64 lines
1.9 KiB
Swift
64 lines
1.9 KiB
Swift
/**
|
||
* File: unbounded_knapsack.swift
|
||
* Created Time: 2023-07-15
|
||
* Author: nuomi1 (nuomi1@qq.com)
|
||
*/
|
||
|
||
/* 完全背包：動態規劃 */
|
||
func unboundedKnapsackDP(wgt: [Int], val: [Int], cap: Int) -> Int {
|
||
let n = wgt.count
|
||
// 初始化 dp 表
|
||
var dp = Array(repeating: Array(repeating: 0, count: cap + 1), count: n + 1)
|
||
// 狀態轉移
|
||
for i in 1 ... n {
|
||
for c in 1 ... cap {
|
||
if wgt[i - 1] > c {
|
||
// 若超過背包容量，則不選物品 i
|
||
dp[i][c] = dp[i - 1][c]
|
||
} else {
|
||
// 不選和選物品 i 這兩種方案的較大值
|
||
dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1])
|
||
}
|
||
}
|
||
}
|
||
return dp[n][cap]
|
||
}
|
||
|
||
/* 完全背包：空間最佳化後的動態規劃 */
|
||
func unboundedKnapsackDPComp(wgt: [Int], val: [Int], cap: Int) -> Int {
|
||
let n = wgt.count
|
||
// 初始化 dp 表
|
||
var dp = Array(repeating: 0, count: cap + 1)
|
||
// 狀態轉移
|
||
for i in 1 ... n {
|
||
for c in 1 ... cap {
|
||
if wgt[i - 1] > c {
|
||
// 若超過背包容量，則不選物品 i
|
||
dp[c] = dp[c]
|
||
} else {
|
||
// 不選和選物品 i 這兩種方案的較大值
|
||
dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])
|
||
}
|
||
}
|
||
}
|
||
return dp[cap]
|
||
}
|
||
|
||
@main
|
||
enum UnboundedKnapsack {
|
||
/* Driver Code */
|
||
static func main() {
|
||
let wgt = [1, 2, 3]
|
||
let val = [5, 11, 15]
|
||
let cap = 4
|
||
|
||
// 動態規劃
|
||
var res = unboundedKnapsackDP(wgt: wgt, val: val, cap: cap)
|
||
print("不超過背包容量的最大物品價值為 \(res)")
|
||
|
||
// 空間最佳化後的動態規劃
|
||
res = unboundedKnapsackDPComp(wgt: wgt, val: val, cap: cap)
|
||
print("不超過背包容量的最大物品價值為 \(res)")
|
||
}
|
||
}
|