Problem 83
Path sum: four ways
NOTE: This problem is a significantly more challenging version of Problem 81.
In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right, by moving left, right, up, and down, is indicated in bold red and is equal to 2297.
| 131 | 673 | 234 | 103 | 18 |
| 201 | 96 | 342 | 965 | 150 |
| 630 | 803 | 746 | 422 | 111 |
| 537 | 699 | 497 | 121 | 956 |
| 805 | 732 | 524 | 37 | 331 |
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 moving left, right, up, and down.
路径和：四个方向
注意：这是第81题的一个极具挑战性的版本。
在如下的5乘5矩阵中，从左上角到右下角任意地向上、向下、向左或向右移动的最小路径和为2297，由标注红色的路径给出。
| 131 | 673 | 234 | 103 | 18 |
| 201 | 96 | 342 | 965 | 150 |
| 630 | 803 | 746 | 422 | 111 |
| 537 | 699 | 497 | 121 | 956 |
| 805 | 732 | 524 | 37 | 331 |
在这个31K的文本文件matrix.txt（右击并选择“目标另存为……”）中包含了一个80乘80的矩阵，求出从左上角到右下角任意地向上、向下、向左或向右移动的最小路径和。