Add example for radix sort

cpp/algorithms/sorting/radix/lib-counting.cpp

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+/*#############################################################################
+## Author: Shaun Reed                                                        ##
+## Legal: All Content (c) 2021 Shaun Reed, all rights reserved               ##
+## About: An example implementation of counting sort using a custom library  ##
+##        + In support of a radix sort implementation                        ##
+##                                                                           ##
+## Contact: shaunrd0@gmail.com  | URL: www.shaunreed.com | GitHub: shaunrd0  ##
+###############################################################################
+*/
+
+#include "lib-counting.hpp"
+
+#include <algorithm>
+#include <vector>
+#include <cstdint>
+
+
+void CountingSort(std::vector<int> &array, int placeValue)
+{
+  std::vector<int> sortedArray(array.size(), 0);
+
+  // Find the maximum value within the array to sort
+  int32_t maxValue = INT32_MIN;
+  for (const auto &val : array) maxValue = (val > maxValue) ? val : maxValue;
+
+  // Create an array with element for all *placeValues* within range of the set
+  // + Not the size of the array to sort, but instead a element of
+  // + tempArray[digit] = 0; Considering only the digit at placeValue of array[n]
+  // Using this vector, we have a place to count all possible digits at placeValue
+  std::vector<int> tempArray(10, 0);
+
+  // Count the occurrences of each digit at this placeValue within the array
+  // + Store the end result as tempArray[digit] = count;
+  // + Where digit is found at the decimal placeValue of each value within array
+  for (const auto &val : array) {
+    // Get the digit at the decimal placeValue of arrayValue
+    auto index = static_cast<size_t>((val / placeValue) % tempArray.size());
+    // Running total of each value with the same digit at decimal placeValue
+    tempArray[index] = tempArray[index] + 1;
+  }
+
+  // Count the values less than or equal to each element of tempArray
+  // + Since each element stores its own count, just add the count at index i-1
+  for (int i = 1; i < tempArray.size(); i++) {
+    tempArray[i] = tempArray[i] + tempArray[i - 1];
+  }
+
+  for (ssize_t arrayIndex = array.size() - 1; arrayIndex >= 0; arrayIndex--) {
+    // Get the value to consider from the unsorted array
+    const int &arrayValue = array[arrayIndex];
+
+    // Get the digit at the decimal placeValue of arrayValue
+    // + Use this index to update count of values as we use them
+    const auto tempIndex =
+        static_cast<size_t>((arrayValue / placeValue) % tempArray.size());
+
+    // Store valueCount as a reference so we can update it
+    int &valueCount = tempArray[tempIndex];
+    // Offset valueCount by 1 to allow for zero index of sortedArray
+    sortedArray[valueCount - 1] = arrayValue;
+    valueCount = valueCount - 1;
+  }
+
+  array = sortedArray;
+}