动态规划入门

 

 

 

 例1：

 

 

 

 

def jianshuiguo(n,ans):
    dp=[[0 for i in range(n+1)]for j in range(n+1)]
    dp[1][0]=ans[1][0]
    # print(dp)
    sum=0
    for i in range(2,n+1):
        for j in range(i):
            if j==0:
                dp[i][j]=dp[i-1][j]+ans[i][j]
            elif i==j-1:
                dp[i][j]=dp[i-1][j-1]+ans[i][j]
            else:
                dp[i][j]=max(dp[i-1][j],dp[i-1][j-1])+ans[i][j]
            if i==n:
                if sum<dp[i][j]:
                    sum=dp[i][j]
    return sum
if __name__=='__main__':
    n=int(input())
    ans=[]
    ans.append([0]*(n+1))
    for i in range(n):
        ans.append(list(map(int,input().rstrip().split())))
    for j in range(len(ans)):
        while len(ans[j])<n+1:
            ans[j].append(0)
    # print(ans)
    print(jianshuiguo(n,ans))

 例2：

 

 

 

 

 

 

 

def taosheng(n,m,x,y,v,c,ans):
    dp=[[0 for i in range(n)]for j in range(m)]
    sum=0
# #左上
    for i in range(x,-1,-1):
        for j in range(y,-1,-1):
            if i==x and j==y:
                dp[i][j]=v+ans[i][j]
            elif i==x:
                dp[i][j]=dp[i][j+1]+ans[i][j]
            elif j==y:
                dp[i][j]=dp[i+1][j]+ans[i][j]
            else:
                dp[i][j]=max(dp[i+1][j],dp[i][j+1])+ans[i][j]
            if dp[i][j]>c:
                dp[i][j]=c
            if dp[i][j]<=0:
                dp[i][j]=-1000000000
#     左下
    for i in range(x,n):
        for j in range(y,-1,-1):
            if i==x and j==y:
                dp[i][j]=v+ans[i][j]
            elif i==x:
                dp[i][j]=dp[i][j+1]+ans[i][j]
            elif j==y:
                dp[i][j]=dp[i-1][j]+ans[i][j]
            else:
                dp[i][j]=max(dp[i][j+1],dp[i-1][j])+ans[i][j]
            if dp[i][j]>c:
                dp[i][j]=c
            if dp[i][j]<=0:
                dp[i][j]=-1000000000
#右上
    for i in range(x,-1,-1):
        for j in range(y,m):
            if i==x and j==y:
                dp[i][j]=v+ans[i][j]
            elif i==x:
                dp[i][j]=dp[i][j-1]+ans[i][j]
            elif j==y:
                dp[i][j]=dp[i+1][j]+ans[i][j]
            else:
                dp[i][j]=max(dp[i][j-1],dp[i+1][j])+ans[i][j]
            if dp[i][j]>c:
                dp[i][j]=c
            if dp[i][j]<=0:
                dp[i][j]=-1000000000
#右下
    for i in range(x,n):
        for j in range(y,m):
            if i==x and j==y:
                dp[i][j]=v+ans[i][j]
            elif i==x:
                dp[i][j]=dp[i][j-1]+ans[i][j]
            elif j==y:
                dp[i][j]=dp[i-1][j]+ans[i][j]
            else:
                dp[i][j]=max(dp[i][j-1],dp[i-1][j])+ans[i][j]
            if dp[i][j]>c:
                dp[i][j]=c
            if dp[i][j]<=0:
                dp[i][j]=-1000000000
    sum=max(max(dp[0][0],dp[n-1][m-1]),max(dp[0][m-1],dp[n-1][0]))
    return sum if sum>0 else -1
if __name__=='__main__':
    n,m,x,y,v,c=map(int,input().split())
    ans=[]
    for i in range(n):
        ans.append(list(map(int,input().rstrip().split())))
    print(taosheng(n,m,x-1,y-1,v,c,ans))