Added Sparse Table for range query (#996)

* Added Sparse Table for range query

* Fixed Lint Warnings

* Fixed comments and Lint warnings

* Fixed comments

* Fixed comments and Lint warnings

* Fixed comments and Lint warnings

* Fixed variable reference Lint warnings

* Added documentation for functions parameters and return statements

* updating DIRECTORY.md

* Added documentation

* Applied namespace range_queries

Co-authored-by: David Leal <halfpacho@gmail.com>

* Updated wikipedia documentation link

* Resolved comments

* Fixed typo

Co-authored-by: David Leal <halfpacho@gmail.com>

* Resolved comments

* Added tests

* Cleaned up debugging statements

* Resolved comments

* Resolved Comments

* Update sparse_table.cpp

* Resolved comments

Co-authored-by: Krishna Vedala <7001608+kvedala@users.noreply.github.com>

* Fixed comments

* Update sparse_table.cpp

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: David Leal <halfpacho@gmail.com>
Co-authored-by: Krishna Vedala <7001608+kvedala@users.noreply.github.com>

DIRECTORY.md

@@ -213,6 +213,7 @@
   * [Heavy Light Decomposition](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/heavy_light_decomposition.cpp)
   * [Mo](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/mo.cpp)
   * [Segtree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/segtree.cpp)
+  * [Sparse Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/sparse_table.cpp)
 
 ## Search
   * [Binary Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/binary_search.cpp)

range_queries/sparse_table.cpp

@@ -0,0 +1,101 @@
+/**
+ * @file sparse_table.cpp
+ * @brief Implementation of [Sparse Table](https://en.wikipedia.org/wiki/Range_minimum_query) data structure
+ *
+ * @details
+ * Sparse Table is a data structure, that allows answering range queries.
+ * It can answer most range queries in O(logn), but its true power is answering range minimum queries
+ * or equivalent range maximum queries). For those queries it can compute the answer in O(1) time.
+ *
+ * * Running Time Complexity \n
+ * * Build : O(NlogN) \n
+ * * Range Query : O(1) \n
+*/
+
+#include <vector>
+#include <cassert>
+#include <iostream>
+#include <algorithm>
+
+/**
+ * @namespace range_queries
+ * @brief Range Queries algorithms
+ */
+namespace range_queries {
+/**
+ * @namespace sparse_table
+ * @brief Range queries using sparse-tables
+ */
+ namespace sparse_table {
+/**
+ * This function precomputes intial log table for further use.
+ * @param n value of the size of the input array
+ * @return corresponding vector of the log table
+ */
+template<typename T>
+std::vector<T> computeLogs(const std::vector<T>& A) {
+    int n = A.size();
+    std::vector<T> logs(n);
+    logs[1] = 0;
+    for (int i = 2 ; i < n ; i++) {
+        logs[i] = logs[i/2] + 1;
+    }
+    return logs;
+}
+
+/**
+ * This functions builds the primary data structure sparse table
+ * @param n value of the size of the input array
+ * @param A array of the input integers
+ * @param logs array of the log table
+ * @return created sparse table data structure
+ */
+template<typename T>
+std::vector<std::vector<T> > buildTable(const std::vector<T>& A, const std::vector<T>& logs) {
+    int n = A.size();
+    std::vector<std::vector<T> > table(20, std::vector<T>(n+5, 0));
+    int curLen = 0;
+    for (int i = 0 ; i <= logs[n] ; i++) {
+        curLen = 1 << i;
+        for (int j = 0 ; j + curLen < n ; j++) {
+            if (curLen == 1) {
+                table[i][j] = A[j];
+            }
+            else {
+                table[i][j] = std::min(table[i-1][j], table[i-1][j + curLen/2]);
+            }
+        }
+    }
+    return table;
+}
+
+/**
+ * This function is the query function to get the range minimum value
+ * @param beg beginning index of the query range
+ * @param end ending index of the query range
+ * @param logs array of the log table
+ * @param table sparse table data structure for the input array
+ * @return minimum value for the [beg, end] range for the input array
+ */
+template<typename T>
+int getMinimum(int beg, int end, const std::vector<T>& logs, const std::vector<std::vector<T> >& table) {
+    int p = logs[end - beg + 1];
+    int pLen = 1 << p;
+    return std::min(table[p][beg], table[p][end - pLen + 1]);
+}
+}
+} // namespace range_queries
+
+/**
+ * Main function
+ */
+int main() {
+    std::vector<int> A{1, 2, 0, 3, 9};
+    std::vector<int> logs = range_queries::sparse_table::computeLogs(A);
+    std::vector<std::vector<int> >  table = range_queries::sparse_table::buildTable(A, logs);
+    assert(range_queries::sparse_table::getMinimum(0, 0, logs, table) == 1);
+    assert(range_queries::sparse_table::getMinimum(0, 4, logs, table) == 0);
+    assert(range_queries::sparse_table::getMinimum(2, 4, logs, table) == 0);
+    return 0;
+}
+