Feature: Added segment_trees Closes #561 (#595)

* Feature: Added segment_trees Closes #561

* doc: documentation improved and explanations added

* updating DIRECTORY.md

* doc: changes in documentation

* doc: suggested doc changes and int types changed

* update: doc change for main function

Co-authored-by: David Leal <[email protected]>

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: David Leal <[email protected]>

Author: 3 people

DIRECTORY.md

@@ -32,6 +32,7 @@
     * [Create Node](https://github.com/TheAlgorithms/C/blob/master/data_structures/binary_trees/create_node.c)
     * [Recursive Traversals](https://github.com/TheAlgorithms/C/blob/master/data_structures/binary_trees/recursive_traversals.c)
     * [Redblacktree](https://github.com/TheAlgorithms/C/blob/master/data_structures/binary_trees/redblacktree.c)
+    * [Segment Tree](https://github.com/TheAlgorithms/C/blob/master/data_structures/binary_trees/segment_tree.c)
     * [Threaded Binary Trees](https://github.com/TheAlgorithms/C/blob/master/data_structures/binary_trees/threaded_binary_trees.c)
   * Dictionary
     * [Dict](https://github.com/TheAlgorithms/C/blob/master/data_structures/dictionary/dict.c)

data_structures/binary_trees/segment_tree.c

@@ -0,0 +1,235 @@
+/**
+ * @file segment_tree.c
+ * @brief segment trees with only point updates
+ * @details
+ * This code implements segment trees. Segment trees are general structures
+ * which allow range based queries in a given array in logN time.
+ * Segment tree with point updates allow update of single element in the array
+ * in logN time.
+ * [Learn more about segment trees
+ * here](https://codeforces.com/blog/entry/18051)
+ * @author [Lakhan Nad](https://github.com/Lakhan-Nad)
+ */
+
+#include <assert.h>   /* for assert */
+#include <inttypes.h> /* for int32 */
+#include <stdio.h>    /* for scanf printf */
+#include <stdlib.h>   /* for malloc, free */
+#include <string.h>   /* for memcpy, memset */
+
+/**
+ * Function that combines two data to generate a new one
+ * The name of function might be misleading actually combine here signifies the
+ * fact that in segment trees we take partial result from two ranges and using
+ * partial results we derive the result for joint range of those two ranges
+ * For Example: array(1,2,3,4,5,6) sum of range [0,2] = 6
+ * and sum of range [3,5] = 15 the combined sum of two range is 6+15=21
+ * @note The function is same to binary function in Discrete Mathematics
+ * @param a pointer to first data
+ * @param b pointer to second data
+ * @param result pointer to memory location where result of combining a and b is
+ * to be stored
+ */
+typedef void (*combine_function)(const void *a, const void *b, void *result);
+
+/**
+ * This structures holds all the data that is required by a segment tree
+ */
+typedef struct segment_tree
+{
+    void *root;       /**< the root of formed segment tree */
+    void *identity;   /**< identity element for combine function */
+    size_t elem_size; /**< size in bytes of each data element */
+    size_t length;    /**< total size of array which segment tree represents*/
+    /** the function to be used to combine two node's
+     * data to form parent's data
+     */
+    combine_function combine;
+} segment_tree;
+
+/**
+ * Builds a Segment tree
+ * It is assumed that leaves of tree already contains data.
+ * @param tree pointer to segment tree to be build
+ */
+void segment_tree_build(segment_tree *tree)
+{
+    size_t elem_size = tree->elem_size;
+    int index = (tree->length - 2);
+    size_t b, l, r;
+    char *ptr = (char *)tree->root;
+    for (; index >= 0; index--)
+    {
+        b = index * elem_size;
+        l = (2 * index + 1) * elem_size;
+        r = (2 * index + 2) * elem_size;
+        tree->combine(ptr + l, ptr + r, ptr + b);
+    }
+}
+
+/**
+ * For point updates
+ * This function updates the element at given index and also updates segment
+ * tree accordingly
+ *
+ * @param tree pointer to segment tree
+ * @param index the index whose element is to be updated (0 based indexing used)
+ * @param val pointer to value that is to be replaced at given index
+ */
+void segment_tree_update(segment_tree *tree, size_t index, void *val)
+{
+    size_t elem_size = tree->elem_size;
+    index = index + tree->length - 1;
+    char *base = (char *)tree->root;
+    char *t = base + index * elem_size;
+    memcpy(t, val, elem_size);
+    while (index > 0)
+    {
+        index = ((index - 1) >> 1);
+        tree->combine(base + (2 * index + 1) * elem_size,
+                      base + (2 * index + 2) * elem_size,
+                      base + index * elem_size);
+    }
+}
+
+/**
+ * Query the segment tree
+ * This function helps in range query of segment tree
+ * This function assumes that the given range is valid
+ * Performs the query in range [l,r]
+ * @param tree pointer to segment tree
+ * @param l the start of range
+ * @param r the end of range
+ * @param res the pointer to memory where result of query is stored
+ */
+void segment_tree_query(segment_tree *tree, long long l, long long r, void *res)
+{
+    size_t elem_size = tree->elem_size;
+    memcpy(res, tree->identity, elem_size);
+    elem_size = tree->elem_size;
+    char *root = (char *)tree->root;
+    l += tree->length - 1;
+    r += tree->length - 1;
+    while (l <= r)
+    {
+        if (!(l & 1))
+        {
+            tree->combine(res, root + l * elem_size, res);
+        }
+        if (r & 1)
+        {
+            tree->combine(res, root + r * elem_size, res);
+        }
+        r = (r >> 1) - 1;
+        l = (l >> 1);
+    }
+}
+
+/**
+ * Initializes Segment Tree
+ * Accquires memory for segment tree
+ * and fill the leaves of segment tree with data from array
+ * @param arr the array data upon which segment tree is build
+ * @param elem_size size of each element in segment tree
+ * @param len total no of elements in array
+ * @param identity the identity element for combine_function
+ * @param func the combine_function used to build segment tree
+ *
+ * @returns pointer to sgement tree build
+ */
+segment_tree *segment_tree_init(void *arr, size_t elem_size, size_t len,
+                                void *identity, combine_function func)
+{
+    segment_tree *tree = malloc(sizeof(segment_tree));
+    tree->elem_size = elem_size;
+    tree->length = len;
+    tree->combine = func;
+    tree->root = malloc(sizeof(char) * elem_size * (2 * len - 1));
+    tree->identity = malloc(sizeof(char) * elem_size);
+    char *ptr = (char *)tree->root;
+    memset(ptr, 0, (len - 1) * elem_size);  // Initializing memory
+    ptr = ptr + (len - 1) * elem_size;
+    memcpy(ptr, arr, elem_size * len);  // copy the leaf nodes i.e. array data
+    memcpy(tree->identity, identity, elem_size);  // copy identity element
+    return tree;
+}
+
+/**
+ * Dispose Segment Tree
+ * Frees all heap memory accquired by segment tree
+ * @param tree pointer to segment tree
+ */
+void segment_tree_dispose(segment_tree *tree)
+{
+    free(tree->root);
+    free(tree->identity);
+}
+
+/**
+ * Prints the data in segment tree
+ * The data should be of int type
+ * A utility to print segment tree
+ * with data type of int
+ * @param tree pointer to segment tree
+ */
+void segment_tree_print_int(segment_tree *tree)
+{
+    char *base = (char *)tree->root;
+    size_t i = 0;
+    for (; i < 2 * tree->length - 1; i++)
+    {
+        printf("%d ", *(int *)(base + i * tree->elem_size));
+    }
+    printf("\n");
+}
+
+/**
+ * Utility for test
+ * A function compare for minimum between two integers
+ * This function is used as combine_function for RMQ
+ * @param a pointer to integer a
+ * @param b pointer to integer b
+ * @param c pointer where minimum of a and b is tored as result
+ */
+void minimum(const void *a, const void *b, void *c)
+{
+    *(int *)c = *(int *)a < *(int *)b ? *(int *)a : *(int *)b;
+}
+
+/**
+ * Test RMQ
+ * Testing Segment tree using
+ * Range Minimum Queries
+ * @returns void
+ */
+static void test()
+{
+    int32_t arr[10] = {1, 0, 3, 5, 7, 2, 11, 6, -2, 8};
+    int32_t identity = __INT32_MAX__;
+    segment_tree *tree =
+        segment_tree_init(arr, sizeof(*arr), 10, &identity, minimum);
+    segment_tree_build(tree);
+    int32_t result;
+    segment_tree_query(tree, 3, 6, &result);
+    assert(result == 2);
+    segment_tree_query(tree, 8, 9, &result);
+    assert(result == -2);
+    result = 12;
+    segment_tree_update(tree, 5, &result);
+    segment_tree_update(tree, 8, &result);
+    segment_tree_query(tree, 0, 3, &result);
+    assert(result == 0);
+    segment_tree_query(tree, 8, 9, &result);
+    assert(result == 8);
+    segment_tree_dispose(tree);
+}
+
+/**
+ * @brief Main Function
+ * @returns 0 on exit
+ */
+int main()
+{
+    test();
+    return 0;
+}