动态规划刷题集python代码

1 最长公共子序列长度

def lcs(x,y,m,n):
    c = [[0]*(n+1)]*(m+1)
    print(len(c),len(c[0]))
    for i in range(m):
        for j in range(n):
            if x[i]==y[j]:
                c[i+1][j+1]=c[i][j]+1
            else:
                c[i+1][j+1]=max(c[i+1][j],c[i][j+1])
    return c[m][n]
x = [1,3,2,5,6]
y = [6,3,2,4,5,7,6]
m,n = 5,7
print(lcs(x,y,m,n))

　　变形有最短编辑距离

2 最长上升子序列长度

def lis(x,m):
    if m == 0:
        return 0
    c = [1]*m #c[i]为以i下标为结尾的最长上升子序列长度，如果m不为0，那么结果至少为1
    for i in range(m):
        for j in range(i):
            if x[i]>x[j]:
                c[i] = max(c[j]+1,c[i]) 
    return max(c)
x = [2,1,5,7,10,4]
m = 6
print(lis(x,m))

3