动态规划刷题集python代码

1 爬楼梯（Fibonacci）

#有一楼梯共M级，若每次只能跨上一级或二级，要走上第M级，共有多少种走法？
def fun(m):
    c = [0]*m
    c[0] = 1
    c[1] = 2
    for i in range(2,m):
        c[i] = c[i-1]+c[i-2]
    return c[m-1]
print(fun(3))

2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

3 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))

4 硬币找零之最少硬币方案

def coinfun(coin,aim):
    max_value = aim+1
    c = [0]+[max_value]*aim
    #两行写法，很python
    # for i in range(1,aim+1):
    #     c[i] = min([c[i-j] if i-j>=0 else max_value for j in coin ])+1
    #常规写法
    for i in range(1,aim+1):
        for j in coin:
            if i-j>=0:
                c[i] = min(c[i],c[i-j]+1)
    if c[aim] == aim+1:
        return -1 #没法找
    return c[aim]
coin = [5,2,3]
aim = 20
print(coinfun(coin,aim))

5 硬币找零之最大找零种数

def coinfun(coin,aim):
    c = [0]*(aim+1)
    c[0]=1
    for j in coin:
        for i in range(1,aim+1):
            if i-j>=0:
                c[i] += c[i-j]
    if c[aim] == 0:
        return -1 #没法找
    return c[aim]
coin = [5,2,3]
aim = 20
print(coinfun(coin,aim))

6 最大连续子序列和

#最大连续子序列和

def maxsub(A):
    dp = [0] *len(A) #以i下表为结尾的最大连续子序列和（大概这个意思，不太准确明白就行）
    dp[0] = A[0]
    for i,item in enumerate(A):
        dp[i] = item+dp[i-1] if dp[i-1]>0 else item
    return max(dp)
A = [3,-1,5,-7,4]
print(maxsub(A))

7 不相邻元素最大累加和

#最大不相邻累加和
def sum1(arr):
    c = [0]*len(arr)
    c[0] = arr[0]
    c[1] = max(arr[0],arr[1])
    for i in range(2,len(arr)):
        c[i] = max(c[i-1],c[i-2]+arr[i])
    return c[-1]
arr = [3, 2, 1, 9, 4, 2]
print(sum1(arr))