Binary_indexed_tree

binary_indexed_tree.cpp

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+//We have an array arr[0 . . . n-1]. We would like to 
+//1 Compute the sum of the first i elements. 
+//2 Modify the value of a specified element of the array arr[i] = x where 0 <= i <= n-1.
+
+//Using the binary indexed tree we store the sum of element in bitree array using the bits
+//bitree[i]=sum of elements from i to j
+//where j =i-(least bit set of i)
+
+// Every node of the BITree stores the sum of n elements where n is a power of 2
+// The number of set bits in the binary representation of a number n is O(Logn). Therefore, we traverse 
+//at-most O(Logn) nodes in both getSum() and update() operations. The time complexity of the construction 
+//is O(nLogn) as it calls update() for all n elements.
+
+
+//Example 1:
+//5                no of elements(n)
+//[1,2,3,4,5]      original array(a)
+//output:
+//[1,3,3,10,5]     bitree
+//15               sum of first five element
+//1 2 4 4 5        updated index at 3(modified array)
+//[1,3,4,11,5]     updated bitree
+
+#include<bits/stdc++.h>  
+using namespace std;
+#define ll long long
+#define ld long double
+const int MOD = 1000000007;
+void updateB(vector<ll> &bitree,vector<ll> &a,ll i,ll sum){         // 1 based indexing i=1 (first element)
+    ll N=bitree.size();  //(n+1)
+    a[i-1]=a[i-1]+sum;
+    for(int k=i;k<N;k+=(k&(-k))){
+        bitree[k]+=sum;
+    }
+}
+ll sumB(vector<ll> &bitree,ll i){        //(5)arr[0...4] -> first five element
+    ll ans=0;
+    for(int k=i;k>0;k-=k&(-k)){
+        ans+=bitree[k];
+    }
+    return ans;
+}
+void consB(vector<ll> &bitree,vector<ll> a){
+    ll N=bitree.size();
+    for(int i=1;i<N;i++){
+        updateB(bitree,a,i,a[i-1]);
+    }
+}
+int main(){
+
+       ll n;
+       cin>>n;
+       vector<ll> a(n);
+       for(int i=0;i<n;i++){
+           cin>>a[i];               //input of array
+       }
+       vector<ll> bitree(n+1,0);
+       consB(bitree,a);
+       for(int i=1;i<=n;i++){
+           cout<<bitree[i]<<" ";
+       }cout<<endl;
+       cout<<sumB(bitree,5)<<endl;;
+       updateB(bitree,a,3,1);     //updated index at 3 by 1
+        for(int i=0;i<n;i++){
+           cout<<a[i]<<" ";
+       }cout<<endl;
+        for(int i=1;i<=n;i++){
+           cout<<bitree[i]<<" ";  //display of bitree
+       }cout<<endl;
+
+    return 0;
+}