数据结构与算法 Farmer John 问题农夫锯木板问题

最新推荐文章于 2025-05-01 22:06:30 发布

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最新推荐文章于 2025-05-01 22:06:30 发布 · 2.2k 阅读

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#数据结构与算法 #C #C++ #Farmer John 问题 #锯木板问题

本文介绍了一个关于农夫John如何在有限成本下将一块长木板锯成若干指定长度的小木板的问题。农民Don会按每块木板的长度收取锯木费用。通过使用类似Huffman编码的策略，选择每次锯取最短的木板以减少总费用。文章探讨了如何设计算法来确定最低成本的锯木方案。

Farmer John wants to repair a small length of the fence around the pasture. He measures the fence and finds that he needs N (1 ≤ N ≤ 20,000) planks of wood, each having some integer length Li (1 ≤ Li ≤ 50,000) units. He then purchases a single long board just long enough to saw into the N planks (i.e., whose length is the sum of the lengths Li). FJ is ignoring the "kerf", the extra length lost to sawdust when a sawcut is made; you should ignore it, too.

FJ sadly realizes that he doesn’t own a saw with which to cut the wood, so he mosies over to Farmer Don’s Farm with this long board and politely asks if he may borrow a saw.

Farmer Don, a closet capitalist, doesn’t lend FJ a saw but instead offers to charge Farmer John for each of the N-1 cuts in the plank