Add solution for 2016 Day 15

src/common/lib/Helper.h

@@ -600,12 +600,15 @@ struct Helper
     return Index2D{-1, -1};
   }
 
-  static int64_t ChineseRemainderTheoremTwo(int64_t mod1, int64_t mod2, int64_t res1, int64_t res2)
+  // Solve for N:
+  // remainder1 = N % mod1
+  // remainder2 = N % mod2
+  static int64_t ChineseRemainderTheoremTwo(int64_t mod1, int64_t mod2, int64_t remainder1, int64_t remainder2)
   {
-    int64_t i = res1;
+    int64_t i = remainder1;
     while (true)
     {
-      if (i % mod2 == res2)
+      if (i % mod2 == remainder2)
         return i;
 
       i += mod1;
@@ -613,17 +616,32 @@ struct Helper
     return 0;
   }
 
-  static int64_t ChineseRemainderTheorem(const std::vector<int64_t>& mods, const std::vector<int64_t>& results)
+  // Solve for N:
+  // remainders = N % mods
+  static int64_t ChineseRemainderTheorem(const std::vector<int64_t>& mods, const std::vector<int64_t>& remainders)
   {
     int64_t currentMod = mods.front();
-    int64_t currentRes = results.front();
+    int64_t currentRem = remainders.front();
     for (int i = 1; i < mods.size(); i++)
     {
-      int64_t result = ChineseRemainderTheoremTwo(currentMod, mods[i], currentRes, results[i]);
-      currentRes = result;
+      int64_t result = ChineseRemainderTheoremTwo(currentMod, mods[i], currentRem, remainders[i]);
+      currentRem = result;
       currentMod = currentMod * mods[i];
     }
-    return currentRes;
+    return currentRem;
+  }
+
+  // Solve for N:
+  // remainders = (start + N) % mods
+  static int64_t ChineseRemainderTheorem(const std::vector<int64_t>& mods,
+                                         std::vector<int64_t> remainders,
+                                         const std::vector<int64_t>& starts)
+  {
+    for (int i = 0; i < mods.size(); i++)
+    {
+      remainders[i] = ((remainders[i] - starts[i]) % mods[i] + mods[i]) % mods[i];
+    }
+    return ChineseRemainderTheorem(mods, remainders);
   }
 
   static uint64_t FastExponentiation(uint64_t start, uint64_t multiplication, uint64_t power, uint64_t mod)