A specialized variant of the Sieve of Eratosthenes can simultaneously tag integer primality and record the count of prime factors for each composite. This technique is particularly effective when searching for numbers within a range whose total number of prime factors (with multiplicity) equals a gi...
343. Integer Break Given a positive integer n, break it into the sum of k positive integers (k >= 2) and maximzie the product of those integers. Return the maximum product you can get. Example 1: Input: n = 2 Output: 1 Explanation: 2 = 1 + 1, 1 × 1 = 1. Example 2: Input: n = 10 Output: 36 Explana...
Longest Increasing Subsequence (LeetCode 300) To find the length of the longest strictly increasing subsequence, define dp[i] as the length of the longest increasing subsequence ending at index i. Initialize all entries to 1. For each element, compare it with all previous elements; if the current el...
Consider a scenario where an automated agent is situated at the top-left corner of a grid defined by m rows and n columns. The agent is strictly limited to movements either towards the right or downwards. The task is to calculate the total number of distinct routes the agent can take to arrive at th...
Dynamic Programing Coin Change Problem def coin_change(coins, amount): dp = [float('inf')] * (amount + 1) dp[0] = 0 for coin in coins: for x in range(coin, amount + 1): dp[x] = min(dp[x], dp[x - coin] + 1) return dp[amount] if dp[amount] != float('inf') else -1 Predict the Winner def predict_winner(...
The problem involves determining the lexicographically largest binary string that can be constructed under constraints derived from a set of pattern strings containing '0', '1', and '-' (wildcard) characters. Each query provides a target string, and the solution must find the maximal answer consiste...
LeetCode 392: Is Subsequence Problem Description Given two strings s and t, determine if s is a subsequence of t. A subsequence is a sequence that can be derived from another sequence by deleting some or no characters without changing the order of the remaining characters. Dynamic Programming Soluti...
Sexagenary Cycle Offset Calculation Converting between Chinese sexagenary cycle notation and absolute year values involves identifying positions with in the 60-year cycle. The cycle combines ten celestial stems with twelve terrestrial branches. Given a target designation composed of one stem and one...
Dynamic programming (DP) is an algorithmic technique for solving problems that exhibit overlapping subproblems and optimal substructure. Overlapping subproblems mean the same smaller instances are solved repeatedly, while optimal substructure implies that an optimal solution to the larger problem ca...
Multi-Dimensional Knapsack Given N items and a knapsack with two constraints: maximum volume capacity V and maximum weight limit M. Each item i has volume c[i], weight w[i], and value v[i]. Find the maximum total value achievable without exceeding either constraint. Unlike basic knapsack problems th...
