The probability of getting exactly n heads in m tossing.

maths/probability_of_n_heads_in_m_tossing.py

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+"""
+The probability of getting exactly n heads in m tossing.
+
+Algorithm Explanation:
+If you toss 0 time -> 0 head
+Distribution [1] -> Meaning: 1 in the 0-index
+
+If you toss 1 time -> 0 or 1 head
+Distribution [0.5 0.5] -> Meaning: 0.5 in both indexes
+
+If you toss 2 times -> 0 to 2 heads
+Distribution [0.25 0.5 0.25] ->
+Meaning:  probability of n heads from the distribution
+{HH, HT, TH, TT}
+
+If you toss 3 times -> 0 to 3 heads
+Distribution [0.125 0.375 0.375 0.125] ->
+Meaning:  probability of n heads from the distribution
+{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
+
+Therefore,
+Probability_distribution(N+1) =
+      [Probability_distribution(N) 0]/2 + [0 Probability_distribution(N)]/2
+
+I used that method in my paper
+Titled: Uncertainty-aware Decisions in Cloud Computing:
+Foundations and Future Directions
+Journal: ACM Computing Surveys (CSUR)
+"""
+
+import numpy as np
+
+
+def probability_of_n_heads_in_m_tossing(head_count: int, toss_count: int) -> int:
+    """
+    Calculate the factorial of specified number (n!).
+
+    >>> import math
+    >>> all(factorial(i) == math.factorial(i) for i in range(20))
+    True
+    >>> Probability_of_n_heads_in_m_tossing(.2,.5)
+    Traceback (most recent call last):
+        ...
+    ValueError: The function only accepts integer values
+    >>> Probability_of_n_heads_in_m_tossing(-1,5)
+    Traceback (most recent call last):
+        ...
+    ValueError: The function is not defined for negative values
+    >>> Probability_of_n_heads_in_m_tossing(3,2)
+    Traceback (most recent call last):
+        ...
+    ValueError: Head count should be smaller than toss count
+
+    >>> Probability_of_n_heads_in_m_tossing(1,1)
+    0.5
+    >>> Probability_of_n_heads_in_m_tossing(0,2)
+    0.25
+    >>> Probability_of_n_heads_in_m_tossing(2,3)
+    0.375
+    """
+    if head_count != int(head_count) or toss_count != int(toss_count):
+        raise ValueError("The function only accepts integer values")
+    if head_count < 0 or toss_count < 0:
+        raise ValueError("The function only accepts positive values")
+    if head_count > toss_count:
+        raise ValueError("Head count should be smaller than toss count")
+    if toss_count > 100:
+        raise ValueError("Limited to 100 tossing to avoid memory issues")
+
+    value = np.ones(1)
+
+    iter1 = 0
+    while iter1 < toss_count:
+        value = np.append(value, [0], axis=0) + np.append([0], value, axis=0)
+        value = value / 2
+        iter1 = iter1 + 1
+
+    return value[head_count]