From 919908818968995635d4f339d622699a827e17f7 Mon Sep 17 00:00:00 2001
From: William Ball <wball1@swarthmore.edu>
Date: Sat, 4 Jul 2020 12:15:24 -0700
Subject: [PATCH] initial commit

---
 insert_digit_anywhere_squares.py | 65 ++++++++++++++++++++++++++++++++
 1 file changed, 65 insertions(+)
 create mode 100644 insert_digit_anywhere_squares.py

diff --git a/insert_digit_anywhere_squares.py b/insert_digit_anywhere_squares.py
new file mode 100644
index 0000000..cbca191
--- /dev/null
+++ b/insert_digit_anywhere_squares.py
@@ -0,0 +1,65 @@
+import math
+
+class Tree:
+    def __init__(self, value, children):
+        self.value = value
+        self.children = []
+        for child in children:
+            self.children.append(Tree(child, []))
+
+    def step(self):
+        if len(self.children) == 0:
+            for val in step(self.value):
+                self.children.append(Tree(val, []))
+            return
+        for child in self.children:
+            child.step()
+
+    def __str__(self):
+        retval = '[' + str(self.value) + ': '
+        for child in self.children:
+            retval += str(child)
+        retval += ']'
+        return retval
+        #return str(self.value) + ': ' + str([str(child) for child in self.children])
+
+    def __repr__(self):
+        return str(self)
+
+    def longest_path(self):
+        if len(self.children) == 0:
+            return [self.value]
+        max_path = []
+        max_length = 0
+        for child in self.children:
+            temp = child.longest_path()
+            if len(temp) > max_length:
+                max_path = temp
+                max_length = len(temp)
+        return [self.value] + max_path
+
+def is_square(x):
+    return int(math.sqrt(x)) == math.sqrt(x)
+
+def step(x):
+    new_xs = []
+    str_x = str(x)
+    for (i,digit) in enumerate(str_x + '0'):
+        for d in range(0,10):
+            temp = str_x[:i] + str(d) + str_x[i:]
+            if not (i == 0 and d == 0):
+                if is_square(int(temp)):
+                    new_xs.append(int(temp))
+    return new_xs
+
+
+def main():
+    tree = Tree(0, [1,4,9])
+    for i in range(200):
+        tree.step()
+    print(tree)
+    print(tree.longest_path())
+
+
+if __name__ == '__main__':
+    main()