huangzj
102 lines
3.7 KiB
Go
102 lines
3.7 KiB
Go
/*
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* @Author : huangzj
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* @Time : 2020/7/31 15:35
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* @Description：背包最优问题工具类
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* 基本场景：给定n个重量为w1w 1，w2w 2 ,w3w 3 ,…,wnw n ，价值为v1v 1 ,v2v 2 ,v3v 3 ,…,vnv n 的物品和容量为CC的背包，求这个物品中一个最有价值的子集，使得在满足背包的容量的前提下，包内的总价值最大
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* 参考地址：https://blog.csdn.net/chanmufeng/article/details/82955730
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*/
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package knapsackOptimization
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type KnapsackOptimization struct {
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BagCapacity int //背包的总容量上限
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BagItemList []*BagItem //背包道具列表
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ItemNum int //道具的数量
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}
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func NewKnapsackOptimization(bagItemList []*BagItem, bagCapacity int) *KnapsackOptimization {
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if bagCapacity <= 0 {
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panic("背包总容量不能小于等于0")
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}
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return &KnapsackOptimization{
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BagCapacity: bagCapacity,
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BagItemList: bagItemList,
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ItemNum: len(bagItemList),
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}
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}
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//通过递归的方式解决上述基本场景，这种方式效率比较低下
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func (cmd *KnapsackOptimization) OptimizePackageByRecursion() int {
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return cmd.knapsackRecursion(cmd.BagItemList, len(cmd.BagItemList)-1, cmd.BagCapacity)
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}
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func (cmd *KnapsackOptimization) knapsackRecursion(bagItemList []*BagItem, index, capacity int) int {
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if index < 0 || capacity <= 0 {
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return 0
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}
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res := cmd.knapsackRecursion(bagItemList, index-1, capacity) //不放第index个物品所得价值
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//放第index个物品所得价值（前提是：第index个物品可以放得下）
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if bagItemList[index].Weight <= capacity {
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res = max(res, bagItemList[index].Value+cmd.knapsackRecursion(bagItemList, index-1, capacity-bagItemList[index].Weight))
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}
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return res
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}
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func (cmd *KnapsackOptimization) KnapsackCycle() int {
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dynamicPlan := cmd.initKnapsackParam() //初始化参数，这边通过动态规划的方式处理，需要一个辅助行和辅助列
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//循环所有的道具，进行动态规划二维数组的组装.
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for i := 1; i <= cmd.ItemNum; i++ {
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for j := 1; j <= cmd.BagCapacity; j++ {
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//如果背包重量不够,则不能装下这个道具
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if j < cmd.BagItemList[i].Weight {
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dynamicPlan[i][j] = dynamicPlan[i-1][j]
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} else {
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//如果背包重量足够的话，判断装入这个道具价值更高，还是不装这个道具价值更高
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dynamicPlan[i][j] = max(dynamicPlan[i-1][j], dynamicPlan[i-1][j-cmd.BagItemList[i].Weight]+cmd.BagItemList[i].Value)
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}
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}
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}
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return dynamicPlan[len(cmd.BagItemList)-1][cmd.BagCapacity-1]
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}
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//通过一维数组实现背包求解
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func (cmd *KnapsackOptimization) KnapsackCycleSimple() int {
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dynamicPlan := cmd.initKnapsackParamSimple()
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for i := 1; i <= cmd.ItemNum; i++ {
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for j := cmd.BagCapacity; j >= cmd.BagItemList[i].Weight; j-- {
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dynamicPlan[j] = max(dynamicPlan[j], dynamicPlan[j-cmd.BagItemList[i].Weight]+cmd.BagItemList[i].Value)
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}
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}
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return dynamicPlan[cmd.BagCapacity]
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}
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func (cmd *KnapsackOptimization) initKnapsackParamSimple() []int {
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itemList := make([]*BagItem, 0)
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itemList = append(itemList, &BagItem{})
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itemList = append(itemList, cmd.BagItemList...)
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cmd.BagItemList = itemList
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return make([]int, cmd.BagCapacity+1)
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}
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//这里需要组成一个辅助数组去判断动态规划的实现
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func (cmd *KnapsackOptimization) initKnapsackParam() [][]int {
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itemList := make([]*BagItem, 0)
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itemList = append(itemList, &BagItem{})
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itemList = append(itemList, cmd.BagItemList...)
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cmd.BagItemList = itemList
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//初始化数组
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dynamicPlan := make([][]int, len(cmd.BagItemList))
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for i := 0; i <= cmd.ItemNum; i++ {
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dynamicPlan[i] = make([]int, cmd.BagCapacity+1)
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}
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return dynamicPlan
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}
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func max(compareNum, otherCompareNum int) int {
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if compareNum > otherCompareNum {
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return compareNum
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}
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return otherCompareNum
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}
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