2D Fenwick Updated

Author: zarif98sjs

Data Structure/00 BIT.cpp

@@ -13,8 +13,8 @@ A data structure to quickly do the following -
 
 Operations
 ----------
-- Add value to an index                 : O(NlogN)
-- Calculate Prefix Sum upto an index    : O(NlogN)
+- Add value to an index                 : O(logN)
+- Calculate Prefix Sum upto an index    : O(logN)
 
 **/
 

Data Structure/01 BIT (POINT update , RANGE query).cpp

@@ -13,8 +13,8 @@ A data structure to quickly do the following -
 
 Operations
 ----------
-- Add value to an index                 : O(NlogN)
-- Calculate Prefix Sum upto an index    : O(NlogN)
+- Add value to an index                 : O(logN)
+- Calculate Prefix Sum upto an index    : O(logN)
 
 **/
 

Data Structure/02 BIT (RANGE update , POINT query).cpp

@@ -14,8 +14,8 @@ A data structure to quickly do the following -
 Operations
 ----------
 
-- Add value to an index                 : O(NlogN)
-- Calculate Prefix Sum upto an index    : O(NlogN)
+- Add value to an index                 : O(logN)
+- Calculate Prefix Sum upto an index    : O(logN)
 
 Modification to do range updates
 --------------------------------

Data Structure/10 2D BIT (POINT update, RANGE query).cpp

@@ -1,7 +1,20 @@
 
 /**
 
-2D BIT
+2D Fenwick Tree
+===============
+
+Description
+-----------
+
+A data structure to quickly do the following -
+1 . Point Update
+2 . Prefix Sum Array Update
+
+Operations
+----------
+- Add value to an index                 : O( (logN)^2 )
+- Calculate Prefix Sum upto an index    : O( (logN)^2 )
 
 **/
 
@@ -13,108 +26,155 @@ using namespace std;
 #define LL long long
 #define PII pair<int,int>
 #define PLL pair<LL,LL>
-#define MP make_pair
 #define F first
 #define S second
-#define INF INT_MAX
+
+#define ALL(x)      (x).begin(), (x).end()
+#define READ        freopen("alu.txt", "r", stdin)
+#define WRITE       freopen("vorta.txt", "w", stdout)
+
+#ifndef ONLINE_JUDGE
+#define DBG(x)      cout << __LINE__ << " says: " << #x << " = " << (x) << endl
+#else
+#define DBG(x)
+#define endl "\n"
+#endif
+
+template<class T1, class T2>
+ostream &operator <<(ostream &os, pair<T1,T2>&p);
+template <class T>
+ostream &operator <<(ostream &os, vector<T>&v);
+template <class T>
+ostream &operator <<(ostream &os, set<T>&v);
 
 inline void optimizeIO()
 {
     ios_base::sync_with_stdio(false);
     cin.tie(NULL);
 }
 
-const int nmax = 1024+5;
-const LL LINF = 1e17;
+const int nmax = 2e5+7;
 
-string to_str(LL x)
-{
-    stringstream ss;
-    ss<<x;
-    return ss.str();
-}
-
-int n;
-int ara[nmax][nmax];
+struct Fenwick2D{
 
+    vector<vector<LL>>BIT;
+    int R,C;
 
+    Fenwick2D (int r,int c) : BIT(r+1,vector<LL>(c+1,0)) , R(r) , C(c) {}
 
-/** 2D BIT / FENWICK TREE **/
-/*** 1 based indexing ***/
+    inline int LSB(int x) {return x&(-x);} /// find the number with first bit set
 
-int BIT[nmax][nmax];
-inline int lowbit(int x)
-{
-    return x&(-x);
-}
+    /// POINT update : adds val to index (x,y)
+    void add(int x,int y,LL val)
+    {
+        for(int i = x ; i<=R ; i += LSB(i))
+            for(int j = y ; j<=C ; j += LSB(j))
+                BIT[i][j] += val;
+    }
 
-inline void update(int x,int y,int val) /** POINT update , adds to the current value . Point = {x,y} **/
-{
-    for(int i = x; i <= n; i += lowbit(i))
-        for(int j = y; j <= n; j += lowbit(j))
-            BIT[i][j] += val;
-}
+    /// prefix sum of [(1,1) , (x,y)] square
+    LL pref(int x,int y)
+    {
+        LL sum = 0;
 
-inline int query(int x,int y) /** RANGE Sum . Range  = [{1,1} , {x,y}] **/
-{
-    int sum = 0;
-    for(int i = x; i > 0; i -= lowbit(i))
-        for(int j = y; j > 0; j -= lowbit(j))
+        for(int i = x ; i>0 ; i -= LSB(i))
+            for(int j = y ; j>0 ; j -= LSB(j))
             sum += BIT[i][j];
 
-    return sum;
-}
-
-int main()
-{
-    //freopen("OUT.txt","w",stdout);
+        return sum;
+    }
 
-    n = 3;
+    /// sum of [(xl,yl) , (xh,yh)] square
+    LL sum(int xl,int yl,int xh,int yh)
+    {
+        LL v1 = pref(xh, yh);
+        LL v2 = pref(xh, yl-1);
+        LL v3 = pref(xl-1, yh);
+        LL v4 = pref(xl-1, yl-1);
+        return v1 - v2 - v3 + v4;
+    }
 
-    int val = 0;
-    for(int i=1; i<=n; i++)
-        for(int j=1; j<=n; j++)
+    void debug()
+    {
+        cout<<"Prefix Sum Array :\n";
+        for(int i=1; i<=R; i++)
         {
-            //cin>>val;
-            val++;
-            ara[i][j] = val;
-            update(i,j,ara[i][j]); /** Initial Update **/
+            for(int j=1; j<=C; j++)
+                cout<<pref(i,j)<<" ";
+            cout<<endl;
         }
+        cout<<endl;
+    }
+};
 
 
-    int query_count;
-    cin>>query_count;
+int main()
+{
+    optimizeIO();
+
+    int r,c,q;
+    cin>>r>>c>>q;
 
-    while(query_count--)
+    Fenwick2D f(r,c);
+
+    for(int i=1;i<=q;i++)
     {
+        f.debug();
+
         int type;
         cin>>type;
 
         if(type==1)
         {
-            /** Add val to {x,y} **/
-            int x,y,val;
+            int x,y;
+            LL val;
             cin>>x>>y>>val;
 
-            update(x,y,val);
+            f.add(x,y,val); /// point update
         }
-        else
+        else if(type==2)
         {
-            /** Sum of Range = [{x1,y1} , {x2,y2}] **/
             int x1,y1,x2,y2;
             cin>>x1>>y1>>x2>>y2;
 
-            int v1 = query(x2, y2);
-            int v2 = query(x2, y1-1);
-            int v3 = query(x1-1, y2);
-            int v4 = query(x1-1, y1-1);
-            int ans = v1 - v2 - v3 + v4;
-            cout<<"Sum : "<<ans<<endl;
+            cout<<f.sum(x1,y1,x2,y2)<<endl; /// range sum
         }
     }
 
+    return 0;
+}
 
+/**
+5 6 5
+2 2 2 4 5 1
+**/
 
-    return 0;
+template<class T1, class T2>
+ostream &operator <<(ostream &os, pair<T1,T2>&p)
+{
+    os<<"{"<<p.first<<", "<<p.second<<"} ";
+    return os;
+}
+template <class T>
+ostream &operator <<(ostream &os, vector<T>&v)
+{
+    os<<"[ ";
+    for(T i:v)
+    {
+        os<<i<<" " ;
+    }
+    os<<" ]";
+    return os;
 }
 
+template <class T>
+ostream &operator <<(ostream &os, set<T>&v)
+{
+    os<<"[ ";
+    for(T i:v)
+    {
+        os<<i<<" ";
+    }
+    os<<" ]";
+    return os;
+}