Knapsack Problem

Mon, 04 May 2026 06:50:17 +0000

0/1 Knapsack Problem: Given weights and profits of n items, maximize the profit without exceeding knapsack capacity. Each item can only be chosen at most once.

Problem statment

You are given a list of items, each with a weight and a profit, along with a backpack with a specified maximum capacity. Your goal is to calculate the maximum profit you can achieve without exceeding the backpack’s capacity. You must select items such that the total weight of the items is less than or equal to the backpack’s capacity. You can select at most one of each item.

Longest Increasing Subsequence

Sat, 20 Dec 2025 06:50:17 +0000

Problem statement

Given a list of strings, return the length of the longest [lexicographically] increasing subsequence (LIS). A subsequence is a a sequence derived from the original by deleting zero or more elements without changing the relative order of the remaining items.

Example:

Input: ["A1", "B2", "B1", "C3", "C2"]
Output: 3
Explanation: The longest subsequence in which each subsequent element is strictly greater (lexicographically) then the element before it is of length 3, e.g. ["A1", "B2", "C3"]

Solution

The first method is brute-force. The idea is that we generate all possible subsequences and return the legnth of the largest one.

Algorithms on Salman's Blog

Knapsack Problem

Problem statment

Longest Increasing Subsequence

Problem statement

Solution