Merge branch 'master' into patch-2

Author: cclauss

graphs/dijkstra_2.py

@@ -1,18 +1,41 @@
 def print_dist(dist, v) -> None:
-    print("\nVertex Distance")
+    """
+    Print vertex distances.
+    >>> print_dist([0.0, 5.0, 8.0, 9.0], 4)
+    Vertex Distance
+    0    0
+    1    5
+    2    8
+    3    9
+    >>> print_dist([0.0, float('inf')], 2)
+    Vertex Distance
+    0    0
+    1    INF
+    >>> print_dist([0.0], 1)
+    Vertex Distance
+    0    0
+    """
+    print("Vertex Distance")
     for i in range(v):
         if dist[i] != float("inf"):
-            print(i, "\t", int(dist[i]), end="\t")
+            print(i, "  ", int(dist[i]))
         else:
-            print(i, "\t", "INF", end="\t")
-        print()
+            print(i, "  ", "INF")
 
 
 def min_dist(mdist, vset, v):
     """
-    Returns the vertex with the minimum distance from the source vertex\
-        that has not been visited.
+    Returns the vertex with the minimum distance from the source vertex
+    that has not yet been visited.
 
+    >>> min_dist([0, 4, 2, float('inf')], [True, False, False, False], 4)
+    2
+    >>> min_dist([0, 4, 2, 1], [True, False, True, False], 4)
+    3
+    >>> min_dist([0, 4, 2, 1], [True, True, True, True], 4)
+    -1
+    >>> min_dist([float('inf'), float('inf')], [False, False], 2)
+    -1
     >>> min_dist([0, 1, 6], [True, False, False], 3)
     1
     """
@@ -27,14 +50,38 @@ def min_dist(mdist, vset, v):
 
 def dijkstra(graph, v, src) -> None:
     """
-    Calculate the shortest path from source to all other vertices\
-        using Dijkstra's algorithm.
+    Runs Dijkstra's algorithm and prints distances.
 
+    Calculate the shortest path from source to all other vertices
+    using Dijkstra's algorithm.
+
+    >>> g = [
+    ...     [0.0, 5.0, float('inf'), 10.0],
+    ...     [float('inf'), 0.0, 3.0, float('inf')],
+    ...     [float('inf'), float('inf'), 0.0, 1.0],
+    ...     [float('inf'), float('inf'), float('inf'), 0.0],
+    ... ]
+    >>> dijkstra(g, 4, 0)
+    Vertex Distance
+    0    0
+    1    5
+    2    8
+    3    9
+    >>> g2 = [
+    ...     [0.0, float('inf')],
+    ...     [float('inf'), 0.0],
+    ... ]
+    >>> dijkstra(g2, 2, 0)
+    Vertex Distance
+    0    0
+    1    INF
+    >>> dijkstra([[0.0]], 1, 0)
+    Vertex Distance
+    0    0
     >>> graph = [[0.0, 1.0, 6.0],\
                 [float("inf"), 0.0, 3.0],\
                 [float("inf"), float("inf"), 0.0]]
     >>> dijkstra(graph, 3, 0) # doctest: +NORMALIZE_WHITESPACE
-    <BLANKLINE>
     Vertex Distance
     0    0
     1    1

maths/number_of_digits.py

@@ -43,6 +43,10 @@ def num_digits_fast(n: int) -> int:
     5
     >>> num_digits_fast(123)
     3
+    >>> num_digits_fast(1000)
+    4
+    >>> num_digits_fast(10**15)
+    16
     >>> num_digits_fast(0)
     1
     >>> num_digits_fast(-1)
@@ -56,7 +60,6 @@ def num_digits_fast(n: int) -> int:
     """
     if not isinstance(n, int):
         raise TypeError("Input must be an integer")
-
     return 1 if n == 0 else math.floor(math.log10(abs(n)) + 1)