Added frog jump calculator

frog-jumps-calc.py

@@ -0,0 +1,108 @@
+#!/usr/bin/env python
+"""
+    File name: frog-jumps-calc.py
+    Author: Dmitry Tsuprunov
+    Date created: September 14, 2019
+    Python Version: 3.7
+"""
+import sys
+
+
+def memo(fn):
+    """
+    Memoizing all the things
+    """
+    cache = {}
+
+    def memo_fn(*args):
+        cached_val = cache.get(args)
+        if cached_val:
+            return cached_val
+        cached_val = fn(*args)
+        cache[args] = cached_val
+        return cached_val
+
+    return memo_fn
+
+
+def possible_jumps(distance, jumps_made=0):
+    """
+    Calculates total number of jumps for all possible paths
+    """
+    if distance == 0:
+        return jumps_made
+    total_jumps = 0
+    for i in range(distance):
+        total_jumps += memo_possible_jumps(i, jumps_made + 1.0)
+    return total_jumps
+
+
+memo_possible_jumps = memo(possible_jumps)
+
+
+def possible_paths(distance):
+    """
+    Calculating total number of possible paths
+    """
+    if distance == 0:
+        return 1.0
+    total = 0
+    for i in range(distance):
+        total += memo_possible_paths(i)
+    return total
+
+
+memo_possible_paths = memo(possible_paths)
+
+
+# def expected_jumps(distance):
+#     if distance == 0:
+#         return 0
+#     return possible_jumps(distance) / possible_paths(distance)
+
+
+def expected_jumps(distance, jumps_made=0, probability=1.0):
+    """
+    Calculates expected number of jumps for all possible paths
+    Probability of jumps for each step calculated recursively
+    by dividing probability for current jump by possible number of following jumps
+    """
+    if distance == 0:
+        return jumps_made * probability
+    probability /= distance
+    expected_jumps_number = 0
+    for i in range(distance):
+        expected_jumps_number += memo_expected_jumps(
+            i, jumps_made + 1.0, probability)
+    return expected_jumps_number
+
+
+memo_expected_jumps = memo(expected_jumps)
+
+if __name__ == "__main__":
+    try:
+        arg = int(sys.argv[1])
+    except:
+        arg = 10
+    try:
+        loop = bool(sys.argv[2])
+    except:
+        loop = False
+
+    if loop:
+        for i in range(1, arg + 1):
+            # This line will print all values for all paths up to selected number
+            # Feel free to test with >>> python3 frog-jumps-calc.py {distance} {loop}
+            num_expected_jumps = expected_jumps(i)
+            num_possible_paths = possible_paths(i)
+            num_possible_jumps = possible_jumps(i)
+            print(f"For a distance {i} there're {num_possible_paths} possible paths "
+                  f"containing {num_possible_jumps} jumps "
+                  f"with expected jumps equal to {num_expected_jumps}.")
+    else:
+        num_expected_jumps = expected_jumps(arg)
+        num_possible_paths = possible_paths(arg)
+        num_possible_jumps = possible_jumps(arg)
+        print(f"For a distance {arg} there're {num_possible_paths} possible paths "
+              f"containing {num_possible_jumps} jumps "
+              f"with expected jumps equal to {num_expected_jumps}.")