[USACO06NOV] Corn Fields (试题来源:Link ) 题目描述 Farmer John has purchased a lush new rectangular pasture composed of \(M\) by \(N (1 ≤ M ≤ 12; 1 ≤ N ≤ 12)\) square parcels. He wants to grow some yummy corn for the cows on a number of squares. Regrettably,…

题面 传送门 Sol 状压一下\(k\),\(f[S]\)表示用过的硬币集合为\(S\)能买到的物品个数 # include <bits/stdc++.h> # define RG register # define IL inline # define Fill(a, b) memset(a, b, sizeof(a)) using namespace std; typedef long long ll; const int _(100005); IL ll Input(){ RG ll x…

题面 在朴素中透着一点新意的状压DP 一个很暴力的思路是枚举位置,状态和硬币,每次二分出向前最多能买到哪里,复杂度爆炸($O(2^knklog$ $n)$) 考虑优化,不妨先预处理一下$goal[i][j]$表示每个硬币$i$在每个位置$j$最多向前能买到哪里,但是这样还是很爆炸,所以我们找来了一个不同寻常的dp状态 我们设$dp[s]$表示在$s$状态下最远能到达哪里,于是有了一个清奇的转移方程$dp[s|(1<<coin)]=max(dp[s|(1<<coin)],goal[c…

题目大意: 你有k(k<=16)个硬币,每个硬币都有自己的面值. 现在你要给n件商品付钱,每件商品也有自己的价格. 然而老板是个奸商,他绝对不会给你找钱. 你每次付钱只能用一个硬币,但是你可以一次性买很多商品. 问你最后最多还能留下多少钱. 思路: 状压DP. f[i]表示状态为i时能买的商品数,i表示你用了哪些硬币. 从小到大枚举每个状态i,然后枚举状态i中的硬币j,是这次付款用的硬币. 二分找一下这些硬币最多能买前面连续的多少个商品. 如果j不在i中,就算作最后剩下的硬币. #include…

[USACO13NOV]没有找零No Change 题目链接 https://www.luogu.org/problemnew/show/3092 做题背景 FJ不是一个合格的消费者,不知法懂法用法,不会拿起法律的武器维护消费者权益 做法 本题涉及的知识点:状态压缩,动态规划,二分答案. 注意物品是依次购买 首先是状态压缩: 压什么?我们注意到k<=16,那么就是压硬币使用集合. 然后是动态规划: 怎么设状态?设dp[i]表示我们选硬币集合i(状压)从一号物品开始最多能买的物品数. 怎么转移?从…

P3092 [USACO13NOV]没有找零No Change 题目描述 Farmer John is at the market to purchase supplies for his farm. He has in his pocket K coins (1 <= K <= 16), each with value in the range 1..100,000,000. FJ would like to make a sequence of N purchases (1 <= N…

题目描述 Farmer John is at the market to purchase supplies for his farm. He has in his pocket K coins (1 <= K <= 16), each with value in the range 1..100,000,000. FJ would like to make a sequence of N purchases (1 <= N <= 100,000), where the ith p…

题目描述 Farmer John is at the market to purchase supplies for his farm. He has in his pocket K coins (1 <= K <= 16), each with value in the range 1..100,000,000. FJ would like to make a sequence of N purchases (1 <= N <= 100,000), where the ith p…

题目描述 Farmer John is at the market to purchase supplies for his farm. He has in his pocket K coins (1 <= K <= 16), each with value in the range 1..100,000,000. FJ would like to make a sequence of N purchases (1 <= N <= 100,000), where the ith p…

这个题有点意思,其实不是特别难,但是不太好想...中间用二分找最大的可买长度就行了. 题干: 题目描述 Farmer John <= K <= ), each with value ..,,. FJ would like to make a sequence of N purchases ( <= N <= ,), <= c(i) <= ,). As he makes this sequence of purchases, he can periodically sto…