Java Notes
HubArray IntroductionArray OperationsArray Programs — FundamentalsArray Interview QuestionsJagged Array in JavaMulti Dimensional ArrayOne Dimensional Arraybreak and continue in JavaDo-While Loop in JavaFor Loop in JavaIf-Else Statements in JavaNested Loops in JavaSwitch-Case in JavaWhile Loop in JavaJava Compilation ProcessFeatures of JavaYour First Java ProgramHistory of JavaJava EditionsJava Program StructureJDK, JRE, and JVMWhat is Java?Immutable Strings in JavaString Class in JavaString Interview QuestionsString MethodsString Programs — FundamentalsStringBuffer in JavaStringBuilder in JavaComments in JavaData Types in JavaIdentifiers in JavaInput and Output in JavaKeywords in JavaOperators in JavaType Casting in JavaVariables in JavaAbstract Class in JavaAbstraction in JavaAnonymous Class in JavaClass and Object in JavaConstructor in JavaEncapsulation in JavaInheritance in JavaInner Class in JavaInterface in JavaMethod Overloading in JavaMethod Overriding in JavaObject Class in JavaObject Cloning in JavaOOPs IntroductionPolymorphism in Javastatic Keyword in Javasuper Keyword in Javathis Keyword in JavaWrapper Class in JavaCollections Framework OverviewCollections Practice ProgramsComparable vs Comparator in JavaGenerics in JavaIterator in JavaArrayList in JavaLinkedList in JavaStack in Java — Collections FrameworkVector in JavaHashMap in JavaHashtable in JavaLinkedHashMap in JavaTreeMap in JavaArrayDeque in JavaDeque Interface in JavaPriorityQueue in JavaHashSet in JavaLinkedHashSet in JavaTreeSet in JavaException Handling Best PracticesCustom Exceptions in JavaException Hierarchy in JavaFinally Block in JavaException Handling Introductionthrow and throws Keywords in JavaTry-Catch Block in JavaBuffered Streams in JavaByte Streams in JavaCharacter Streams in JavaDeserialization in JavaFile Class in JavaJava NIO PackageSerialization in JavaDate and Time API in Java 8Default and Static Methods in InterfacesFunctional Interface in Java 8Lambda Expression in Java 8Method Reference in Java 8Optional Class in Java 8Stream API in Java 8Creating Threads in JavaDaemon Threads in JavaExecutor Framework in JavaInter-Thread Communication in JavaMultithreading Programs in JavaRunnable Interface in JavaSynchronization in JavaThread Class in JavaThread IntroductionThread Life Cycle in JavaThread Priority in JavaBatch Processing in JDBCCallableStatement in JDBCJDBC ArchitectureJDBC IntroductionJDBC ProjectsMySQL Connection with JDBCPreparedStatement in JDBCResultSet in JDBCStatement Interface in JDBCTransaction Management in JDBCCookies in ServletsExpression Language (EL)GenericServletHttpServletJSP IntroductionJSP Tags and JSTLMVC ArchitectureRequest and Response ObjectsServlet IntroductionServlet Life CycleSession TrackingDependency InjectionAPI GatewayConfig ServerDocker DeploymentEureka Server - Service DiscoverySpring BeansCRUD ApplicationException Handling in Spring BootJWT Authentication — Java ProgrammingREST API with Spring BootSpring SecuritySpring Boot IntroductionSpring Data JPAValidation in Spring BootSpring Core ContainerSpring Framework IntroductionDynamic Programming in JavaGraph Data Structure in JavaHashing in JavaHeap (DSA)Linked List in JavaQueue in JavaRecursion in JavaSearching Algorithms in JavaSorting Algorithms in JavaStack in Java — DSA in JavaTime ComplexityTree Data Structure in JavaAdapter Design PatternBuilder Design PatternFactory Design PatternMVC Pattern — Java ProgrammingObserver Design PatternSingleton Design PatternArray Programs — PracticeBasic Java ProgramsCollection ProgramsJDBC ProgramsMultithreading ProgramsOOP ProgramsPlacement Coding QuestionsString Programs — PracticeBanking System — Java ProgrammingChat ApplicationE-Commerce BackendEmployee Management SystemLibrary Management System — Java ProgrammingSpring Boot Fullstack ProjectStudent Management System — Java ProgrammingCoding Interview QuestionsCollections Interview QuestionsCore Java Interview QuestionsJDBC Interview QuestionsMultithreading Interview QuestionsOOPs Interview QuestionsSpring Framework Interview QuestionsJava Cheat SheetImportant Formulas & ConceptsImportant Java ProgramsQuick Revision Notes — Java ProgrammingJava Master Course - Learning Roadmap
Master recursion — base cases, recursive thinking, call stack visualization, tail recursion, memoization, backtracking, and converting recursion to iteration.
What is Recursion?
A method that calls itself to solve a problem by breaking it into smaller subproblems of the same type. Every recursive solution has:
- Base case — stops the recursion (prevents infinite loop)
- Recursive case — reduces the problem and calls itself
java example
// Structure of every recursive function
returnType solve(problem) {
if (baseCase) {
return simpleSolution; // Stop here
}
// Break into smaller problem
return combine(solve(smallerProblem)); // Self-call
}Classic Recursive Problems
Fibonacci
Example
// Naive O(2^n) — VERY SLOW (exponential)
int fibNaive(int n) {
if (n <= 1) return n;
return fibNaive(n - 1) + fibNaive(n - 2);
}
// Memoized O(n) — FAST (store computed values)
int fibMemo(int n, int[] memo) {
if (n <= 1) return n;
if (memo[n] != 0) return memo[n]; // Already computed
memo[n] = fibMemo(n - 1, memo) + fibMemo(n - 2, memo);
return memo[n];
}
// Iterative O(n) — BEST (no stack overhead)
int fibIterative(int n) {
if (n <= 1) return n;
int prev2 = 0, prev1 = 1;
for (int i = 2; i <= n; i++) {
int curr = prev1 + prev2;
prev2 = prev1;
prev1 = curr;
}
return prev1;
}
Power Function
java example
// Naive: O(n)
double power(double base, int exp) {
if (exp == 0) return 1;
if (exp < 0) return 1.0 / power(base, -exp);
return base * power(base, exp - 1);
}
// Fast power: O(log n) — divide and conquer
double fastPower(double base, int exp) {
if (exp == 0) return 1;
if (exp < 0) return 1.0 / fastPower(base, -exp);
double half = fastPower(base, exp / 2);
if (exp % 2 == 0) {
return half * half; // Even: x^n = (x^(n/2))²
} else {
return half * half * base; // Odd: x^n = (x^(n/2))² × x
}
}Tower of Hanoi
java example
void towerOfHanoi(int n, char from, char to, char aux) {
if (n == 1) {
System.out.println("Move disk 1 from " + from + " to " + to);
return;
}
towerOfHanoi(n - 1, from, aux, to); // Move n-1 disks to auxiliary
System.out.println("Move disk " + n + " from " + from + " to " + to);
towerOfHanoi(n - 1, aux, to, from); // Move n-1 disks from auxiliary to target
}
// Time: O(2^n), Space: O(n) stackBacktracking
Example
// N-Queens Problem
public class NQueens {
public List<List<String>> solveNQueens(int n) {
List<List<String>> solutions = new ArrayList<>();
char[][] board = new char[n][n];
for (char[] row : board) Arrays.fill(row, '.');
solve(board, 0, solutions);
return solutions;
}
private void solve(char[][] board, int row, List<List<String>> solutions) {
if (row == board.length) {
solutions.add(construct(board));
return;
}
for (int col = 0; col < board.length; col++) {
if (isSafe(board, row, col)) {
board[row][col] = 'Q'; // Choose
solve(board, row + 1, solutions); // Explore
board[row][col] = '.'; // Un-choose (backtrack)
}
}
}
private boolean isSafe(char[][] board, int row, int col) {
// Check column above
for (int i = 0; i < row; i++)
if (board[i][col] == 'Q') return false;
// Check upper-left diagonal
for (int i = row-1, j = col-1; i >= 0 && j >= 0; i--, j--)
if (board[i][j] == 'Q') return false;
// Check upper-right diagonal
for (int i = row-1, j = col+1; i >= 0 && j < board.length; i--, j++)
if (board[i][j] == 'Q') return false;
return true;
}
}
Generating All Subsets
Example
public List<List<Integer>> subsets(int[] nums) {
List<List<Integer>> result = new ArrayList<>();
backtrack(nums, 0, new ArrayList<>(), result);
return result;
}
private void backtrack(int[] nums, int start, List<Integer> current, List<List<Integer>> result) {
result.add(new ArrayList<>(current)); // Add current subset
for (int i = start; i < nums.length; i++) {
current.add(nums[i]); // Choose
backtrack(nums, i + 1, current, result); // Explore
current.remove(current.size() - 1); // Un-choose
}
}
Recursion vs Iteration
Example
// Every recursion CAN be converted to iteration (using explicit stack)
// Recursive tree traversal
void inorder(TreeNode node) {
if (node == null) return;
inorder(node.left);
process(node);
inorder(node.right);
}
// Iterative equivalent
void inorderIterative(TreeNode root) {
Stack<TreeNode> stack = new Stack<>();
TreeNode curr = root;
while (curr != null || !stack.isEmpty()) {
while (curr != null) {
stack.push(curr);
curr = curr.left;
}
curr = stack.pop();
process(curr);
curr = curr.right;
}
}
Interview Questions
Q1: What are the two essential parts of a recursive function?
Answer: Base case (termination condition that returns without recursing) and recursive case (breaks problem into smaller subproblem and calls itself). Missing a base case causes StackOverflowError.
Q2: What is the difference between head and tail recursion?
Answer: Head recursion: recursive call happens before processing (e.g., solve(n-1); process(n);). Tail recursion: recursive call is the LAST operation (e.g., return solve(n-1, accumulator);). Tail recursion can be optimized to iteration by compilers (not JVM though).
Q3: How does memoization improve recursive solutions?
Answer: It caches previously computed results. Without memo, fibonacci(50) makes ~2^50 calls (duplicate subproblems). With memo, each subproblem is solved once and stored — reducing to O(n) calls.
Q4: What is the maximum recursion depth in Java?
Answer: Depends on stack size (default ~512KB-1MB, roughly 5000-10000 frames). Can be increased with -Xss JVM flag. For deeper recursion, convert to iterative with explicit stack.
Q5: Explain backtracking with an example.
Answer: Backtracking explores solutions incrementally, abandoning paths that violate constraints. Pattern: Choose → Explore (recurse) → Un-choose (backtrack). Example: N-Queens places queens row by row, backs up when no safe column exists.
Q6: When should you use recursion vs iteration?
Answer: Recursion: tree/graph traversal, divide-and-conquer, backtracking, problems with recursive structure (Towers of Hanoi). Iteration: simple loops, performance-critical code, deep recursion risks. Many interviewers expect recursive solutions.
Exam Focus
Revise definitions, diagrams, examples, and short-answer points for Recursion in Java.
Interview Use
Prepare one clear explanation, one practical example, and one common mistake for this Java Master Course topic.
Search Terms
java-master-course, java master course, java, master, course, dsa, recursion, recursion in java
Related Java Master Course Topics
Continue learning this concept
DSA in JavaDynamic Programming in JavaComplete guide to Dynamic Programming in Java covering memoization, tabulation, classical DP problems (Fibonacci, Knapsack, LCS, LIS, Coin Change), time/space optimization, and interview patterns.DSA in JavaGraph Data Structure in JavaComplete guide to graphs — representation, BFS, DFS, shortest path algorithms, topological sort, and classic graph problems in Java.DSA in JavaHashing in JavaComplete guide to hashing — hash functions, collision resolution, HashMap internals, custom hashCode/equals, and applications of hashing in problem-solving.DSA in JavaHeap (DSA)Complete guide to Heap data structure in Java covering Min Heap, Max Heap, heap operations, heapify algorithm, PriorityQueue class, heap sort, and applications with detailed implementations.DSA in JavaLinked List in JavaComplete guide to Linked Lists — Singly, Doubly, and Circular linked lists with Java implementations, operations, and classic interview problems.DSA in JavaQueue in JavaComplete guide to Queue data structure — FIFO principle, circular queue, priority queue, deque, BFS applications, and classic problems.