Freaks City

Problem Statement Given a positive integer n, determine the smallest number of perfect squares that sum to n. A perfect square is an integer equal to the square of another integer — for example, 1, 4, 9, and 16 are perfect squares; 3 and 11 are not. Naive Recursiev Approach A top-down recursive solution defines minSquares(x) as the minimum coun ...

Problem Statement Given an integer array fee where fee[i] represents the cost to step onto the ith stair. After paying this fee, you may advance either one or two steps upward. You can begin climbing from either stair 0 or stair 1 without incurring any initial expense. Calcluate and return the minimum cost required to reach beyond the final sta ...

Competition Summary Overview Problem Details Problem 1: Prime Number Identification Problem 2: Range Maximum Queries Problem 3: Dynamic Median Finding 20 Point Solution 100 Point Solution Problem 4: Magic Stone Path Optimization Basic Dynamic Programming Approach Problem 5: Strategic Decision Making Summer Training Competition Day1 O ...

Longest Valid Parentheses Given a string containing only '(' and ')', find the length of the longest valid (well-formed and contiguous) parentheses substring. Dynamic Programming Solution Define dp[i] as the length of the longest valid parentheses ending at position i. To each character at index i: If s[i] is '(', set dp[i] = 0 If s[i] is ')', ...

Problem Analysis and Solution Given two arrays, the goal is to pair elements from each array to maximize the sum of their products. Since positive multiplied by positive yields positive, and negative multiplied by negative also yields positive, we can seperate both arrays into positive and negative components. The optimal strategy is to pair la ...

Problem A: Tree Value Maximization Approach Define subtree_value[i] as the value generated by the subtree rooted at node i: subtree_value[i] = subtree_size[i] + Σ subtree_value[j] for all children j of i. The initial selection of i as root gives subtree_size[i] value, followed by contributions from its subtrees. Direct computation for each root ...

Bitmask Dynamic Programming (Bitmask DP) is a technique used to solve problems where the state of a system can be represented by a small set of binary flags. By using an integer's bits to store boolean information—where each bit corresponds to a specific element's status—we can compactly represent and manipulate complex configurations. Core Con ...

Greedy Algorithm: Minimum Cameras to Monitor a Binary Tree Given a binary tree, we need to place cameras on nodes such that every node in the tree is monitored. A camera placed on a node monitors itself, its parenet, and its immediate children. Determine the minimum number of cameras required. Approach We can solve this problem using a greedy a ...

Date Statistics The first four digits are fixed. Generate the last four digits using nested loops, record valid dates, then verify if these dates can be formed. Verification method: Since it's a subsequence problem, we can skip elements but maintain relative order. For the given 100 numbers, match each digit sequentially with the 8-digit date. ...

The 0/1 knapsack problem involves selecting items where each item can be either taken or left (0 or 1 decision). Given N items with weights and values, maximize the total value without exceeding cpaacity V. #include <iostream> #include <algorithm> using namespace std; const int MAX = 1001; int dp[MAX][MAX]; int weights[MAX], values ...