Merge pull request matthewsamuel95#617 from Arman1611/add-fenwick

Add Fenwick Tree Implementation

Author: matthewsamuel95

Graph/FenwickTree/Fenwick.java

@@ -0,0 +1,52 @@
+class Fenwick
+{
+    private final long a[];
+    
+    public Fenwick(int n)
+    {
+        this.a=new long[n+1];
+    }
+    
+    public void update(final int index,final int value)
+    {
+        int effectiveIndex=index+1;
+        
+        while(effectiveIndex>0 && effectiveIndex<a.length)
+        {
+            a[effectiveIndex]+= value;
+            effectiveIndex = getNext(effectiveIndex);
+        }
+    }
+    
+    public long query(final int left,final int right)
+    {
+        if(left>right) return 0;
+        
+        return query(right+1)-query(left);
+    }
+    
+    private long query(int i)
+    {
+        if(i<=0) return 0;
+        if(i>=a.length) i=a.length-1;
+        
+        long sum=0;
+        
+        while(i>0)
+        {
+            sum+=a[i];
+            i=getParent(i);
+        }
+        return sum;
+    }
+    
+    private int getNext(final int effectiveIndex)
+    {
+        return effectiveIndex+((~effectiveIndex+1) & effectiveIndex));
+    }
+    
+    private int getParent(final int effectiveIndex)
+    {
+         return effectiveIndex-((~effectiveIndex+1) & effectiveIndex));
+    }
+}

README.md

@@ -96,6 +96,7 @@ ACM-ICPC Algorithms is a collection of important algorithms and data structures
    * [SPFA SSSP](/Graph/SPFA%20SSSP)
    * [Targan SCC](/Graph/TarganSCC)
    * [Topo Sort](/Graph/TopoSort)
+   * [Fenwick Tree](/Graph/FenwickTree)
 * [Greedy Algorithms](/Greedy)
    * [Activity Selection](/Greedy/ActivitySelection)
    * [Containership](/Greedy/ContainerShip)