add a solution for 3178

Author: fishercoder1534

Diff for: src/main/java/com/fishercoder/solutions/fourththousand/_3178.java

@@ -16,4 +16,25 @@ public int numberOfChild(int n, int k) {
             }
         }
     }
+
+    public static class Solution2 {
+        /**
+         * Also, my completely original solution, much more elegant and efficient.
+         */
+        public int numberOfChild(int n, int k) {
+            //n - 1 is the number of steps is takes to finish from one end to the other
+            // 2 * (n - 1) is the whole round trip, so after this, it's back to the starting point
+            //so we only need to handle the modulo remainder of 2 * (n - 1)
+            k = k % ((n - 1) * 2);
+            if (k < n) {
+                //in this case, we can directly return k
+                return k;
+            } else {
+                //in this case, it's in the reverse direction, we deduct the number of steps needed to finish the forward direction first
+                k -= n - 1;
+                //then return the correct child index
+                return n - k - 1;
+            }
+        }
+    }
 }

Diff for: src/test/java/com/fishercoder/fourththousand/_3178Test.java

@@ -8,15 +8,18 @@
 
 public class _3178Test {
     private static _3178.Solution1 solution1;
+    private static _3178.Solution2 solution2;
 
     @BeforeEach
     public void setup() {
         solution1 = new _3178.Solution1();
+        solution2 = new _3178.Solution2();
     }
 
     @Test
     public void test1() {
         assertEquals(1, solution1.numberOfChild(3, 5));
+        assertEquals(1, solution2.numberOfChild(3, 5));
     }
 
     @Test