Fenwick Tree Added

Fenwick Tree/fenwick.cpp

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+// Fenwick Tree is also known as binary indexed tree
+#include <iostream>
+
+using namespace std;
+
+/*         n --> No. of elements present in input array.  
+    BITree[0..n] --> Array that represents Binary Indexed Tree. 
+    arr[0..n-1] --> Input array for which prefix sum is evaluated. */
+
+// Returns sum of arr[0..index]. This function assumes
+// that the array is preprocessed and partial sums of
+// array elements are stored in BITree[].
+int getSum(int BITree[], int index)
+{
+    int sum = 0; // Iniialize result
+
+    // index in BITree[] is 1 more than the index in arr[]
+    index = index + 1;
+
+    // Traverse ancestors of BITree[index]
+    while (index > 0)
+    {
+        // Add current element of BITree to sum
+        sum += BITree[index];
+
+        // Move index to parent node in getSum View
+        index -= index & (-index);
+    }
+    return sum;
+}
+
+// Updates a node in Binary Index Tree (BITree) at given index
+// in BITree. The given value 'val' is added to BITree[i] and
+// all of its ancestors in tree.
+void updateBIT(int BITree[], int n, int index, int val)
+{
+    // index in BITree[] is 1 more than the index in arr[]
+    index = index + 1;
+
+    // Traverse all ancestors and add 'val'
+    while (index <= n)
+    {
+        // Add 'val' to current node of BI Tree
+        BITree[index] += val;
+
+        // Update index to that of parent in update View
+        index += index & (-index);
+    }
+}
+
+// Constructs and returns a Binary Indexed Tree for given
+// array of size n.
+int *constructBITree(int arr[], int n)
+{
+    // Create and initialize BITree[] as 0
+    int *BITree = new int[n + 1];
+    for (int i = 1; i <= n; i++)
+        BITree[i] = 0;
+
+    // Store the actual values in BITree[] using update()
+    for (int i = 0; i < n; i++)
+        updateBIT(BITree, n, i, arr[i]);
+
+    // Uncomment below lines to see contents of BITree[]
+    //for (int i=1; i<=n; i++)
+    //     cout << BITree[i] << " ";
+
+    return BITree;
+}
+
+// Driver program to test above functions
+int main()
+{
+    int freq[] = {2, 1, 1, 3, 2, 3, 4, 5, 6, 7, 8, 9};
+    int n = sizeof(freq) / sizeof(freq[0]);
+    int *BITree = constructBITree(freq, n);
+    cout << "Sum of elements in arr[0..5] is "
+         << getSum(BITree, 5);
+
+    // Let use test the update operation
+    freq[3] += 6;
+    updateBIT(BITree, n, 3, 6); //Update BIT for above change in arr[]
+
+    cout << "\nSum of elements in arr[0..5] after update is "
+         << getSum(BITree, 5);
+
+    return 0;
+}