mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-27 18:36:28 +08:00
e720aa2d24
* Sync recent changes to the revised Word. * Revised the preface chapter * Revised the introduction chapter * Revised the computation complexity chapter * Revised the chapter data structure * Revised the chapter array and linked list * Revised the chapter stack and queue * Revised the chapter hashing * Revised the chapter tree * Revised the chapter heap * Revised the chapter graph * Revised the chapter searching * Reivised the sorting chapter * Revised the divide and conquer chapter * Revised the chapter backtacking * Revised the DP chapter * Revised the greedy chapter * Revised the appendix chapter * Revised the preface chapter doubly * Revised the figures
110 lines
3.8 KiB
Swift
110 lines
3.8 KiB
Swift
/**
|
||
* File: knapsack.swift
|
||
* Created Time: 2023-07-15
|
||
* Author: nuomi1 (nuomi1@qq.com)
|
||
*/
|
||
|
||
/* 0-1 背包：暴力搜索 */
|
||
func knapsackDFS(wgt: [Int], val: [Int], i: Int, c: Int) -> Int {
|
||
// 若已选完所有物品或背包无剩余容量，则返回价值 0
|
||
if i == 0 || c == 0 {
|
||
return 0
|
||
}
|
||
// 若超过背包容量，则只能选择不放入背包
|
||
if wgt[i - 1] > c {
|
||
return knapsackDFS(wgt: wgt, val: val, i: i - 1, c: c)
|
||
}
|
||
// 计算不放入和放入物品 i 的最大价值
|
||
let no = knapsackDFS(wgt: wgt, val: val, i: i - 1, c: c)
|
||
let yes = knapsackDFS(wgt: wgt, val: val, i: i - 1, c: c - wgt[i - 1]) + val[i - 1]
|
||
// 返回两种方案中价值更大的那一个
|
||
return max(no, yes)
|
||
}
|
||
|
||
/* 0-1 背包：记忆化搜索 */
|
||
func knapsackDFSMem(wgt: [Int], val: [Int], mem: inout [[Int]], i: Int, c: Int) -> Int {
|
||
// 若已选完所有物品或背包无剩余容量，则返回价值 0
|
||
if i == 0 || c == 0 {
|
||
return 0
|
||
}
|
||
// 若已有记录，则直接返回
|
||
if mem[i][c] != -1 {
|
||
return mem[i][c]
|
||
}
|
||
// 若超过背包容量，则只能选择不放入背包
|
||
if wgt[i - 1] > c {
|
||
return knapsackDFSMem(wgt: wgt, val: val, mem: &mem, i: i - 1, c: c)
|
||
}
|
||
// 计算不放入和放入物品 i 的最大价值
|
||
let no = knapsackDFSMem(wgt: wgt, val: val, mem: &mem, i: i - 1, c: c)
|
||
let yes = knapsackDFSMem(wgt: wgt, val: val, mem: &mem, i: i - 1, c: c - wgt[i - 1]) + val[i - 1]
|
||
// 记录并返回两种方案中价值更大的那一个
|
||
mem[i][c] = max(no, yes)
|
||
return mem[i][c]
|
||
}
|
||
|
||
/* 0-1 背包：动态规划 */
|
||
func knapsackDP(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)
|
||
// 状态转移
|
||
for i in stride(from: 1, through: n, by: 1) {
|
||
for c in stride(from: 1, through: cap, by: 1) {
|
||
if wgt[i - 1] > c {
|
||
// 若超过背包容量，则不选物品 i
|
||
dp[i][c] = dp[i - 1][c]
|
||
} else {
|
||
// 不选和选物品 i 这两种方案的较大值
|
||
dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1])
|
||
}
|
||
}
|
||
}
|
||
return dp[n][cap]
|
||
}
|
||
|
||
/* 0-1 背包：空间优化后的动态规划 */
|
||
func knapsackDPComp(wgt: [Int], val: [Int], cap: Int) -> Int {
|
||
let n = wgt.count
|
||
// 初始化 dp 表
|
||
var dp = Array(repeating: 0, count: cap + 1)
|
||
// 状态转移
|
||
for i in stride(from: 1, through: n, by: 1) {
|
||
// 倒序遍历
|
||
for c in stride(from: cap, through: 1, by: -1) {
|
||
if wgt[i - 1] <= c {
|
||
// 不选和选物品 i 这两种方案的较大值
|
||
dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])
|
||
}
|
||
}
|
||
}
|
||
return dp[cap]
|
||
}
|
||
|
||
@main
|
||
enum Knapsack {
|
||
/* Driver Code */
|
||
static func main() {
|
||
let wgt = [10, 20, 30, 40, 50]
|
||
let val = [50, 120, 150, 210, 240]
|
||
let cap = 50
|
||
let n = wgt.count
|
||
|
||
// 暴力搜索
|
||
var res = knapsackDFS(wgt: wgt, val: val, i: n, c: cap)
|
||
print("不超过背包容量的最大物品价值为 \(res)")
|
||
|
||
// 记忆化搜索
|
||
var mem = Array(repeating: Array(repeating: -1, count: cap + 1), count: n + 1)
|
||
res = knapsackDFSMem(wgt: wgt, val: val, mem: &mem, i: n, c: cap)
|
||
print("不超过背包容量的最大物品价值为 \(res)")
|
||
|
||
// 动态规划
|
||
res = knapsackDP(wgt: wgt, val: val, cap: cap)
|
||
print("不超过背包容量的最大物品价值为 \(res)")
|
||
|
||
// 空间优化后的动态规划
|
||
res = knapsackDPComp(wgt: wgt, val: val, cap: cap)
|
||
print("不超过背包容量的最大物品价值为 \(res)")
|
||
}
|
||
}
|