Solution.

README.md

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+Solution for a code challenge:
+
+- The challenge is to create a program that computes some basic statistics on a collection of small positive integers. You can assume all values will be less than 1000.
+- The `DataCapture` object accepts numbers and returns an object for querying statistics about the inputs. Specifically, the returned object supports querying how many numbers in the collection are less than a value, greater than a value, or within a range.
+
+# Executing
+
+The solution is implemented in a single file, and it's targeting `python39`.
+
+To execute the example you can just run `python app.py` assuming you are using the correct version, and
+that you are located in the directory for this project.
+
+# About the solution
+
+The problem can be divided in two parts,
+
+1. An object capable of _gathering_ an arbitrary amount of numbers, (assumed to be positive, and less than 1001).
+2. Generate an object that can query in constant time, counts numbers in certain ranges.
+
+So, with the first object we construct a _frequency function_ that will tell us how many repetition of a given
+number we have.
+
+Then we define a function that would be the _integral_ of the frequency function, such that whenever we _evaluate it_
+we'll get how many numbers exist that are less than _it_.
+
+When we say function, we are not talking about a function in programming terms, we are talking about a discrete function as a _rule of correspondence_, and internally in this code it's represented a list where the nth element of the 
+list, is the evaluation for the number (n-1).

app.py

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+#!/usr/bin/env python3
+
+
+class Stats:
+    def __init__(self, data):
+        """
+        Here we create a _table_ (dictionary), with the
+        frequency for the numbers contained in data,
+        which should take a linear amount of time in the
+        input length, then we execute a loop of constant
+        amount of iteration, which adds 1002 steps.
+        But it's constant.
+        So overall the __init__ method, should take
+        a linear amount of time, in the data length.
+        """
+        _data = {}
+        for v in data:
+            _data[v] = _data.get(v, 0) + 1
+
+        _list, prev = [], 0
+        for i in range(0, 1002):
+            new = _data.get(i, 0) + prev
+            _list.append(new)
+            prev = new
+        self._list = _list
+
+    def less(self, value):
+        """
+        This method executes in constant time, because
+        it's a list access by element.
+        """
+        returnable = self._list[value - 1]
+        # print(value, returnable)
+        return returnable
+
+    def between(self, m, M):
+        """
+        This method executes in constant time, because
+        it's consuming two times a constant method,
+        plus an arithmetic operation.
+        """
+        return self.less(M + 1) - self.less(m - 1)
+
+    def greater(self, value):
+        """
+        This method executes in constant time, because
+        it's consuming two times a constant method,
+        plus an arithmetic operation.
+        """
+        return self.less(1001) - self.less(value + 1)
+
+
+class DataCapture:
+    def __init__(self, *args, **kwargs):
+        self._values = []
+
+    def add(self, *values):
+        """
+        This method is actually cheating, but the explanation is
+        the extend method on a list, will the same amount
+        of time as the count of objects you are adding.
+        If you intend to consume this method to add
+        a single element then it's a constant time, but is
+        you are adding a _list_ of methods (by using the positional
+        arguments), it will take a linear time in the arguments.
+        """
+        self._values.extend(values)
+
+    def build_stats(self):
+        """
+        Here we delegate everything to the Stats
+        init, the init for the Stats object,
+        will receive a _sorted list_,
+        which I think it's a good assumption to start
+        with.
+        """
+        return Stats(sorted(self._values))
+
+
+if __name__ == "__main__":
+    # Example code execution
+    capture = DataCapture()
+    capture.add(3)
+    capture.add(9)
+    capture.add(3)
+    capture.add(4)
+    capture.add(6)
+    stats = capture.build_stats()
+
+    val = stats.less(4)
+    print("Less 4: (2)      \t", val, val == 2)
+    val = stats.between(3, 6)
+    print("Between 3, 6: (4)\t", val, val == 4)
+    val = stats.greater(4)
+    print("Greater 4: (2)   \t", val, val == 2)