From 87889957e653dc748b28b18ccd20d6a2cc4d14b9 Mon Sep 17 00:00:00 2001
From: Rukmini Meda <44504940+Rukmini-Meda@users.noreply.github.com>
Date: Sun, 31 May 2020 01:09:58 +0530
Subject: [PATCH] Fenwick tree implemented in Dart (#3007)

---
 Fenwick_Tree/Fenwick_Tree.dart | 159 +++++++++++++++++++++++++++++++++
 1 file changed, 159 insertions(+)
 create mode 100644 Fenwick_Tree/Fenwick_Tree.dart

diff --git a/Fenwick_Tree/Fenwick_Tree.dart b/Fenwick_Tree/Fenwick_Tree.dart
new file mode 100644
index 0000000000..ee51585b18
--- /dev/null
+++ b/Fenwick_Tree/Fenwick_Tree.dart
@@ -0,0 +1,159 @@
+/**
+ *    Fenwick Tree
+ * -------------------------
+ * Binary Indexed tree or Fenwick tree is used to solve
+ * range queries optimally. It has O(n) space complexity,
+ * O(logn) time complexity to update, O(nlog(n)) time complexity to build
+ * and O(logn) time complexity to find sum in a given range.
+ * 
+ */
+// Importing required libraries
+import 'dart:io';
+
+// Updating the tree with respect to any updates or construction
+void updateBITTree(List tree, int n, int index, int val){
+    index = index + 1;
+
+    while(index <= n){
+        tree[index] += val;
+        index += index & ( - index);        
+    }
+
+}
+
+// Method to find the sum till a given index
+int getSum(List tree, int index){
+
+    int total = 0;
+    index = index + 1;
+
+    while(index > 0){
+        total += tree[index];
+        index -= index & ( - index );
+    }
+
+    return total;
+}
+
+// Method to find sum between a range using the above method.
+int findSum(List tree, int left, int right){
+    if(left > right){
+        return -1;
+    }
+    else if(left == right){
+        return getSum(tree, left) - getSum(tree, left - 1);
+    }
+    else{
+        if(left > 0){
+            return getSum(tree,right) - getSum(tree,left) + (getSum(tree, left) - getSum(tree, left - 1));
+        }
+        else if(left == 0){
+            return getSum(tree,right);
+        }
+        else{
+            return -1;
+        }
+    }
+}
+
+// Driver method of the program
+void main(){
+
+    // Input of number of array elements
+    print("Enter number of elements in the array:");
+    var input = stdin.readLineSync();
+    int n = int.parse(input);
+
+    // Input of array elements
+    print("Enter array elements:");
+    input = stdin.readLineSync();
+    var lis = input.split(" ");
+    List array = lis.map(int.parse).toList();
+    
+    // Fenwick tree initialization
+    List tree_BIT = List(n + 1);
+    for(int i = 0; i < n + 1; i ++){
+        tree_BIT[i] = 0;
+    }
+    
+    // Tree construction
+    for(int i = 0; i < n; i ++){
+        updateBITTree(tree_BIT, n, i, array[i]);
+    }
+    
+    // Input of number of queries
+    print("Enter number of queries:");
+    input = stdin.readLineSync();
+    int q = int.parse(input);
+
+    // Input of queries
+    print("Enter queries:");
+    for(int i = 0 ; i < q ; i ++){
+
+        print("Enter 1 to update, 2 to find sum:");
+        input = stdin.readLineSync();
+        int choice = int.parse(input);
+        switch(choice){
+
+            case 1: 
+                // Input for updates
+                print("Enter index and value to update");
+                input = stdin.readLineSync();
+                lis = input.split(" ");
+                List choices = lis.map(int.parse).toList();
+                array[choices[0]] += choices[1];
+                // Updating value
+                updateBITTree(tree_BIT, n, choices[0], choices[1]);
+                break;
+            case 2: 
+                // Input for sum queries
+                print("Enter range to find the sum");
+                input = stdin.readLineSync();
+                lis = input.split(" ");
+                List choices = lis.map(int.parse).toList();
+                // Finding sum
+                int result = findSum(tree_BIT,choices[0],choices[1]);
+                print(result);
+                break;
+        }
+    }
+}
+
+/**
+ * 
+ *   Sample Input 
+ * ------------------------------------
+ * Enter number of elements in the array:
+ * 12
+ * Enter array elements:
+ * 2 1 1 3 2 3 4 5 6 7 8 9
+ * Enter number of queries:
+ * 5
+ * Enter 1 to update, 2 to find sum:
+ * 2
+ * Enter range to find the sum
+ * 0 5
+ * Enter 1 to update, 2 to find sum:
+ * 1
+ * Enter index and value to update
+ * 3 9
+ * Enter 1 to update, 2 to find sum:
+ * 2
+ * Enter range to find the sum
+ * 0 5
+ * Enter 1 to update, 2 to find sum:
+ * 2
+ * Enter range to find the sum
+ * 5 9
+ * Enter 1 to update, 2 to find sum:
+ * 2
+ * Enter range to find the sum
+ * 8 8
+ * 
+ *   Sample Output
+ * ----------------------------------------
+ * 12
+ * 21
+ * 25
+ * 6
+ */