6/25/24 assignment math 480

6_18_2024_catalan/catalan.py

@@ -1,12 +1,14 @@
 import itertools
 
+
 def parenthesizations(n):
   """
   Returns a set of all possible parenthesizations of length n.
 
   Parameters:
     n (int): The length of the parenthesizations.
-
+  """
+  """
   Returns:
     A set of strings, where each inner string represents a valid parenthesization of length n.
 
@@ -17,16 +19,20 @@ def parenthesizations(n):
   if n == 0:
     return {""}
   else:
-    # TODO
-    pass
+    result = set()
+    for i in range(n):
+      for left in parenthesizations(i):
+          for right in parenthesizations(n - 1 - i):
+              result.add('(' + left + ')' + right)
+    return result
+
 
 def product_orders(n):
   """
   Returns a set of all possible ways to multiply of n elements.
 
   Parameters:
-    n (int): The number of elements multiplied.
-
+    n (int):  The number of elements multiplied.
   Returns:
     A set of strings where each string represents a way to multiply n elements.
 
@@ -41,8 +47,17 @@ def product_orders(n):
   elif n == 2:
     return {"?*?"}
   else:
-    # TODO
-    pass
+    result = set()
+    for i in range(1, n):
+      for left in product_orders(i):
+          for right in product_orders(n - i):
+              if left == '?':
+                result.add(left+ '*(' + right + ')')
+              elif right == '?':
+                result.add('(' + left + ')*' + right)
+              else:
+                result.add('('+ left +')*('+ right+')')
+    return result
 
 def permutations_avoiding_231(n):
   """
@@ -61,8 +76,20 @@ def permutations_avoiding_231(n):
   if n < 3:
     return set(itertools.permutations(range(1, n+1)))
   else:
-    # TODO
-    pass
+    result = set()
+
+    for i in set(itertools.permutations(range(1, n+1))):
+      result.add(i)  
+      for j in range(2, n):
+          for k in range(j):
+              if i[k] > i[j]:
+                  for l in range(k+1, j):
+                      if i[l] > i[j] and i[l] > i[k]:
+                          result.add(i)
+                          result.remove(i)
+
+    return result  
+
 
 def triangulations(n):
   """
@@ -76,13 +103,32 @@ def triangulations(n):
     A set of tuple of pairs, where each pair represents an internal edge in the triangulation.
 
   Example:
-  >>> triangulations(3)
+  >>> triangulations(5)
   {((0, 3), (1, 3)), ((1, 4), (2, 4)), ((1, 3), (1, 4)), ((0, 2), (2, 4)), ((0, 2), (0, 3))}
   """
   if n < 3:
     return set()
   elif n == 3:
     return {tuple()}
   else:
-    pass
-    # TODO
+    result = set()
+    for i in range(n-2):
+      for j in range(i+2, n):
+        if i != 0 or j != n-1:
+          edge = (i, j)
+          polygon1_size = j-i+1
+          polygon2_size = n-(j-i)+1
+          for polygon1 in triangulations(polygon1_size):
+            for polygon2 in triangulations(polygon2_size):
+              modfied_polygon2 = tuple()
+              for (k,l) in polygon2:
+                k= (i-k)%n
+                l= (i-l)%n
+                smaller = min(k,l)
+                larger = max(k,l)
+                modfied_polygon2 += ((smaller,larger),)
+                result.add(tuple(sorted(polygon1 + (edge,) + ((smaller,larger),))))
+          result.add(tuple(sorted(polygon1 + modfied_polygon2 + (edge,))))
+    return result
+
+

6_20_2024_SYT/main.ipynb

@@ -116,7 +116,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.5"
+   "version": "3.11.9"
   }
  },
  "nbformat": 4,

6_25_2024_parenthesization_pytorch/data/parenthesizations_1.csv

@@ -0,0 +1,5 @@
+parenthesization,valid
+(),1
+)(,0
+((,0
+)),0

6_25_2024_parenthesization_pytorch/data/parenthesizations_2.csv

@@ -0,0 +1,17 @@
+parenthesization,valid
+()(),1
+(()),1
+)))(,0
+())(,0
+)(((,0
+))(),0
+(((),0
+()((,0
+)()(,0
+)((),0
+(()(,0
+())),0
+((((,0
+))((,0
+)))),0
+)()),0

6_25_2024_parenthesization_pytorch/data/parenthesizations_3.csv

@@ -0,0 +1,65 @@
+parenthesization,valid
+()()(),1
+()(()),1
+(())(),1
+(()()),1
+((())),1
+))))((,0
+())()(,0
+()((((,0
+)))()(,0
+()()((,0
+))((((,0
+)()))),0
+()(((),0
+)))((),0
+)(((((,0
+)())(),0
+))(()(,0
+)(()(),0
+())(((,0
+)()((),0
+()(()(,0
+))()((,0
+)((()(,0
+)))(((,0
+)()(((,0
+(((()),0
+()())(,0
+)))))(,0
+())))(,0
+((())(,0
+(()))),0
+(((((),0
+(()()(,0
+())))),0
+))()(),0
+(())((,0
+())()),0
+)(())),0
+((()((,0
+))())(,0
+(()(((,0
+(()((),0
+()))(),0
+()())),0
+)(()((,0
+()))((,0
+))))(),0
+)((((),0
+)))()),0
+)())((,0
+((()(),0
+)))))),0
+)()))(,0
+)()()(,0
+))(()),0
+(()))(,0
+())((),0
+)()()),0
+)(())(,0
+)((()),0
+))())),0
+(((()(,0
+((((((,0
+))(((),0