Problem 1: Narcissistic Numbers (Armstrong Numbers) A Narcissistic number (also known as an Armstrong number or PPDI) is a 3-digit number where the sum of the cubes of its digits equals the number itself. For example: $1^3 + 5^3 + 3^3 = 153$. for candidate in range(100, 1000): hundreds = candidate /...
Linear structures consist of a finite sequence of elements with identical properties. Common linear data structures include arrays, linked lists, stacks, queues, and strings. While linear structures follow a continuous logical arrangement, their physical storage may be either contiguous or non-conti...
This article examines several algorithmic problems featuring dynamic programming, state management, and graph traversal techniques. Problem 1: Frozen Dumplings Consider a scenario where daily dumpling prices vary, and storage costs accrue for each day a dumpling is kept. Given prices for n days and...
Sliding Window Algorithm Paterns Core Implementation Template const slidingWindowSolution = (inputString) => { // Initialize tracking variables let [primaryVar, secondaryVar] = [initialValue1, initialValue2]; // Set window boundaries let windowStart = 0; const results = []; for (let windowEnd = 0...
The task is to identify the longest common prefix shared among all strings in a given array. For instance, with an input like ['abc', 'abcd', 'abd'], the result should be 'ab'. Approach 1: Brute Force Itertaion A straightforward method involves incrementally building prefixes and verifying each one...
Copy List with Random Pointer This problem is a classic deep copy scenario, similar to graph cloning (e.g., LeetCode 133). Approach: Traverse the list once to copy the next pointers. During this traversal, store the mapping between original nodes and their copies in a hash map. Traverse the list a s...
Given an array of integers nums and an integer target, return the indices of two numbers that add up to the target value. Example: Input: nums = [3, 4, 2], target = 6 Output: [1, 2] Explanation: nums[1] + nums[2] equals 6 Approaches Brute Force Method: Iterate through each element and check every ot...
Calculating the power of a number $x^n$ is a fundamental operation. While the most straightforward approach involves iterative multiplication, more efficient techniques exist to handle large exponents or performance-critical applications. The Linear Time Approach The most intuitive method to compute...
Counting Pairs Whose Product is a Perfect Square Given an array of length N, count the number of index pairs (i, j) where i < j such that the product A[i] * A[j] is a perfect square (a non-negative integer square). Approach For a non-zero integer x, define its square-free component as x divided b...
Matrix Chain Mulitplication Matrix chain multiplication finds the optimal parenthesization to minimize scalar multiplications. The recurrence relation is: m[i,j] = 0 if i = j min(m[i,k] + m[k+1,j] + p[i-1]*p[k]*p[j]) for i ≤ k < j if i < j Three nested loops are required: Outer loop: chain len...