Freaks City

01 Knapsack Problem Statement Given N items and a knapsack with capacity m, each item has a volume v[i] and value w[i]. Each item can be selected at most once. Determine which items to select so that the total volume does not exceed the knapsack's capacity and the total value is maximized. Approach Let dp[i][j] denote the maximum value achievab ...

Given an array of integers candidates and a target value target, find all unique combinations in candidates where the numbers sum to target. Key constraints: Each number can only be used once in each combination. All numbers (including the target) are positive integers. The result set must not contain duplicate combinations. Examples Example ...

Given two singly-linked lists that are already sorted in ascending order, produce a single sorted linked list that interleaves all node from both input lists. Examples Input: list1 = [1, 2, 4], list2 = [1, 3, 4] Output: [1, 1, 2, 3, 4, 4] Input: list1 = [], list2 = [] Output: [] Input: list1 = [], list2 = [0] Output: [0] Implementation strate ...

Finding Perfect Numbers in C: A Complete Guide Understanding Perfect Numbers A perfect number is a positive integer that is equal to the sum of its proper divisors, excluding itself. For example, 6 is a perfect number because its divisors (1, 2, 3) sum to 6 (1+2+3=6). Other perfect numbers include 28, 496, and 8128. Perfect numbers have inte ...

This problem requires implementing a program that prints a sandglass pattern using a specified character. For instance, given 17 asterisks, the output should follow this format: ***** *** * *** ***** A sandglass shape has these characteristics: each row contains an odd number of characters, all rows are center-aligned, adjacent rows diffe ...

Problem Description A dream once led to an unusual elevator that operates differently from typical ones. Each floor has a number K_i (0 ≤ K_i ≤ N), and the elevator can move up or down by exactly K_i floors when the corresponding button is pressed. The elevator has four buttons: open, close, go up, and go down. Given a building with N floors, e ...

LeetCode 343: Integer Break Given an integer n, break it into the sum of k positive integers, where k >= 2, and maximize the product of those integers. Return the maximum product you can get. Dynamic Programmign Approach The problem can be solved using dynamic programming. The key insight is that the maximum product for a number i depends on ...

Stack-Based Index Tracking Calculating the maximum length of well-formed parenthesis substrings requires maintaining a dynamic baseline for distance measurements. A stack storing character indices provides an efficient mechanism for this. Initialize the data structure with -1 to act as a virtual boundary before the string begins. Process the in ...

Integer Partitioning for Maximum Product To maximize the product of integers summing up to a target value n, dynamic programming tracks optimal sub-solutions. Define an array maxProduct where maxProduct[val] represents the highest achievable product from partitioning the integer val. Since partitioning 0 or 1 yields no valid product, the base c ...

Definition A suffix automaton (SAM) for a string (s) is the minimal deterministic finite automaton (DFA) that accepts all suffixes of (s). Formally: A SAM is a directed acyclic graph (DAG) where nodes represent states and edges represent transitions. The source node (t_0) serves as the initial state. All states are reachable from (t_0). Each t ...