题目描述

M×N的矩阵，从左上角走，只能向右或者向下走，要求走过的每个元素的值加起来的和最大，步数不限

代码实现

import numpy as np
def max_way(a,m,n):
    
    dp=[[0]*n for i in range(m)]
    dp[0][0]=a[0][0]
    for i in range(1,m):
        dp[i][0]=dp[i-1][0]+a[i][0]
    for j in range(1,n):
        dp[0][j]=dp[0][j-1]+a[0][j]
    
    for i in range(1,m):
        for j in range(1,n):
            dp[i][j]=max(dp[i-1][j]+a[i][j],dp[i][j-1]+a[i][j])
    #print(dp)
    #求矩阵中元素的最大值
    ls=[]
    for i in range(m):
        ls.append(max(dp[i]))
    
    return max(ls)



a=[[2,5,6,4],[5,8,7,3],[9,5,1,4]]
#不使用numpy
# =============================================================================
# print(len(a))#行数
# print(len(a[0]))#列数
# #使用numpy
# row=np.shape(a)[0]#求矩阵的行数
# col=np.shape(a)[1]#求矩阵的列数
# print(row,col)
# =============================================================================
print(max_way(a,3,4))

输出