R中的背包问题:如何在R中使用循环来检查每个项目而不是整个列

# 背包问题解决函数
knapsack <- function(weights, values, capacity) {
  n <- length(weights)  # 项目数量
  dp <- matrix(0, nrow = n + 1, ncol = capacity + 1)  # 动态规划表
  
  # 填充动态规划表
  for (i in 1:n) {
    for (j in 1:capacity) {
      if (weights[i] <= j) {
        dp[i+1, j+1] <- max(dp[i, j+1], values[i] + dp[i, j+1-weights[i]])
      } else {
        dp[i+1, j+1] <- dp[i, j+1]
      }
    }
  }
  
  # 回溯找出最优解
  selected_items <- vector("integer", n)
  i <- n
  j <- capacity
  while (i > 0 && j > 0) {
    if (dp[i, j] != dp[i-1, j]) {
      selected_items[i] <- 1
      j <- j - weights[i]
    }
    i <- i - 1
  }
  
  # 返回最优解
  return(list(selected_items = selected_items, total_value = dp[n+1, capacity+1]))
}

# 示例数据
weights <- c(2, 3, 4, 5)  # 项目的重量
values <- c(3, 4, 5, 6)  # 项目的价值
capacity <- 8  # 背包的容量

# 调用背包问题解决函数
result <- knapsack(weights, values, capacity)

# 输出最优解
cat("Selected items:", result$selected_items, "\n")
cat("Total value:", result$total_value, "\n")