USACO08MAR River Crossing S - Complete Knapsack and Interval DP Solutions
Problem Link
Luogu P2904 [USACO08MAR] River Crossing S
Approach 1: Copmlete Knapsack DP
First, observe the problem constraints. We need to transport all (n) cows across the river, minimizing the total time. Suppose we make (k) trips, and on the (i)-th trip we take (a_i) cows. Then (a_1 + a_2 + \dots + a_k = n). This can be viewed as having (n) ...
Posted on Thu, 30 Jul 2026 16:26:47 +0000 by nblackwood
Dynamic Programming Approaches to Knapsack Problems for Coding Competitions
01 Knapsack Problem
Problem Statement
Given item_count items and a knapsack with capacity capacity, each item has a weight w and value val. Calculate the maximum total value achievable without exceeding the knapsack capacity.
Input Example:
5 20
1 6
2 5
3 8
5 15
3 3
Output Example:
37
Solution Idea
The 01 knapsack problem restricts each item ...
Posted on Tue, 21 Jul 2026 17:11:09 +0000 by chrisdarby