Palindromic Substrings Problem Statement Given a string, count how many palindromic substrings it contains. Substrings that start or end at different positions are considered distinct even if they consist of the same characters. Solution using Dynamic Programming We define a two‑dimensional Boolean...
Fibonacci Number (LeetCode 509) The Fibonacci seqeunce is defined as: F(0) = 0 F(1) = 1 F(n) = F(n - 1) + F(n - 2) for n > 1 Example: Input: n = 4 Output: 3 (Sequence: 0, 1, 1, 2, 3) Solution using constant space: class Solution: def fib(self, n: int) -> int: if n < 2: return n # Initialize...
Greeting Code #include <iostream> int main() { std::cout << "Competition Day!" << '\n'; return 0; } Neighbor Sum Array #include <iostream> #include <vector> using namespace std; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int len; cin >>...
A knapsack problem involves selecting items with given weights and values to maximize total value without exceeding a capacity limit. It appears in resource allocation, scheduling, logistics, and investment scenarios. Problem Categories Binary Knapsack — Each item can be taken at most once. Given n...
Peanut Harvesting Problem Problem Description Traverse an R x C grid of peanut plants starting at the top-left corner and exiting at the bottom-right corner. Each cell holds a non-negative integer representing the number of peanuts available at that location. You may only move right or downward at a...
Consider processing graph updates in reverse. The state for each node represents the minimum cost required to become 'safe'. Each update modifies only a single node b_i, requiring an examination of its neighbors. A square root decomposition approach based on vertex degree allows for efficient handli...
This article covers several dynamic programming problems, including finding the maximum subarray sum, the longest increasing subsequence, the longest common subsequence, the longest palindromic substring, and finding the longest path in a Directed Acyclic Graph (DAG). Maximum Subarray Sum This probl...
Problem Overview Luogu P1509 "Finding a Girlfriend" presents a multi-constraint 0/1 knapsack problem. Given n items, each with three attributes rmb_i (money), rp_i (reputation), and time_i (time spent), the goal is to maximize the number of selected items such that the sum of rmb_i does no...
Simulation Contest 2 Solutions Current Progress: Linear DP, Knapsack Problems, Intervals Challenging Problems 1038 [NOIP2008] Paper Passing Tags High-Dimensional DP Approach The challenge lies in ensuring that the path from (1,1) to (n,m) and back from (n,m) to (1,1) do not overlap. It can be treate...
Problem A: Minimum Function Summation Given the function f(x) = min_{i∈ℕ⁺}, compute the sum Σ_{i=1}^{n} f(i) modulo 10^9+7 across multiple test cases. Constraints: n ≤ 10^16, T ≤ 10^4. Solution Approach: Analyze the frequency of each value in the sequence f(i). For a particular value x, we need to c...