Freaks City

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) ...

Re-rooting DP is a tree-DP variant that looks intimidating at first, yet becomes very mechenical once the pattern is recognized. The following problems illustrate the key techniques. Problem 1 – USACO 2012 FEB "Nearby Cows" Task: for every node i compute the sum of weights of all nodes whose distance to i is at most K. Constraints: n ...

Problem Statement Farmer John has N farms (2 ≤ N ≤ 10^4) connected by M roads (1 ≤ M ≤ 5×10^4). Multiple roads between the same pair of farms are allowed. Bassie starts patrolling from farm 1. Every road must be traversed exactly once in each direction, and the path must end back at farm 1. Output any valid sequence of farms that satisfies the ...