// File: unbounded_knapsack.go // Created Time: 2023-07-23 // Author: Reanon (793584285@qq.com) package chapter_dynamic_programming import "math" /* Complete knapsack: Dynamic programming */ func unboundedKnapsackDP(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][c-wgt[i-1]]+val[i-1]))) } } } return dp[n][cap] } /* Complete knapsack: Space-optimized dynamic programming */ func unboundedKnapsackDPComp(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++ { for c := 1; c <= cap; c++ { if wgt[i-1] > c { // If exceeding the knapsack capacity, do not choose item i dp[c] = dp[c] } else { // 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] }