急急急~~英文翻译

For n = 0, the initialization clearly gives the shortest path lengths subject to the constraint of no intermediate nodes on paths.
由于受限于路径中无中间节点，如n=0，则一开始就已经很明确地给出了最短路径长度。
Now, suppose for a given n, L (i, j) in the above algorithm gives the shortest path lengths using nodes 1 to n n+1 as intermediate nodes.
现在，给n一个定值，将节点1至n+1作为中间节点，上述算法中的L（i, j）给出了最短路径长度。
Then the shortest path length from i to j, allowing nodes 1 to n+1 as possible intermediate nodes, either contains node n+1 on the shortest path or doesn't contain node n+1.
那么，允许节点1至n+1作为中间节点的话，从i至j的最短路径长度中既不包括最短路径中的节点n+1也不包括节点n+1。
For the first case, the constrained shortest path from i to j goes from i to n+1 and then from n+1 to j, giving the length in the final term of the equation in step 2 of the problem.
第一种情况下，给出问题第二步方程最终期的长度，则从i至j的受限的最短路径从i到n+1，再从n+1到j。，
For the second case, the constrained shortest path is the same as the one using nodes 1 to n as possible intermediate node