Problem 81

Path sum: two ways

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 $2427$.

$$
\begin{pmatrix}
\color{red}{131} & 673 & 234 & 103 & 18\\
\color{red}{201} & \color{red}{96} & \color{red}{342} & 965 & 150\\
630 & 803 & \color{red}{746} & \color{red}{422} & 111\\
537 & 699 & 497 & \color{red}{121} & 956\\
805 & 732 & 524 & \color{red}{37} & \color{red}{331}
\end{pmatrix}
$$

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

路径和：两个方向

在如下的$5 \times 5$矩阵中，从左上方到右下方始终只向右或向下移动的最小路径和为$2427$，由标注红色的路径给出。

在文本文件matrix.txt中包含了一个$80 \times 80$的矩阵，求从该矩阵的左上方到右下方始终只向右或向下移动的最小路径和。