Backpack III 完全背包
Given n kind of items with size Ai and value Vi( each item has an infinite number available
) and a backpack with size m. What's the maximum value can you put into the backpack?
Given 4 items with size [2, 3, 5, 7]
and value [1, 5, 2, 4]
, and a backpack with size 10
. The maximum value is 15
.
完全背包问题,即每件物体可取任意件。dp[i,j]表示为前i个物体填满背包可获得的最大价值。DP方程转换为dp[i,j] = max(dp[i-1,j], dp[i, j - Ai] + Vi)。这样转换的复杂度为O(NV),要快于从0-1背包转化过来的从i-1上讨论的转化方程O(NV^2)。
注意这里与0-1背包不一样因为第i件物品可以添加多件.所以DP可以在已加入当前物体的状态下继续添加.
代码入下:
class Solution: # @param {int[]} A an integer array # @param {int[]} V an integer array # @param {int} m an integer # @return {int} an array def backPackIII(self, A, V, m): n = len(A) dp = [0] * (m + 1) for i in xrange(n): for j in xrange(A[i], m + 1): dp[j] = max(dp[j], dp[j - A[i]] + V[i]) return dp[m]
posted on 2016-07-18 15:56 Sheryl Wang 阅读(285) 评论(0) 编辑 收藏 举报