Find the sum of number of set bits in a range of numbers

Author: mmbhatk

README.md

@@ -35,6 +35,7 @@ This directory contains various types of algorithm questions like Dynamic Progra
 4. [Math](algorithms/math)
 5. [Misc](algorithms/miscellaneous)
 6. [Sorting](algorithms/sorting)
+7. [Bit Manipulation](algorithms/bit_manipulation)
 
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algorithms/bit_manipulation/range_sum_set_bits.py

@@ -0,0 +1,19 @@
+# Question: Find the sum of number of set bits in all the numbers in the range [1, n].
+
+def countBits(n):
+    
+    """ Consider a number x and half of the number (x//2).
+    The binary representation of x has all the digits as
+    the binary representation of x//2 followed by an additional
+    digit at the last position. Therefore, we can find the number
+    of set bits in x by finding the number of set bits in x//2
+    and determining whether the last digit in x is 0 or 1. """
+
+    res = [0] * (n+1)
+    for i in range(1, n+1):
+        res[i] = res[i//2] + (i & 1)
+    return sum(res)
+    
+
+# Extension: Find the sum of number of set bits in all the numbers in the range [m, n].
+# Answer: In countBits(m, n), return sum(res) - sum(res[:m])