88 lines
2.6 KiB
Go
88 lines
2.6 KiB
Go
// File: knapsack.go
|
|
// Created Time: 2023-07-23
|
|
// Author: Reanon (793584285@qq.com)
|
|
|
|
package chapter_dynamic_programming
|
|
|
|
import "math"
|
|
|
|
/* 0-1 Knapsack: Brute force search */
|
|
func knapsackDFS(wgt, val []int, i, c int) int {
|
|
// If all items have been chosen or the knapsack has no remaining capacity, return value 0
|
|
if i == 0 || c == 0 {
|
|
return 0
|
|
}
|
|
// If exceeding the knapsack capacity, can only choose not to put it in the knapsack
|
|
if wgt[i-1] > c {
|
|
return knapsackDFS(wgt, val, i-1, c)
|
|
}
|
|
// Calculate the maximum value of not putting in and putting in item i
|
|
no := knapsackDFS(wgt, val, i-1, c)
|
|
yes := knapsackDFS(wgt, val, i-1, c-wgt[i-1]) + val[i-1]
|
|
// Return the greater value of the two options
|
|
return int(math.Max(float64(no), float64(yes)))
|
|
}
|
|
|
|
/* 0-1 Knapsack: Memoized search */
|
|
func knapsackDFSMem(wgt, val []int, mem [][]int, i, c int) int {
|
|
// If all items have been chosen or the knapsack has no remaining capacity, return value 0
|
|
if i == 0 || c == 0 {
|
|
return 0
|
|
}
|
|
// If there is a record, return it
|
|
if mem[i][c] != -1 {
|
|
return mem[i][c]
|
|
}
|
|
// If exceeding the knapsack capacity, can only choose not to put it in the knapsack
|
|
if wgt[i-1] > c {
|
|
return knapsackDFSMem(wgt, val, mem, i-1, c)
|
|
}
|
|
// Calculate the maximum value of not putting in and putting in item i
|
|
no := knapsackDFSMem(wgt, val, mem, i-1, c)
|
|
yes := knapsackDFSMem(wgt, val, mem, i-1, c-wgt[i-1]) + val[i-1]
|
|
// Return the greater value of the two options
|
|
mem[i][c] = int(math.Max(float64(no), float64(yes)))
|
|
return mem[i][c]
|
|
}
|
|
|
|
/* 0-1 Knapsack: Dynamic programming */
|
|
func knapsackDP(wgt, val []int, cap int) int {
|
|
n := len(wgt)
|
|
// Initialize dp table
|
|
dp := make([][]int, n+1)
|
|
for i := 0; i <= n; i++ {
|
|
dp[i] = make([]int, cap+1)
|
|
}
|
|
// State transition
|
|
for i := 1; i <= n; i++ {
|
|
for c := 1; c <= cap; c++ {
|
|
if wgt[i-1] > c {
|
|
// If exceeding the knapsack capacity, do not choose item i
|
|
dp[i][c] = dp[i-1][c]
|
|
} else {
|
|
// The greater value between not choosing and choosing item i
|
|
dp[i][c] = int(math.Max(float64(dp[i-1][c]), float64(dp[i-1][c-wgt[i-1]]+val[i-1])))
|
|
}
|
|
}
|
|
}
|
|
return dp[n][cap]
|
|
}
|
|
|
|
/* 0-1 Knapsack: Space-optimized dynamic programming */
|
|
func knapsackDPComp(wgt, val []int, cap int) int {
|
|
n := len(wgt)
|
|
// Initialize dp table
|
|
dp := make([]int, cap+1)
|
|
// State transition
|
|
for i := 1; i <= n; i++ {
|
|
// Traverse in reverse order
|
|
for c := cap; c >= 1; c-- {
|
|
if wgt[i-1] <= c {
|
|
// The greater value between not choosing and choosing item i
|
|
dp[c] = int(math.Max(float64(dp[c]), float64(dp[c-wgt[i-1]]+val[i-1])))
|
|
}
|
|
}
|
|
}
|
|
return dp[cap]
|
|
}
|