多重背包中多次背包 O(VN) 算法2 (线性动规) 带参考程序_sy2006



多重背包中多次背包 O(VN) 算法2 (线性动规) 带参考程序_sy2006

其实解决多次背包问题还可以用线性动规的方法(类似NOIP2009普及组道路游戏的算法)

设背包容量t,物品件数n,每件物品体积m[i],价值s[i],可用次数c[i](0表示无限制)

用 b[j,i] 记录到容量为j的情况下物品i使用次数,f[j] 记录容量为j的情况的最优解。

动规的时候,将j从1到t循环一次,分别求解f[j]

对于每个f[j],可以从f[j-m[i]] (i=1..n)得来

转移方程为f[j]=max(f[j-m[i]]+s[i]) (i=1..n, 且满足 j>=m[i] , b[j-m[i],i]<c[i])

            且 b[j]=b[j-m[i]]; b[j,i]:=b[j,i]+1;


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