(for question 1) public static String addBinaryStrings(String a, String b) { if ((null == a) || (null == b)) return null; return int2bstring(bstring2int(a) + bstring2int(b)); } public static int bstring2int(String a) { int sum = 0; int multiplier = 1; while (a.length() > 0) { String lastChar = a.substring(a.length()-2, a.length()); if (lastChar.equals("1")) sum += multiplier; multiplier *= 2; a = a.substring(0, a.length()-1); } return sum; } public static String int2bstring(int i) { if (0 == i) return "0"; String s = ""; while (i > 0) { if ((i % 2) == 0) { s = "1" + s; } else { s = "0" + s; } i /= 2; } return s; }

A: int distance( int num1, int num2 ) { int distance; while( num1 != 0 && num2 != 0 ) { distance += num1&1!=num2&1; num1=num1>>1; num2=num2>>1; } return distance; } B: int distanceSum( std::vector nums ) { std::unordered_map digits; for( auto& num : nums ) { int digit = 1; while( num != 0 ) { digits[digit]+=num&1; num = num>>1; digit++; } } int distanceSum = 0; for( auto& p : digits ) { distanceSum += nums.length()-p.second; } return distanceSum; }

for Problem C: /** * This solution is O(n) *I wrote it this way so its easier to be understood. **/ public int getHammingTotalFromBinaryNumbersList(List binaryNumbers){ Map binaryCounter = new HashMap; // Key is the _[1 or 0] on the binary number, so if you're at position 1, and you get 0, the key will be 0_1 String positionKey; int totalCount; int maxPosition = 0; foreach(String binaryNumber in binaryNumbers){ if(binaryNumber.Length-1 > maxPosition){ maxPosition = binaryNumber.Length-1; } for(i = 0; i

10001 10101 int GetHammingDistance(string s1, string s2) { Debug.Assert(s1.Length == s2.Length); int distance = 0; for(int i=0; i input, int n, out List distances) { if(n==2) { distances.Add(GetHammingDistance(input[0], input[1])); } for(int i=0; i {XY} GetAllPairsHammingDistance(zyx, 2, "")=> {XY, ZY} GetAllPairsHammingDistance(zxy, 2, "")=> {XY, ZY, ZX} XYZ 0 1 2 = 3 X Y Z | | | 0 1 | Y | |_ 0 1 = 2 Y Z | | | |_Z |_Y

Problem 1. Add two binary numbers represented as ASCII strings with result also in form of an ASCII string // // Add two binary strings, the solution as follows: // 1) convert binary strings to unsigned integers // 2) Add resulting integers // 3) Convert the result back to binary string // 4) Reverse the string to obtain the resulting string // // // Convert binary ASCII string to unsigned integer by successive divide by 2 // uint binStr_to_uint(const char *pStr, int *size) { char *pEnd = pStr; uint num = 0; while(*pEnd) num = (num >= 1; //divide by 2 } *pStr = 0; //terminate the string } // Reverse a string void reverseString(char *pStr) { char *pEnd = pStr; while(*pEnd++) ; pEnd -= 2; //point to last string char char *pTmp; while(pStr size2 ? size1 : size2; char *pResult = malloc(sizeRes + 2); //add space for carry and EOS if(pResult == 0) return 0; uint_to_binStr(num2, pResult); reverseString(pResult); return (pResult); } Problem 2. Find Humming distance between two numbers. The problem did not specify what format the numbers are in, so I assumed unsigned integers. // // Find Humming distance // int hummingDistnce(uint num1, uint num2) { num1 = num1 ^ num2; //Humming distance is simply an XOR num2 = 0; while(num1) { ++num2; //count '1' bits num1 &= num1 - 1; } return num2; } The second part of the problem is simple, just traverse the list selecting pairs of numbers and call hummingDistance() function each time.

Corrections to my previous example: // Convert binary ASCII string to unsigned integer by successive divide by 2 should say ....multiply by 2 instead of divide by 2

Another minor error fix, function uint_to_binStr(uint num) definition should also have a pointer to char parameter like below: void uint_to_binStr(uint num, char *pStr)

Third correction, In function reverseString(), the temporary char variable should be defined as "char tmp;" instead of "char *pTmp", so the code block should be: char tmp; while(pStr < pEnd) { tmp = *pEnd; *pEnd-- = *pStr; *pStr++ = tmp;

(for question 2) public static int hammingDistance(String a, String b) { int numDigits = Math.max(a.length(), b.length()); int numDiff = 0; for (int i = 0; i < numDigits; i++) { String ithDigitA = extractDigit(a, i, numDigits); String ithDigitB = extractDigit(b, i, numDigits); if (!ithDigitA.equals(ithDigitB)) numDiff++; } return numDiff; } public static String extractDigit(String a, int i, int n) { if (i < n - a.length()) return "0"; return a.substring(i-n+a.length(), i-n+a.length()+1); } public static int setHamming(String[] a) { int numDiff = 0; int numDigits = 0; for (int i = 0; i < a.length; i++) { numDigits = Math.max(numDigits, i); } for (int i = 0; i < numDigits; i++) { int num0s = 0; int num1s = 0; for (String aa : a) { String ithDigitAA = extractDigit(aa, i, numDigits); if (ithDigitAA.equals("0")) { num0s++; } else { num1s++; } } numDiff += (num0s * num1s); } return numDiff; }