Freaks City

Generating the complete power set of a collection involves binary decisions at each element. The recursive approach branches twice: once including the current element and once excluding it. public void enumerateSubsets(int[] data, List<Integer> buffer, int idx) { if (idx == data.length) { System.out.println(buffer); re ...

2023 Edition Day 1 G. Constructing an MST with Product Weights (Easy) We are given a sequence (a) (with (|a_i| \le 10^6)), and we must build an undirected graph on (n) vertices ((n \le 2\cdot 10^5)) where the weight of edge ((i,j)) equals (a_i a_j). The goal is to compute the weight of the minimum spanning tree. First, sort (a); this has no eff ...

Problem Description A subsequence is obtained from a string by deleting zero or more characters without changing the order of remaining elements. The original string qualifies as its own subsequence. For a given lowercase string s of length n (1 ≤ n ≤ 1000), count how many subsequences contain exactly k ditsinct letter types (1 ≤ k ≤ 26). Retur ...

Problem A: 24-Hour Time Calculation Given the current time $A$ and a duration $B$ in hours, the task is to determine the start time of an event using a 24-hour clock format. Since the clock cycles every 24 hours, the solution involves a simple modular arithmetic operation. The resulting time is calculated as $(A + B) \pmod{24}$. #include < ...

Recursive Permutation Generation This approach generates all permutations through recursive swaps. The algorithm fixes each character at the first position and recursively permutes the remaining substring. public class PermutationGenerator { public static void main(String[] args) { String text = "abc"; permute( ...

Dragon Slayer Pathfinding with Binary Enumeration Coordinate scaling converts decimal start/end points to integers for grid processing. Binary enumeration efficiently searches all possible wall removal combinations. #include <iostream> #include <vector> #include <bitset> using namespace std; struct Barrier { int x_start, ...

The task is to generate all possible combinations of r distinct numbers from the set {1, 2, ..., n}. A combination is an unordered selection, meaning {1, 2, 3} is the same as {3, 2, 1}. We need to print each combination on a new line, with numbers sorted in ascending order and each number occupying exactly three characters of space. The combina ...

Problem A: Counting Digit Holes The task requires calculating the total number of closed loops (holes) in a sequence of digits. Digits '0', '6', and '9' contain one loop each, while '8' contains two loops. The solution involves iterating through the string and accumulating the count based on the digit encountered. #include <iostream> #inc ...

This article addresses the problem of finding the coefficient of the $x^n y^m$ term in the expansion of the polynomial $(ax + by)^k$. The solution involves applying the binoimal theorem and calculating combinations modulo 10007. Binomial Theorem Application The binomial theorem states that $(x+y)^k = \sum_{i=0}^{k} \binom{k}{i} x^{k-i} y^i$. In ...

Directed Edge Orientation with Out-Degree ConstraintGiven an undirected graph, determine the number of ways to orient all edges such that every vertex has an out-degree of exactly 1. The result should be modulo 998244353.For such an orientation to exist, the number of edges must exactly equal the number of vertices, i.e., m = n. Furthermore, ev ...