Project Euler：Problem 81 Path sum: two ways

最新推荐文章于 2021-02-28 17:14:18 发布

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最新推荐文章于 2021-02-28 17:14:18 发布

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分类专栏：欧拉计划 python 文章标签： Project Euler 动态规划

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本文介绍了一个动态规划问题，即在一个80x80的矩阵中寻找从左上角到右下角的最小路径和，仅允许向右或向下移动。通过逐步计算每个位置的最小路径和来解决该问题。

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In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right, by only moving to the right and down, is indicated in bold red and is equal to 2427.

⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ 131201630537805673968036997322343427464975241039654221213718150111956331 ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟

Find the minimal path sum, in matrix.txt (right click and "Save Link/Target As..."), a 31K text file containing a 80 by 80 matrix, from the top left to the bottom right by only moving right and down.

很显然要动态规划

除去矩阵最上面一行和最左边一行，dp[i][j]=min(dp[i+1][j],dp[i][j+1])

ls=[]
for line in open("matrix.txt"):
    #print(line)
    a=line.split(',')
    a=[int(i) for i in a]
    ls.append(a)


#先计算第一行和第一列
for i in range(78,-1,-1):
    ls[79][i]=ls[79][i]+ls[79][i+1]
    ls[i][79]=ls[i][79]+ls[i+1][79]

for i in range(78,-1,-1):
    for j in range(78,-1,-1):
        ls[i][j]=ls[i][j]+min(ls[i+1][j],ls[i][j+1])

print(ls[0][0])