Update basic-calculator-iv.py

Python/basic-calculator-iv.py

@@ -5,6 +5,62 @@
 #        to_list:  O(d * tlogt)
 # Space: O(e + d * t), e is the number of evalvars
 
+# Given an expression such as expression = "e + 8 - a + 5" and
+# an evaluation map such as {"e": 1} (given in terms of evalvars = ["e"] and evalints = [1]),
+# return a list of tokens representing the simplified expression, such as ["-1*a","14"]
+# - An expression alternates chunks and symbols, with a space separating each chunk and symbol.
+# - A chunk is either an expression in parentheses, a variable, or a non-negative integer.
+# - A variable is a string of lowercase letters (not including digits.)
+#   Note that variables can be multiple letters, and note that variables never
+#   have a leading coefficient or unary operator like "2x" or "-x".
+#
+# Expressions are evaluated in the usual order:
+# brackets first, then multiplication, then addition and subtraction. 
+# For example, expression = "1 + 2 * 3" has an answer of ["7"].
+#
+# The format of the output is as follows:
+# - For each term of free variables with non-zero coefficient,
+#   we write the free variables within a term in sorted order lexicographically.
+#   For example, we would never write a term like "b*a*c", only "a*b*c".
+# - Terms have degree equal to the number of free variables being multiplied,
+#   counting multiplicity. (For example, "a*a*b*c" has degree 4.)
+#   We write the largest degree terms of our answer first,
+#   breaking ties by lexicographic order ignoring the leading coefficient of the term.
+# - The leading coefficient of the term is placed directly to the left with an asterisk separating it 
+#   from the variables (if they exist.) A leading coefficient of 1 is still printed.
+# - An example of a well formatted answer is ["-2*a*a*a", "3*a*a*b", "3*b*b", "4*a", "5*c", "-6"] 
+# - Terms (including constant terms) with coefficient 0 are not included.
+#    For example, an expression of "0" has an output of [].
+#
+# Examples:
+#
+# Input: expression = "e + 8 - a + 5", evalvars = ["e"], evalints = [1]
+# Output: ["-1*a","14"]
+#
+# Input: expression = "e - 8 + temperature - pressure",
+# evalvars = ["e", "temperature"], evalints = [1, 12]
+# Output: ["-1*pressure","5"]
+#
+# Input: expression = "(e + 8) * (e - 8)", evalvars = [], evalints = []
+# Output: ["1*e*e","-64"]
+#
+# Input: expression = "7 - 7", evalvars = [], evalints = []
+# Output: []
+#
+# Input: expression = "a * b * c + b * a * c * 4", evalvars = [], evalints = []
+# Output: ["5*a*b*c"]
+#
+# Input: expression = "((a - b) * (b - c) + (c - a)) * ((a - b) + (b - c) * (c - a))",
+# evalvars = [], evalints = []
+# Output: 
+# ["-1*a*a*b*b","2*a*a*b*c","-1*a*a*c*c","1*a*b*b*b","-1*a*b*b*c","-1*a*b*c*c",
+#  "1*a*c*c*c","-1*b*b*b*c","2*b*b*c*c","-1*b*c*c*c","2*a*a*b","-2*a*a*c","-2*a*b*b",
+#  "2*a*c*c","1*b*b*b","-1*b*b*c","1*b*c*c","-1*c*c*c","-1*a*a","1*a*b","1*a*c","-1*b*c"]
+#
+# Note:
+# - expression will have length in range [1, 1000].
+# - evalvars, evalints will have equal lengths in range [0, 1000].
+
 class Poly(collections.Counter):
     def __init__(self, expr=None):
         if expr is None: