Merge pull request #2681 from markwang1992/01bag

0-1背包理论基础(二)增加Go一维dp数组,二维dp数组移至0-1背包理论基础(一),增加相应注释
This commit is contained in:
程序员Carl
2024-08-23 11:06:16 +08:00
committed by GitHub
2 changed files with 76 additions and 29 deletions

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@ -437,6 +437,58 @@ print(dp[n - 1][bagweight])
### Go ### Go
```go ```go
package main
import (
"fmt"
)
func main() {
var n, bagweight int // bagweight代表行李箱空间
fmt.Scan(&n, &bagweight)
weight := make([]int, n) // 存储每件物品所占空间
value := make([]int, n) // 存储每件物品价值
for i := 0; i < n; i++ {
fmt.Scan(&weight[i])
}
for j := 0; j < n; j++ {
fmt.Scan(&value[j])
}
// dp数组, dp[i][j]代表行李箱空间为j的情况下,从下标为[0, i]的物品里面任意取,能达到的最大价值
dp := make([][]int, n)
for i := range dp {
dp[i] = make([]int, bagweight + 1)
}
// 初始化, 因为需要用到dp[i - 1]的值
// j < weight[0]已在上方被初始化为0
// j >= weight[0]的值就初始化为value[0]
for j := weight[0]; j <= bagweight; j++ {
dp[0][j] = value[0]
}
for i := 1; i < n; i++ { // 遍历科研物品
for j := 0; j <= bagweight; j++ { // 遍历行李箱容量
if j < weight[i] {
dp[i][j] = dp[i-1][j] // 如果装不下这个物品,那么就继承dp[i - 1][j]的值
} else {
dp[i][j] = max(dp[i-1][j], dp[i-1][j-weight[i]]+value[i])
}
}
}
fmt.Println(dp[n-1][bagweight])
}
func max(x, y int) int {
if x > y {
return x
}
return y
}
``` ```
### Javascript ### Javascript

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@ -322,46 +322,41 @@ import (
) )
func main() { func main() {
var n, bagweight int // 读取 M 和 N
fmt.Scan(&n, &bagweight) var M, N int
fmt.Scan(&M, &N)
weight := make([]int, n) costs := make([]int, M)
value := make([]int, n) values := make([]int, M)
for i := 0; i < n; i++ { for i := 0; i < M; i++ {
fmt.Scan(&weight[i]) fmt.Scan(&costs[i])
} }
for j := 0; j < n; j++ { for j := 0; j < M; j++ {
fmt.Scan(&value[j]) fmt.Scan(&values[j])
} }
dp := make([][]int, n) // 创建一个动态规划数组dp初始值为0
for i := range dp { dp := make([]int, N + 1)
dp[i] = make([]int, bagweight+1)
}
for j := weight[0]; j <= bagweight; j++ { // 外层循环遍历每个类型的研究材料
dp[0][j] = value[0] for i := 0; i < M; i++ {
} // 内层循环从 N 空间逐渐减少到当前研究材料所占空间
for j := N; j >= costs[i]; j-- {
for i := 1; i < n; i++ { // 考虑当前研究材料选择和不选择的情况,选择最大值
for j := 0; j <= bagweight; j++ { dp[j] = max(dp[j], dp[j-costs[i]] + values[i])
if j < weight[i] {
dp[i][j] = dp[i-1][j]
} else {
dp[i][j] = max(dp[i-1][j], dp[i-1][j-weight[i]]+value[i])
}
} }
} }
fmt.Println(dp[n-1][bagweight]) // 输出dp[N],即在给定 N 行李空间可以携带的研究材料最大价值
fmt.Println(dp[N])
} }
func max(a, b int) int { func max(x, y int) int {
if a > b { if x > y {
return a return x
} }
return b return y
} }
``` ```