M. Nguyen - Dynamic Programming

.vscode/settings.json

@@ -0,0 +1,7 @@
+{
+    "python.testing.pytestArgs": [
+        "tests"
+    ],
+    "python.testing.unittestEnabled": false,
+    "python.testing.pytestEnabled": true
+}

lib/max_subarray.py

@@ -9,4 +9,16 @@ def max_sub_array(nums):
         return 0
     if len(nums) == 0:
         return 0
-    pass
+
+    # default both variables to the first index b/c the first index is the max value and max ending thus far
+    max_so_far = nums[0]
+    max_ending_here = nums[0]
+
+    for i in range(1, len(nums)):
+
+        max_ending_here = max(max_ending_here + nums[i], nums[i])
+
+        # continue updating value of variable as we itr
+        max_so_far = max(max_so_far, max_ending_here)
+
+    return max_so_far

lib/newman_conway.py

@@ -7,4 +7,31 @@ def newman_conway(num):
         Time Complexity: ?
         Space Complexity: ?
     """
-    pass
+    # <-------- NEWMAN CONWAY CONCEPT --------> 
+    # P(1) = 1
+    # P(2) = 1
+    # for all n > 2
+    # P(n) = P(P(n - 1)) + P(n - P(n - 1))
+
+    # base case -> if num is either 0 or 1
+    if num == 0:
+        raise ValueError
+    if num == 1:
+        return '1'
+
+    # P(1) = 1; P(2) = 1, P(3) = 2
+    sequence = [0, 1, 1]
+
+    # initialize string with starting values
+    # remamnining values will be appended to string 
+    newman_conway_str = "1 1 "
+
+    # need to start range at index 3
+    for i in range(3, num + 1):
+        # calculating next value to append 
+        sequence.append(sequence[sequence[i - 1]] + sequence[i - sequence[i - 1]])
+
+        # must convert to string 
+        newman_conway_str += f"{sequence[i]} "
+
+    return newman_conway_str[:-1]