EPI: primitive multiply (CPP)

Author: jsgoller1

elements-of-programming-interviews/.gitignore

@@ -1 +1,2 @@
-cpp/cpp_build/**
+cpp/cpp_build/**
+Scratchpad.ipynb

elements-of-programming-interviews/cpp/primitive_multiply.cc

@@ -1,7 +1,60 @@
 #include "test_framework/generic_test.h"
+
+void printBin(unsigned long long val, size_t len, const std::string& suffix) {
+  std::string binval;
+  for (size_t i = 0; i < len; i++) {
+    binval.append(val & 1 ? "1" : "0");
+    val >>= 1;
+  }
+  reverse(binval.begin(), binval.end());
+  printf("%s (%s)\n", binval.c_str(), suffix.c_str());
+}
+
+unsigned long long Add(unsigned long long a, unsigned long long b) {
+  /*
+    total = a^b
+    carry = (a & b) << 1
+    while carry:
+        newTotal = total ^ carry
+        newCarry = (total & carry) << 1
+        total, carry = newTotal, newCarry
+    return total
+  */
+  unsigned long long total = a ^ b;
+  unsigned long long carry = (a & b) << 1;
+  while (carry) {
+    unsigned long long newTotal = total ^ carry;
+    carry = (total & carry) << 1;
+    total = newTotal;
+  }
+  return total;
+}
+
 unsigned long long Multiply(unsigned long long x, unsigned long long y) {
-  // TODO - you fill in here.
-  return 0;
+  /*
+  - Can only use assignment, comparisons, and bitwise operations (&, |, ~, ^)
+  - Lshift is a multiply by 2
+  - Clearing the lowest bit and setting all to the right of it: subtract 1
+  - Adding: bitwise xor with carry
+    (3+3=6)
+    11 +
+    11 =
+   110
+  - Multiply can be iterative addition, but without subtraction this will be
+    hard
+  - Multiply: prod = 0. Until b=0, if lowest bit is set, add prod+=a. Right
+    shift b, leftshift a. (3*3=9) 11 * 11 = 1001 (5*5=25) 101 * 101 = 11001
+  */
+  unsigned long long prod = 0;
+  while (y) {
+    if (y & 1) {
+      prod = Add(x, prod);
+    }
+    y >>= 1;
+    x <<= 1;
+  }
+
+  return prod;
 }
 
 int main(int argc, char* argv[]) {

elements-of-programming-interviews/problem_mapping.js

@@ -72,7 +72,7 @@ problem_mapping = {
         },
         "4.05 Compute product without arithmetical operators": {
             "C++: primitive_multiply.cc": {
-                "passed": 0,
+                "passed": 10006,
                 "total": 10006
             },
             "Java: PrimitiveMultiply.java": {