MAN AHL interview

puzzles/interviews/man_AHL/rand_num_next.py

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+import random
+import bisect
+
+class RandomGen(object):
+
+    def __init__(self, random_nums, probabilities):
+        assert len(random_nums), 'Random number list is empty.'
+        assert len(random_nums) == len(probabilities), 'Random numbers and probabilities do not match.'
+        assert abs(1. - sum(probabilities)) < 0.0000001, 'Probabilities do not sum to 1.'
+            
+        # Values that may be returned by next_num()
+        self._random_nums = random_nums
+        # Probability of the occurence of random_nums.
+        # Actually we create range table here, such that all random numbers
+        # ranging from (tbl[i-1],tbl[i]] map to random_number[i] 
+        self._range_table = probabilities
+        for i in range(1,len(self._range_table)):
+            self._range_table[i] += self._range_table[i-1]
+         # All random numbers which are not in any range will map 
+         # to last _random_num. Therefore there is no point to have
+         # last _random_num probability range in the table.
+        self._range_table.pop()
+
+
+    def next_num(self):
+        """
+        Returns one of the randomNums. When this method is called
+        multiple times over a long period, it should return the
+        numbers roughly with the initialized probabilities.
+        """
+        r = random.random()
+        return self._random_nums[bisect.bisect_left(self._range_table, r)]
+
+
+def test_init(random_nums, probabilities):
+    try:
+        rg = RandomGen(random_nums, probabilities)
+    except AssertionError as e:
+        return
+    assert False, "Had to be assert, but no assert could be detected."
+
+
+def test(input, rep_count = 1000):
+    generate_stat = { _1 : 0 for _1,_ in input.items() }
+    rg = RandomGen([key for key in input.keys()], [val for val in input.values()])
+    for i in range(rep_count):
+        generate_stat[rg.next_num()] += 1
+    
+    for rnum, rnum_stat in generate_stat.items():
+        stat_prob = rnum_stat/rep_count
+        orig_prob = input[rnum]
+        print('{}: orig: {}  actual: {}'.format(rnum, orig_prob, stat_prob))
+    print('')
+
+
+if __name__ == '__main__':
+    test_init([], []) # Empty list of numbers not allowed
+    test_init([1, 2], [1. ]) # Probabilities don't match
+    test_init([1, 2], [ 0.1, 0.1]) # Probabilities don't sum to 1.
+    test({0 : 0.5,
+          1 : 0.25,
+          2 : 0.25 })
+    test({-1 : 0.01,
+           0 : 0.3,
+           1 : 0.58,
+           2 : 0.1,
+           3 : 0.01 }, 100)
+    test({-1 : 0.01,
+           0 : 0.3,
+           1 : 0.58,
+           2 : 0.1,
+           3 : 0.01 }, 100000)