Freaks City

Manacher's Algorithm for Longest Palindromic Substring Identifying the longest palindromic substring within a string requires handling both odd and even-length palindromes. A common approach involves expanding from each center, but this method fails to detect even-length palindromes. The solution is to insert a delimiter character between each ...

SMU Summer 2024 Contest Round 8 - Problem Solutions Problem 1: Product Approach Observing that the constraint \(\prod_{i=1}^N L_i \le 10^5\) implies that N cannot exceed 16, since \(2^{17} > 10^5\). This allows us to solve the problem using straightforward brute force enumeration of all possible combinations. Implementation #include <bits ...

The contest comprised 11 problems with varying difficulty levels based on technical depth: High Solvability (8/11): Problems A, B, C, D, H, I, J, K generally follow standard patterns. Low Solvability (3/11): E, F, G involve complex nested algorithms or obscure insights. The following sections detail the solutions for the most instructive prob ...

1. Binary Tree Categories Full Binary Tree: A binary tree where all nodes have either 0 or 2 children, and all leaf nodes are at the same level. For depth k, the tree contains (2^k - 1) nodes. Complete Binary Tree: A binary tree where all levels except possibly the last are completely filled, and all nodes are as far left as possible. Binary Se ...

Given two sorted integer arrays nums1 and nums2 in non-decreasing order, with lengths m and n respectively, merge them into nums1 while maintaining sorted order. Implementation Code function merge(nums1, m, nums2, n) { let i = nums1.length - 1; m--; n--; while(n >= 0) { while(m >= 0 && nums1[m] > nums2[n ...

Probabilistic Path Enumeration in Directed Acyclic Graphs Given a directed acyclic graph (DAG) consisting of $V$ vertices and $E$ edges, each edge $e_k$ possesses an independent activation probability $p_k$. The objective is to compute the expected number of functional paths originating from vertex $0$ and terminating at vertex $V-1$. A path is ...

Competition Overview The problem difficulty is generally estimated as F < A = J = I < L = G = E < C = K = H. The contest featured a mix of standard algorithms and optimization problems. Below is the detailed analysis and solution for each problem. Problem F: Prefix Sum Threshold Problem Statement:Given an initial score of 1500 and a sequence o ...

Given an m x n board of characters and a list of strings words, return all words on the board. Each word must be constructed from letters of sequentially adjacent cells, where adjacent cells are horizontally or vertically neighboring. The same letter cell may not be used more than once in a word. 1. Trie with DFS Build a trie from the given wor ...

Stack and Queue in C++ STL The C++ Standard Library provides implementations of both stack and queue data structures. These are fundamental containers that follow specific access orders—LIFO (Last In, First Out) for stacks and FIFO (First In, First Out) for queues. Stack Interface push(element): Inserts an element at the top pop(): Removes the ...

Given a string, identify the length of its longest contiguous substring containing no duplicate cahracters. Example 1: Input: "abcabcbb" Output: 3 Explanation: The longest substring without repeating characters is "abc", which has a length of 3. Example 2: Input: "bbbbb" Output: 1 Explanation: The longest substrin ...