I completed java lab 09.

README.md

@@ -16,7 +16,9 @@
     * Is the **blank** object mutable or immutable? How can you tell?
 
 ```text
-PUT ANSWER TO #2 HERE
+Blank object is mutable because it's original value
+ can be changed by
+a method
 ```
 
 ```java
@@ -47,7 +49,8 @@ public class Puzzler {
     * Explain how the return values from #3 and #4 differ.
 
 ```text
-PUT ANSWER TO #5 HERE
+The return of 3 is double/variable
+while the return type of 4 is an object
 ```
 
 ```java
@@ -87,14 +90,17 @@ Recall that aliases are two variables that refer to the same object.
     * Put the output in the text block below
 
 ```text
-PUT ANSWER TO #2 HERE
+(5, 8)
+(5, 8)
 ```
 
 3. At the end of main, are p1 and p2 aliased? Why or why not?
     * Put your answer in the text block below
 
 ```text
-PUT ANSWER TO #3 HERE
+No, at the end of main p1 and p2
+they both have the same value
+they refer to different instances
 ```
 
 ```java
@@ -142,7 +148,10 @@ for (int i = 0; i < s.length(); i++) {
     * Screenshot your output and add it to your project as Part3_2.jpg
 3. Generalize the code so that it works on any string.
     * What could you do to generalize it more?
-
+```
+ you could split up the for loop into a 
+ seperate method to generalize it more.
+```
 ## Part 4: Large Numbers
 
 Many encryption algorithms depend on the ability to raise large integers to a power. Below is a method that implements an efficient algorithm for integer exponentiation:

src/BigIntRewrite.java

@@ -1,5 +1,21 @@
+import java.math.BigInteger;
 public class BigIntRewrite {
     public static void main(String[] args) {
-
+        int x = 2;
+                int n = 10;
+                BigInteger result = bigPow(x,n);
+        System.out.println(x + "^" + n + "=" + result);
+    }
+    public static BigInteger bigPow(int x, int n) {
+        if (n == 0) return BigInteger.ONE;
+        // find x to the n/2 recursively
+        BigInteger t = bigPow(x, n / 2);
+        // if n is even, the result is t squared
+        // if n is odd, the result is t squared times x
+        if (n % 2 == 0) {
+            return t.multiply(t);
+        } else {
+            return t.multiply(t).multiply(BigInteger.valueOf(x));
+        }
     }
 }

src/StringPlayground.java

@@ -1,4 +1,22 @@
 public class StringPlayground {
     public static void main(String[] args) {
+        System.out.println(cntParanthesis("(3+7))"));
+        System.out.println(cntParanthesis("(((((3+7))"));
+        System.out.println(cntParanthesis("((100+790909))"));
+        System.out.println(cntParanthesis("(3+7))))))"));
+
+    }
+
+    public static int cntParanthesis(String s) {
+        int count = 0;
+        for (int i = 0; i < s.length(); i++) {
+            char c = s.charAt(i);
+            if (c == '(') {
+                count++;
+            } else if (c == ')') {
+                count--;
+            }
+        }
+        return count;
     }
 }