diff --git a/assignment2/csp.py b/assignment2/csp.py
index c7c0d61..9dbd3be 100644
--- a/assignment2/csp.py
+++ b/assignment2/csp.py
@@ -58,9 +58,16 @@ class CSP:
         """
 
         def revise(csp, xi, xj) -> bool:
+            """Reduce the domain of xi if possible
+
+            Returns
+            -------
+            bool
+                Whether or not there was a domain reduction
+            """
             revised = False
             for x in set(csp.domains[xi]):
-                if not any(
+                if not any(  # translation of algorithm's forall expression.
                     [
                         (x, y) in csp.binary_constraints[(xi, xj)]
                         for y in csp.domains[xj]
@@ -97,39 +104,57 @@ class CSP:
             A solution if any exists, otherwise None
         """
 
-        def backtrack(csp, assignment: dict[str, Any]) -> dict | None:
+        def backtrack(csp, assignment: dict[str, Any]) -> dict[str, Any] | None:
+            """The recursive engine of backtracking_search.
+
+            Returns
+            -------
+            dict[str, Any]
+                The solution to bubble up
+            None
+                If current branch has no solution
+            """
+            # this is read from stdout in sudoku.py. important to 2c).
+            # yes, it couldv'e been done differently, but this is
+            # quick and unintrusive.
             print("i have been called")
-            if len(assignment) == len(csp.variables):
+            if len(assignment) == len(csp.variables):  # completion condition
                 return assignment  # base-case
             var = select_unassigned_variable(csp, assignment)
             for value in order_domain_values(csp, var, assignment):
                 if not consistent(csp, var, value, assignment):
-                    continue
+                    continue  # do nothing (skip iteration)
                 assignment[var] = value
                 if result := backtrack(csp, assignment):
-                    return result
+                    return result  # return if not failure
                 assignment.pop(var)
             print("i have failed")
             return None  # failure
 
         def consistent(csp, var, value, assignment) -> bool:
+            """Helper function to determine if an arc is consistent"""
             for v in assignment:
                 if (var, v) in csp.binary_constraints.keys():
                     if (value, assignment[v]) not in csp.binary_constraints[(var, v)]:
                         return False
-                if (v, var) in csp.binary_constraints.keys():
+                if (v, var) in csp.binary_constraints.keys():  # bi-birectional
                     if (value, assignment[v]) not in csp.binary_constraints[(v, var)]:
                         return False
             return True
 
         def select_unassigned_variable(csp, assignment) -> str:
+            """Helper function to find a variable that is yet to be assigned."""
             for v in csp.variables:
                 if v not in assignment.keys():
                     return v
             return "this shouldn't happen"
 
-        # choose least constrained value
         def order_domain_values(csp, var, assignment) -> list[Any]:
+            """Helper function to order the domain values.
+            Orders on the least constrained value
+            """
+
+            # calculate a sorting key by counting constraints
             def compare(value) -> int:
                 s = 0
                 for neighbor in [
@@ -145,7 +170,7 @@ class CSP:
 
             return sorted(list(csp.domains[var]), key=compare)
 
-        return backtrack(self, {})
+        return backtrack(self, {})  # start with no assignments
 
 
 def alldiff(variables: list[str]) -> list[tuple[str, str]]:
diff --git a/assignment2/delivery.pdf b/assignment2/delivery.pdf
index 92ac6f8..8394388 100644
Binary files a/assignment2/delivery.pdf and b/assignment2/delivery.pdf differ