each adjacent pairs of elements in the list arg
+def itr_intersperse (l, itr):
+    for x in product (itr, repeat=len (l) - 1):
+        yield ''.join(alternate (l, x))
+
+# # How many are there?
+
+def itr_len (itr):
+    c = 0
+    for i in itr:
+        c += 1
+    return c
+
+print itr_len (itr_intersperse (digits, ['', ' ']))
+
+# Now let's insert a maximum of 8 addition or subtraction operators between the numbers, like this:
+
+# 1+2+3+4+5+6+7-8+9
+# 12-3+4+5-67-8+9
+# 1+2+34+5-6-7-89
+# 12-34+56+78+9
+# 1+23456-78-9
+# 12345+6789
+# etc.
+
+# Notice that those arithmetic expressions equate to different values:
+
+# 1+2+3+4+5+6+7-8+9 = 29
+# 12-3+4+5-67-8+9 = -48
+# 1+2+34+5-6-7-89 = -60
+# 12-34+56+78+9 = 121
+# 1+23456-78-9 = 23370
+# 12345+6789 = 19134
+# etc.
+
+# 2) Write a program that generates all possible expressions in this way.
+
+# returns an iterator to expressions that sum to n
+def expr_sum (n):
+    return ifilter (lambda x: eval(x) == n, itr_intersperse (digits, ['', '+', '-']))
+
+# How many sum to 100?
+print itr_len (expr_sum (100))
+
+# 3) Write a program that finds all such expressions for any sum.
+
+# Which sum is the most popular, i.e. has the most expressions?
+sums = map (eval, itr_intersperse (digits, ['', '+', '-']))
+
+from collections import Counter
+
+sum_counter = Counter ()
+for s in sums:
+    sum_counter[s] += 1
+
+print sum_counter.most_common(1)[0][0]
+
+# 4) Bonus: We can haz pretty data viz?
+
+# Like how about a histogram of the number of expressions with sums from -23456788 to 123456789. (A log scale might help. Maybe binning, too.)
+
+from matplotlib.pyplot import hist, show, bar
+
+show (hist (sums, range = (-23456788, 123456789), bins = 50, normed = True, log = True))