From 751e369a9900d05f266b88e106113715dee1bf27 Mon Sep 17 00:00:00 2001
From: "GASSER Thibaud (PRESTA EXT)" <thibaud.gasser@externe.e-i.com>
Date: Wed, 24 Jan 2024 17:14:24 +0100
Subject: [PATCH] [wip]: simplifying multilinear polynomials

---
 simplify-poly/solution.py | 87 +++++++++++++++++++++++++++++++++++++++
 simplify-poly/tests.py    | 24 +++++++++++
 2 files changed, 111 insertions(+)
 create mode 100644 simplify-poly/solution.py
 create mode 100644 simplify-poly/tests.py

diff --git a/simplify-poly/solution.py b/simplify-poly/solution.py
new file mode 100644
index 0000000..366e030
--- /dev/null
+++ b/simplify-poly/solution.py
@@ -0,0 +1,87 @@
+# https://www.codewars.com/kata/55f89832ac9a66518f000118/
+
+import re
+from dataclasses import dataclass
+
+@dataclass
+class Term:
+    coef: int
+    variables: str
+    
+    def __repr__(self):
+        return f"Term(coef={self.coef}, vars={self.variables})"
+    
+    def __str__(self):
+        a = str(self.coef) if self.coef != 1 else ""
+        a = "-" if a == "-1" else a
+        b = "".join(self.variables)
+        return f"{a}{b}"
+
+    def __add__(self, other):
+        print(f"add {self} {other}")
+        if self.variables == other.variables:
+            r = Term(self.coef+other.coef, self.variables)
+            print(r)
+            return r
+        else:
+            print(self.variables, other.variables)
+        raise ArithmeticError("Variables do not match")
+
+    def __lt__(self, other):
+        return (len(self.variables) < len(other.variables)) and (self.variables < other.variables)
+    
+    def __eq__(self, other):
+        return self.coef == other.coef and self.variables == other.variables
+
+
+def parse_term(inp: str) -> Term:
+    sign, coef, variables = '', [], []
+    for n in inp:
+        if n == '-':
+            sign = '-'
+        elif n.isnumeric():
+            coef.append(n)
+        elif n.isalpha():
+            variables.append(n) 
+    
+    c = -1 if sign == '-' else 1
+    c *= int("".join(coef)) if coef else 1
+    return Term(c, sorted(variables))
+
+
+def simplify(poly):
+    print(poly)
+    
+    # parse
+    pattern = r"([+-]?\d*\w+)"
+    terms = sorted(parse_term(t) for t in re.findall(pattern, poly))
+    
+    print(terms)
+    
+    # simplify
+    simplified_terms = []
+    for term in terms:
+        if not simplified_terms:
+            simplified_terms.append(term)
+            continue
+
+        previous = simplified_terms.pop()
+        try:
+            res = previous + term
+            if res.coef != 0:
+                simplified_terms.append(res)
+        except ArithmeticError as e:
+            print("no match")
+            simplified_terms.append(previous)
+            simplified_terms.append(term)
+    
+    # build output str
+    res = ""
+    for term in simplified_terms:
+        s = str(term)
+        if res and not s.startswith("-"):
+            res += "+"
+            res += s
+        else:
+            res += s
+    return res
diff --git a/simplify-poly/tests.py b/simplify-poly/tests.py
new file mode 100644
index 0000000..aa5ac53
--- /dev/null
+++ b/simplify-poly/tests.py
@@ -0,0 +1,24 @@
+import codewars_test as test
+from solution import simplify
+
+test.it("Test reduction by equivalence")
+test.assert_equals(simplify("dc+dcba"), "cd+abcd")
+
+test.assert_equals(simplify("2xy-yx"),"xy")
+
+test.assert_equals(simplify("-a+5ab+3a-c-2a"),"-c+5ab")
+
+test.it("Test monomial length ordering")
+test.assert_equals(simplify("-abc+3a+2ac"),"3a+2ac-abc")
+
+test.assert_equals(simplify("xyz-xz"),"-xz+xyz")
+
+test.it("Test lexicographic ordering")
+test.assert_equals(simplify("a+ca-ab"),"a-ab+ac")
+
+test.assert_equals(simplify("xzy+zby"),"byz+xyz")
+
+test.it("Test no leading +")
+test.assert_equals(simplify("-y+x"),"x-y")
+
+test.assert_equals(simplify("y-x"),"-x+y")
\ No newline at end of file