chore: import upstream snapshot with attribution

range_queries/prefix_sum_array.cpp

@@ -0,0 +1,85 @@
+/**
+ * @file
+ * @brief
+ * [Prefix Sum
+ * Array](https://en.wikipedia.org/wiki/Prefix_sum) data structure
+ * implementation.
+ *
+ * @details
+ * Prefix Sum Array is a data structure, that allows answering sum in some range
+ * queries. It can answer most sum range queries in O(1), with a build time
+ * complexity of O(N). But it hasn't an update querie.
+ *
+ * * Running Time Complexity \n
+ * * Build : O(N) \n
+ * * Range Query : O(1) \n
+ * @author [Paulo Vitor Lima Borges](https://github.com/PauloVLB)
+ */
+
+#include <cassert>   /// for assert
+#include <iostream>  /// for IO operations
+#include <vector>    /// for std::vector
+
+/**
+ * @namespace range_queries
+ * @brief Range Queries algorithms
+ */
+namespace range_queries {
+/**
+ * @namespace prefix_sum_array
+ * @brief Range sum queries using prefix-sum-array
+ */
+namespace prefix_sum_array {
+
+std::vector<int64_t> PSA{};
+
+/**
+ * @brief function that builds the PSA
+ * @param original_array original array of values
+ * @returns void
+ */
+void build(const std::vector<int64_t>& original_array) {
+    PSA.clear();
+    PSA.push_back(0);
+    for (std::size_t i = 1; i < original_array.size(); ++i) {
+        PSA.push_back(PSA.back() + original_array[i]);
+    }
+}
+/**
+ * @brief query function
+ * @param beg begin of the interval to sum
+ * @param end end of the interval to sum
+ * @returns sum of the range [beg, end]
+ */
+int64_t query(int64_t beg, int64_t end) { return PSA[end] - PSA[beg - 1]; }
+
+}  // namespace prefix_sum_array
+}  // namespace range_queries
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+    std::vector<int64_t> values{0,  123, 0,  2,  -2, 5,
+                                24, 0,   23, -1, -1};  // original array
+
+    range_queries::prefix_sum_array::build(values);
+    // queries are of the type: sum of the range [a, b] = psa[b] - psa[a-1]
+
+    assert(range_queries::prefix_sum_array::query(1, 10) ==
+           173);  // sum of the entire array
+    assert(range_queries::prefix_sum_array::query(4, 6) ==
+           27);  // the sum of the interval [4, 6]
+    assert(range_queries::prefix_sum_array::query(5, 9) ==
+           51);  // the sum of the interval [5, 9]
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // run self-test implementations
+    return 0;
+}