多重背包问题1、2

it2026-10-05 1

所有背包思想来自闫总的ACWing

题目链接：https://www.acwing.com/problem/content/4/

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朴素算法：

#include<iostream> using namespace std; int N,V; int dp[3000]; int main(){ cin>>N>>V; int v,w,s; for(int i=0;i<N;i++){ cin>>v>>w>>s; for(int j=V;j>=0;j--){ for(int k=1;k*v<=j&&k<=s;k++){ dp[j]=max(dp[j],dp[j-k*v]+k*w); } } } cout<<dp[V]<<endl; return 0; }

二进制优化算法： ①把一个数x分解为：1+2+4+…+(x-1-2-4) 括号内数值大于0 ②多重背包——>化为01背包问题

/* 多重背包的二进制优化二进制优化 1+2+4+...+(n-1-2-4-...) */ #include<iostream> #include<vector> using namespace std; struct Good{ int v,w; }; int dp[20020]; vector<Good>goods; int main(){ int n,m; cin>>n>>m; for(int i=0;i<n;i++){ int v,w,s; cin>>v>>w>>s; for(int k=1;s>=k;k*=2){ s-=k; goods.push_back({k*v,k*w}); } if(s>0)goods.push_back({s*v,s*w}); } for(auto good: goods) for(int j=m;j>=good.v;j--) dp[j]=max(dp[j],dp[j-good.v]+good.w); cout<<dp[m]<<endl; return 0; }

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