UIL CS: Recursion & Loops

This is part of the UIL CS study series. See also:

• Number Systems
• Java Fundamentals
• Bitwise & Boolean
• OOP & Generics
• Collections & Algorithms
• Practice Resources

Main topic list: https://www.uiltexas.org/files/academics/UILCS-JavaTopicList2526.pdf

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8. Recursion Tracing (example)

static int f(int n) {
    if (n <= 1) return 1;
    return n * f(n - 2);
}

Trace $f(7)$:

$$\begin{aligned} f(7) &= 7 \cdot f(5) \\ f(5) &= 5 \cdot f(3) \\ f(3) &= 3 \cdot f(1) \\ f(1) &= 1 \end{aligned}$$

Back-substitute:

$$\begin{aligned} f(3) &= 3 \cdot 1 = 3 \\ f(5) &= 5 \cdot 3 = 15 \\ f(7) &= 7 \cdot 15 = 105 \end{aligned}$$

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9. Tracing a Nested Loop (example)

int count = 0;
for (int i = 1; i <= 3; i++) {
    for (int j = 1; j <= i; j++) {
        count += i + j;
    }
}
System.out.println(count);

Trace:

• $i=1$: $j=1 \rightarrow$ add $(1+1)=2 \rightarrow$ count=2
• $i=2$: $j=1 \rightarrow$ add $3 \rightarrow$ count=5 $j=2 \rightarrow$ add $4 \rightarrow$ count=9
• $i=3$: $j=1 \rightarrow$ add $4 \rightarrow$ count=13 $j=2 \rightarrow$ add $5 \rightarrow$ count=18 $j=3 \rightarrow$ add $6 \rightarrow$ count=24

Output: $24$

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10. Math.random() and Random

Math.random()

Returns double in $[0.0, 1.0)$

Common patterns:

int x = (int)(Math.random() * 10);          // 0..9
int y = (int)(Math.random() * 6) + 1;       // 1..6
int z = (int)(Math.random() * (b - a + 1)) + a; // a..b

Random class

Random r = new Random(); // or new Random(seed)
int a = r.nextInt(10);       // 0..9
int b = r.nextInt(6) + 1;    // 1..6
double d = r.nextDouble();   // [0.0, 1.0)
boolean ok = r.nextBoolean();

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12. Pass-By-Value in Java

Java always passes primitive values by value. For objects, reference copies are passed. Assigning to a parameter doesn't change the original reference.

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13. Exceptions/Errors

• Recognize common runtime errors (e.g., NullPointerException, NumberFormatException, array index errors).
• Checked exceptions require try/catch or throws declaration.
• The compiler only checks syntax and type safety; actual variable values exist at run time.
• Local, uninitialized variables will throw a compiler (syntax) error if you attempt to use them. On the other hand, class-level variables (both instance fields and static) are provided a default value by the compiler, and thus do not throw errors.
  • Numeric default values (e.g., short, int, long, float, double): $0$, $0.0$, or $0.0f$
  • Boolean default value: false
  • Char default value: '\u0000'
  • Reference type default value (e.g., String): null

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15. Arrays & Strings

Arrays: traversal, indexing, mutation. Multi-dimensional arrays.

Strings: substring, charAt, concatenation. String to char array: "abc".toCharArray().