merging

Author: chrislucas

python/Xor/.idea/Xor.iml

@@ -2,4 +2,11 @@ https://www.geeksforgeeks.org/given-a-set-find-xor-of-the-xors-of-all-subsets/
 https://www.geeksforgeeks.org/sum-xor-possible-subsets/
 https://www.geeksforgeeks.org/maximum-xor-using-k-numbers-1-n/
 https://www.geeksforgeeks.org/calculate-xor-1-n/
-http://codeforces.com/blog/entry/10229
+http://codeforces.com/blog/entry/10229
+
+Teorias
+https://accu.org/index.php/journals/1915
+https://en.wikipedia.org/wiki/Symmetric_difference
+
+https://github.com/hypersolid/competitive-programming/blob/master/hackerrank/algorithms/dp/Xor-And-Sum.java
+https://github.com/havelessbemore/hackerrank/blob/master/algorithms/dynammic_programming/xor-and-sum.java

python/Xor/.idea/misc.xml

@@ -0,0 +1,35 @@
+All About XOR
+https://accu.org/index.php/journals/1915
+
+
+http://mathworld.wolfram.com/XOR.html
+https://www.physicsforums.com/threads/xor-in-set-theory.743760/
+
+Equal Sum and XOR
+https://www.geeksforgeeks.org/equal-sum-xor/
+
+
+Find two numbers from their sum and XOR
+https://www.geeksforgeeks.org/find-two-numbers-sum-xor/
+
+
+https://math.stackexchange.com/questions/2572213/sum-of-xor-matrix
+
+https://stackoverflow.com/questions/36477623/given-an-xor-and-sum-of-two-numbers-how-to-find-the-number-of-pairs-that-satisf
+
+
+https://www.hackerrank.com/challenges/maximizing-xor/problem
+https://www.hackerrank.com/contests/hourrank-13/challenges/sum-vs-xor/problem
+https://www.codechef.com/ACM16CHN/problems/CHN16H
+
+
+
+Theory - cyclic shifts bitwise
+https://www.codechef.com/SNCKPB16/problems/MINSHIFT
+https://www.geeksforgeeks.org/rotate-bits-of-an-integer/
+https://cboard.cprogramming.com/c-programming/145685-cycle-shift-bitwise-operators-help-pls.html
+
+
+Symmetric difference
+https://en.wikipedia.org/wiki/Symmetric_difference
+https://math.stackexchange.com/questions/84184/relation-between-xor-and-symmetric-difference

python/Xor/.idea/workspace.xml

@@ -1,3 +1,6 @@
+from math import log10, floor
+
+
 def isPowerOf2(n):
     return (n & (n - 1)) == 0
 
@@ -11,6 +14,7 @@ def sum_n_xor(n):
         acc = acc ^ x
     return acc
 
+
 def sum_n_xor2(n):
     o = n & 3
     if o == 0:
@@ -23,8 +27,17 @@ def sum_n_xor2(n):
         return 0
 
 
+def count_bits_base2(n):
+    return floor(log10(n) / log10(2)) + 1
+
+
+print(count_bits_base2(10))
+print(count_bits_base2(1 << 50))
+print(count_bits_base2(15))
+'''
 print([(x, sum_n_xor(x)) for x in range(4, 25)])
 print([(x, sum_n_xor2(x)) for x in range(4, 25)])
+'''
 
 if __name__ == '__main__':
     pass

python/Xor/raw/Xor

@@ -1,9 +1,10 @@
 '''
 https://www.hackerrank.com/challenges/xor-and-sum/problem
+https://en.wikipedia.org/wiki/Binary_number#Binary_counting
 '''
 
 
-def toDec(str_bin):
+def to_dec(str_bin):
     a, e = 0, 0
     for i in range(len(str_bin) - 1, -1, -1):
         a += (1 if str_bin[i] == '1' else 0) << e
@@ -26,11 +27,56 @@ def naive_test(a, b):
 def solver():
     bin_a = input()
     bin_b = input()
-    a, b = toDec(bin_a), toDec(bin_b)
+    a, b = to_dec(bin_a), to_dec(bin_b)
     return naive_test(a, b)
 
 
-print(solver())
+_LIMIT_SUM = 314159
+_M = 1000000007
+
+
+def solver2():
+    bin_a = input()
+    bin_b = input()
+    _sz_a = len(bin_a)
+    _sz_b = len(bin_b)
+    buffer_binary_a = [0] * _sz_a
+    acc_buffer_binary_b = [0] * _sz_b
+    acc_buffer_inv_binary_b = [0] * _sz_b
+    acc = 0
+    power_of_2 = 1
+    for x in range(_sz_a - 1, -1, -1):
+        buffer_binary_a[_sz_a - 1 - x] = 1 if bin_a[x] == '1' else 0
+
+    for x in range(_sz_b - 1, -1, -1):
+        idx = _sz_b - 1 - x
+        acc_buffer_binary_b[idx] = 1 if bin_b[x] == '1' else 0
+        if x < _sz_b - 1:
+            acc_buffer_binary_b[idx] += acc_buffer_binary_b[idx - 1]
+
+    for x in range(0, _sz_b):
+        acc_buffer_inv_binary_b[x] = 1 if bin_b[x] == '1' else 0
+        if x > 0:
+            acc_buffer_inv_binary_b[x] += acc_buffer_inv_binary_b[x - 1]
+
+    for x in range(0, _LIMIT_SUM):
+        xth_bit_a = buffer_binary_a[x] if x < _sz_a else 0
+        xth_bit_b = acc_buffer_binary_b[x] if x < _sz_b else acc_buffer_binary_b[_sz_b - 1]
+        if xth_bit_a == 1:
+            acc += (((_LIMIT_SUM+1-xth_bit_b)%_M)*(power_of_2%_M))%_M
+        else:
+            acc += ((xth_bit_b%_M)*(_M%power_of_2))%_M
+        power_of_2 = (power_of_2%_M)*(2%_M)%_M
+
+    for x in range(0, _sz_b):
+        acc += (power_of_2*acc_buffer_inv_binary_b[_sz_b-1-x])%_M
+        acc %= _M
+        power_of_2 = (power_of_2%_M)*(2%_M)%_M
+
+    return acc
+
+
+solver2()
 
 if __name__ == '__main__':
     pass

python/Xor/raw/problems

@@ -0,0 +1,6 @@
+https://www.hackerrank.com/challenges/dynamic-programming-classics-the-longest-common-subsequence/problem
+https://www.hackerrank.com/challenges/unbounded-knapsack/problem
+https://www.hackerrank.com/challenges/xor-and-sum/problem
+https://www.hackerrank.com/challenges/longest-increasing-subsequent/problem
+https://www.hackerrank.com/challenges/summing-pieces/problem
+https://www.hackerrank.com/challenges/sum-vs-xor/problem