Merge pull request #113 from 19-1-skku-oss/pbranch

Finalize fenwick tree

Python/data_structures/tree/binary tree/fenwick_tree.py

@@ -1,29 +1,40 @@
-from __future__ import print_function
-class FenwickTree:
-
-    def __init__(self, SIZE): # create fenwick tree with size SIZE
-        self.Size = SIZE
-        self.ft = [0 for i in range (0,SIZE)]
-
-    def update(self, i, val): # update data (adding) in index i in O(lg N)
-        while (i < self.Size):
-            self.ft[i] += val
-            i += i & (-i)
-
-    def query(self, i): # query cumulative data from index 0 to i in O(lg N)
-        ret = 0
-        while (i > 0):
-            ret += self.ft[i]
-            i -= i & (-i)
-        return ret
-
-if __name__ == '__main__':
-    f = FenwickTree(100)
-    f.update(1,20)
-    f.update(4,4)
-    print (f.query(1))
-    print (f.query(3))
-    print (f.query(4))
-    f.update(2,-5)
-    print (f.query(1))
-    print (f.query(3))
+'''
+Recomand studying segment tree first.
+Fanwick tree is made to save more memory space(than segment).
+So it is upgrade version of segment tree.
+Its time complexity iof update is O(log N) and use less memory.
+Crusal point of fenwick tree is that partcial sum algorithms can make interval sum.
+
+'''
+from __future__ import print_function
+class FenwickTree:
+
+    def __init__(self, SIZE): # Create fenwick tree with size SIZE
+        self.Size = SIZE
+        self.ft = [0 for i in range (0,SIZE)]
+
+    def update(self, i, val): # Update data (adding) in index i in O(lg N)
+        while (i < self.Size):
+            self.ft[i] += val
+            i += i & (-i)
+            # i += i & (-i) this means adding 1 to lowest "1" location.
+            # Need to understand bit operation.
+
+    def query(self, i): # Query cumulative data from index 0 to i in O(lg N)
+        ret = 0
+        while (i > 0):
+            ret += self.ft[i]
+            i -= i & (-i)
+            # i += i & (-i) this means adding 1 to lowest "1" location.
+        return ret
+
+if __name__ == '__main__': # Main for test
+    f = FenwickTree(100)
+    f.update(1,20)
+    f.update(4,4)
+    print (f.query(1))
+    print (f.query(3))
+    print (f.query(4))
+    f.update(2,-5)
+    print (f.query(1))
+    print (f.query(3))