Calculate the factorial of a non-negative integer n (denoted as n!), which is the product of all positive integers less than or equal to n. Base case is 0! = 1. Often implemented recursively.

Factorial of a Number

Compute the n-th Fibonacci number, where F(0) = 0, F(1) = 1, and F(n) = F(n-1) + F(n-2) for n > 1. Naive recursion is simple but inefficient; often requires memoization or dynamic programming for optimization.

Fibonacci Sequence

Implement pow(x, n), which calculates x raised to the power n (x^n). Can be solved efficiently using recursion and the principle of exponentiation by squaring.

Power of a Number (x^n)

Generate all possible unique permutations (rearrangements of characters) of a given input string. This is a classic backtracking problem.

Permutations of a String

Given an array `nums` of distinct integers, return all possible permutations (orderings) of the elements. Solved using backtracking.

Permutations of an Array

Given n pairs of parentheses, generate all combinations of well-formed (valid) parentheses strings. Uses backtracking to ensure parentheses are balanced.

Generate Parentheses

Given a string containing digits 2-9, return all possible letter combinations mapped from a standard phone keypad. Uses backtracking to explore combinations.

Letter Combinations of Phone Number

Given an m x n grid of characters and a word, determine if the word exists in the grid by moving horizontally or vertically to adjacent cells. The same cell cannot be used more than once. Solved with DFS/backtracking.

Word Search in 2D Board

Place N queens on an N×N chessboard such that no two queens attack each other (same row, column, or diagonal). Find all distinct solutions or configurations. A classic backtracking problem.

N-Queens Problem

Write a function to solve a Sudoku puzzle by filling the empty cells ('.') with digits 1-9, following Sudoku rules. Assumes a unique solution exists. Uses backtracking with constraint checking.

Sudoku Solver

Given a set of non-negative integers and a target sum, determine if there is a subset of the given set whose elements sum up to the target sum. Can be solved using recursion/backtracking or dynamic programming.

Subset Sum Problem

Given two integers n and k, return all possible combinations of k numbers chosen from the range [1, n]. The order of elements within a combination doesn't matter.

Combinations (k out of n)

Given a string s, partition s such that every substring in the partition is a palindrome. Return all possible palindrome partitionings of s. Uses backtracking, often combined with palindrome checks.