01背包问题

题目来源：acwing

2. 01背包问题 - AcWing题库

N=1005
#f[i][j]:i件物品，体积为j 属性：总价值max
#分割：不要第i件物品，f[i][j]=f[i-1][j]
#要第i件物品：f[i-1][j-v(i)]+w[i]
f=[[0 for i in range(N)]for i in range(N)]
a=[0 for i in range(N)]
b=[0 for i in range(N)]
n,v=map(int,input().split())
for i in range(1,n+1):
    a[i],b[i]=map(int,input().split())
for i in range(1,n+1):
    for j in range(1,v+1):
        if j>=a[i]:
            f[i][j]=max(f[i][j],f[i-1][j-a[i]]+b[i])
        else:
            f[i][j]=f[i-1][j]
            
print(f[n][v])
    
    

区分01背包和完全背包的优化： 二维 =>一维：

N=1005
#f[i][j]:i件物品，体积为j 属性：总价值max
#分割：不要第i件物品，f[i][j]=f[i-1][j]
#要第i件物品：f[i-1][j-v(i)]+w[i]
f=[0 for i in range(N)]
a=[0 for i in range(N)]
b=[0 for i in range(N)]
n,v=map(int,input().split())
for i in range(1,n+1):
    a[i],b[i]=map(int,input().split())
for i in range(1,n+1):
    for j in range(v,a[i]-1,-1):
            f[j]=max(f[j],f[j-a[i]]+b[i])
            
print(f[v])