0-1背包问题的Python代码

0-1背包问题的Python代码

def test_2_wei_bag_problem1(bag_size, weight, value) -> int: 
	rows, cols = len(weight), bag_size + 1
	dp = [[0 for _ in range(cols)] for _ in range(rows)]
    
	# 初始化dp数组. 
	for i in range(rows): 
		dp[i][0] = 0
	first_item_weight, first_item_value = weight[0], value[0]
	for j in range(1, cols): 	
		if first_item_weight <= j: 
			dp[0][j] = first_item_value

	# 更新dp数组: 先遍历物品, 再遍历背包. 
	for i in range(1, len(weight)): 
		cur_weight, cur_val = weight[i], value[i]
		for j in range(1, cols): 
			if cur_weight > j: # 说明背包装不下当前物品. 
				dp[i][j] = dp[i - 1][j] # 所以不装当前物品. 
			else: 
				# 定义dp数组: dp[i][j] 前i个物品里，放进容量为j的背包，价值总和最大是多少。
				dp[i][j] = max(dp[i - 1][j], dp[i - 1][j - cur_weight]+ cur_val)

	print(dp)


if __name__ == "__main__": 
	bag_size = 10
	weight = [2,2,6,5,4]
	value = [6,3,5,4,6]
	test_2_wei_bag_problem1(bag_size, weight, value)

运行出来的动态规划结果表：

[[0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6], 
 [0, 0, 6, 6, 9, 9, 9, 9, 9, 9, 9], 
 [0, 0, 6, 6, 9, 9, 9, 9, 11, 11, 14], 
 [0, 0, 6, 6, 9, 9, 9, 10, 11, 13, 14], 
 [0, 0, 6, 6, 9, 9, 12, 12, 15, 15, 15]]