Freaks City

Guess Number Higher or Lower II We need to solve a game where we guess a number between 1 and n. Each wrong guess costs the amount equal to the guessed number. The goal is to find the minimum amount of money needed to guarantee a win regardless of which number is selected. Brute-Force Recursion class Solution { public: int calculateMinCost( ...

House Robber I The classic house robber problem involves selecting houses to rob such that adjacent houses cannot both be robbed, maximizing total profit. For each house, there are two choices: rob it or skip it. The decision at each position aims to maximize accumulated wealth. State Defniition: wealth[i] represents the maximum money obtainabl ...

Definition Search algorithms systematically explore state spaces to find optimal solutions or count valid configurations through exhaustive enumeration. This approach leverages understanding of state transitions to navigate possible states. Search Algorithm Applications When explicit enumeration becomes infeasible (e.g., permutations for n=100 ...

Maximum Product of Splitted Binary Tree Given a binary tree with root node, remove exactly one edge to split the tree into two separate subtrees. The goal is to maximize the product of the sums of both resulting subtrees. Return the result modulo 10^9 + 7. Approach The key insight is that during a depth-first search that calculates subtree sums ...

A player collects trading cards with n distinct types. Each draw yields card type i with probability pi. Duplicate cards convert to coins, where k coins can be exchanged for one missing card. The process continues until all card types are collected. Compute the expected number of draws required. Input Format First line: n (card types) and k (co ...

Dynamic programming (DP) is an optimization paradigm that solves complex problems by decomposing them into overlapping subproblems whose solutions are cached to avoid recomputation. It relies on two key properties: optimal substructure and overlapping subprobelms. Optimal substructure means an optimal solution can be built from optimal solution ...

Maximizing Minimum Distance Between ElementsGiven an array of unique positions and a number of items to place, the goal is to position the items such that the minimum absolute difference between any two items' positions is maximized.Example 1:Input: positions = [1,2,3,4,7], items = 3Output: 3Explanation: Placing items at positions 1, 4, and 7 y ...

Leveraging Python's Built-in Data Structures Python's native data structures offer efficient solutions for common programming tasks. Dictionaries provide rapid key-based lookups, ideal for frequency analysis: phrase = "algorithm efficiency" frequency_map = {} for character in phrase: frequency_map[character] = frequency_map.get(ch ...

Problem Overview: The 0/1 Knapsack Given a maximum capacity (or time limit) W and N distinct items, where each item has a weight (or time cost) and a value, the objective is to maximize the total value of selected items without exceeding the given capacity. Each item can be chosen at most once. Constraints Maximum Capacity W: 1 ≤ W ≤ 1000 Numb ...

Problem Analysis Given (n) where (1 \le n \le 20), we need to count the number of ways to completely cover the interval ([1, n]) using segments where each segment connects two coprime numbers. First, preprocess all coprime pairs ({a, b}) where (\gcd(a, b) = 1) and (a < b). Note that ({1, 1}) is excluded. When (n = 20), there are exactly 127 ...