Day-25: Bit manipulation problems

Author: mandliya

README.md

@@ -2,9 +2,9 @@
 This repository will contain random algorithm and data structure problems I resolve to solve at least one a day.
 
 ## Current Streak
-**23 days**
+**25 days**
 ## Longest streak
-23 days (August 17, 2015 - Sept 08, 2015)
+25 days (August 17, 2015 - Sept 10, 2015)
 
 ## Include Directiory
 Include directory and sub directories contain STL like header file implementation of various algorithms and data structures. Following header only implementation,
@@ -52,3 +52,6 @@ please let me know.
 ### Bit Manipulation
     - Determine if a number is a power of 2.
     - Add two binary number represented as string.
+    - Determine the next power of 2 for a given number.
+    - Using bit manipulation determine if a number is multiple of 3.
+    - Determine endianess of the machine, print a number in reverse Endianess.

bit_manipulation/multiple_of_3.cpp

@@ -0,0 +1,68 @@
+/**
+ * Check if a given number is multiple of 3
+ * Basic way of doing is : if sum of digits of number is multiple of 3,
+ * number is divisible by 3.
+ *
+ * However another efficient way of doing it is:
+ * Count the number of set bits at even positions.
+ * Count the number of set bits at odd positions.
+ * if difference is multiple of 3, number will be multiple of 3.
+ *
+ * Proof:
+ * We can prove it by taking the example of 11 in decimal numbers.
+ * (It will apply to 3 in binary numbers as well.)
+ * AB = 10A + B ( A and B are digits of number AB)
+ * AB = 11A + (B - A)
+ * Clearly if (B-A) is multiple of 11, number would be muliple of 11.
+ * We can do it similarly for 3 digits
+ * ABC = 100A + 10B + C
+ *     = 99A + A + 11B - B + C
+ *     = 11(9A + B) + (A - B + C)
+ * Clearly if A-B+C is multiple of 11, ABC would be multiple as well.
+ * similarly for 4 digits
+ * ABCD = 1000A + 100B + 10C + D
+ *      = (1001A – 999B + 11C) + (D + B – A -C )
+ *      So, if (B + D – A – C) is a multiple of 11 then is ABCD.
+ */
+
+#include <iostream>
+
+bool is_multiple_of_3( int n )
+{
+  // change to positive if negative
+  if ( n < 0 ) {
+    n = -n;
+  }
+  if ( n == 0 ) {
+    return true;
+  }
+  if ( n == 1 ) {
+    return false;
+  }
+  int even_count = 0;
+  int odd_count = 0;
+  while ( n ) {
+    if ( n & 1 ) {
+      ++odd_count;
+    }
+    n >>= 1;
+    if ( n & 1 ) {
+      ++even_count;
+    }
+    n >>= 1;
+  }
+  return is_multiple_of_3( even_count - odd_count );
+}
+
+int main()
+{
+  int num;
+  std::cout << "Enter a number:";
+  std::cin >> num;
+  if (is_multiple_of_3(num))  {
+    std::cout << num << " is multiple of 3" << std::endl;
+  } else {
+    std::cout << num << " is not a multiple of 3" << std::endl;
+  }
+  return 0;
+}

bit_manipulation/next_power_of_2.cpp

@@ -0,0 +1,28 @@
+/*
+ * Write a function that, for a given no n, finds a number p which is greater than or equal to n and is a power of 2.
+ */
+#include <iostream>
+
+int next_power_of_2( int num ) {
+  //already a power of 2
+  if (num && !(num & (num-1))) {
+    return num;
+  }
+  //count till msb set bit
+  int count = 0;
+  while ( num != 0 ) {
+    num >>= 1;
+    count++;
+  }
+  return (1 << count);
+}
+
+int main()
+{
+  std::cout << "Enter a number:";
+  int num;
+  std::cin >> num;
+  std::cout << "Next power of 2 which is greater than or equal to " << num
+            << " is: " << next_power_of_2(num) << std::endl;
+  return 0;
+}

bit_manipulation/reverseEndianness.cpp

@@ -0,0 +1,68 @@
+#include <iostream>
+#include <cstdio>
+
+enum endianess {
+  LITTLE_ENDIAN_MACHINE = 0,
+  BIG_ENDIAN_MACHINE
+};
+
+endianess determine_endianess()
+{
+  unsigned int num = 1;
+  char * c = (char *) &num;
+  if (*c == 1) {
+    return LITTLE_ENDIAN_MACHINE;
+  } else {
+    return BIG_ENDIAN_MACHINE;
+  }
+}
+
+void printBytes( char * start, int size)
+{
+  for ( int i = 0; i < size; ++i ) {
+    printf("%.2x ", start[i] );
+  }
+  std::cout << std::endl;
+}
+
+int reverseEndianNess( int num )
+{
+  int byte1, byte2, byte3, byte4;
+  byte1 = (num & 0x000000FF) >> 0;
+  byte2 = (num & 0x0000FF00) >> 8;
+  byte3 = (num & 0x00FF0000) >> 16;
+  byte4 = (num & 0xFF000000) >> 24;
+  return ((byte1 << 24) | (byte2 << 16) | (byte3 << 8) | (byte4 << 0));
+}
+
+int main() {
+  endianess sys_endianess = determine_endianess();
+  if (sys_endianess == LITTLE_ENDIAN_MACHINE) {
+    std::cout << "System is little endian\n\n";
+  } else {
+    std::cout << "System is big endian\n\n";
+  }
+
+  int num = 0x01234567;
+  std::cout << "Num in decimal:    " << num << std::endl;
+  std::ios::fmtflags f(std::cout.flags());
+  std::cout << "Num in hexadecimal:" << std::hex << num << std::endl;
+  std::cout.flags( f );
+  std::cout << "Printing individual bytes:\n";
+  printBytes((char*)&num, sizeof(num));
+
+  std::cout << std::endl;
+  std::cout << "Num in reversed endianness:\n";
+  int num1 = reverseEndianNess(num);
+
+  std::cout << "Num in decimal    :" << num1 << std::endl;
+
+  f = std::cout.flags();
+  std::cout << "Num in hexadecimal:" << std::hex << num1 << std::endl;
+  std::cout.flags( f );
+  std::cout << "Printing individual bytes:\n";
+  printBytes((char*)&num1, sizeof(num1));
+
+  return 0;
+
+}