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完全背包问题

news 来源：原创 2025/5/28 3:17:58

def knapsack(n, bag_weight, weight, value):
    dp = [[0] * (bag_weight + 1) for _ in range(n)]

    # 初始化
    for j in range(weight[0], bag_weight + 1):
        dp[0][j] = dp[0][j - weight[0]] + value[0]

    # 动态规划
    for i in range(1, n):
        for j in range(bag_weight + 1):
            if j < weight[i]:
                dp[i][j] = dp[i - 1][j]
            else:
                dp[i][j] = max(dp[i - 1][j], dp[i][j - weight[i]] + value[i])

    return dp[n - 1][bag_weight]

# 输入
n, bag_weight = map(int, input().split())
weight = []
value = []
for _ in range(n):
    w, v = map(int, input().split())
    weight.append(w)
    value.append(v)

# 输出结果
print(knapsack(n, bag_weight, weight, value))

n,v = map(int,input().split())
weigh = [0]+list(map(int,input().split()))
value = [0]+list(map(int,input().split()))
dp = [[0]*(v+1) for _ in range(n+1)]

for i in range(1,n+1):
    for j in range(v+1):
        if weigh[i]> j:
            dp[i][j] = dp[i-1][j]
        else:
            dp[i][j] = max(dp[i-1][j],dp[i][j-weigh[i]]+value[i])
print(dp[n][v])

# 完全背包问题解法

题目链接：52. 携带研究材料（第七期模拟笔试）