gistfile1.txt

<|dummy_86|>We are given a star graph edge list. Wait what does "star graph" means? Actually not exactly star graph. The provided edges: they are given as pairs like (8287, 6251) etc. Actually, it's a graph with many edges. But the question says: "I will give you the edge list of a star graph and I want you to find a path from the center node to a leaf node". The provided edges are many. Actually, look carefully: The graph provided is: (8287, 6251), (6251, 7840), ... There's many edges.

We need to find a valid path from 8287 to 5653. So we are given an edge list, and we must find a path from node 8287 to node 5653. Let's try to see if we can follow the edges. The provided edges appear to be in a star graph structure. But wait: Check edge: "Here's the list of edges: (8287, 6251), (6251, 7840), (7840, 4271), ..." Actually, note that each edge is given as a pair. But the provided edges appear to be "8287" appears in many pairs, and then they sometimes include other pairs that don't connect directly to 8287. Wait, let's see: There's edge (8287, 6251), then edge (6251, 7840) so that means 6251 connects to 7840. Then edge (7840, 4271) means 7840 is connected with 4271. Then edge (4271, 4805) then (4805, 1220) then (1220, 5263) then (5263, 3133) then (3133, 5113) then (5113, 3626) then (3626, 5362) then (8287, 5593) then (5593, 5505) then (5505, 7283) then (7283, 4825) then (4825, 6692) then (6692, 9255) then (9255, 9859) then (9859, 4919) then (4919, 3180) then (3180, 9508). Then (8287, 3463) then (3463, 2112) then (2112, 4304) then (4304, 4385) then (4385, 9595) then (9595, 7740) then (7740, 9235) then (9235, 5471) then (5471, 3181) then (3181, 5853) then (8287, 7920) then (7920, 1663) then (1663, 5975) then (5975, 2316) then (2316, 2916) then (2916, 1918) then (1918, 3059) then (3059, 5739) then (5739, 7050) then (7050, 8033) then (8287, 7850) then (7850, 3605) then (3605, 2402) then (2402, 4294) then (4294, 8650) then (8650, 8522) then (8522, 1453) then (1453, 7635) then (7635, 8208) then (8208, 5653) then (8287, 9583) then (9583, 3357) then (3357, 9053) then (9053, 9812) then (9812, 9831) then (9831, 5638) then (5638, 9314) then (9314, 7709) then (7709, 7605) then (7605, 7443) then (8287, 6265) then (6265, 1622) then (1622, 3601) then (3601, 8406) then (8406, 2672) then (2672, 2103) then (2103, 3902) then (3902, 2380) then (2380, 1573) then (1573, 4889) then (8287, 2662) then (2662, 7504) then (7504, 9894) then (9894, 2859) then (2859, 2141) then (2141, 9243) then (9243, 4029) then (4029, 8961) then (8961, 3410) then (3410, 1733).

We need a valid path from 8287 to 5653. We need to check: which edges involve 5653? There is an edge: (8208, 5653) is in the list. Meanwhile, 8208 is connected to 8208 <-> ? Actually, there's an edge (7635, 8208). Before that, (1453, 7635). And (8522, 1453) then (8650, 8522). And (4294, 8650) then (2402, 4294) then (3605, 2402) then (7850, 3605) and (8287,7850). So it seems we have a path from 8287 to 5653 through: 8287 -> 7850 -> 3605 -> 2402 -> 4294 -> 8650 -> 8522 -> 1453 -> 7635 -> 8208 -> 5653. Let's check each edge:

Edge list: (8287,7850) is in list? Yes: (8287, 7850) is in the list. Next, (7850, 3605) is in list? Yes: (7850, 3605) is in list. Next, (3605,2402) is in list? Yes: (3605, 2402) is in list. Next, (2402,4294) is in list? Yes: (2402,4294) is in list. Next, (4294,8650) is in list? Yes: (4294,8650) is in list. Next, (8650,8522) is in list? Yes: (8650,8522) is in list. Next, (8522,1453) is in list? Yes: (8522,1453) is in list. Next, (1453,7635) is in list? Yes: (1453,7635) is in list. Next, (7635,8208) is in list? Yes: (7635,8208) is in list. Next, (8208,5653) is in list? Yes: (8208,5653) is in list.

Thus a valid path is: 8287 -> 7850 -> 3605 -> 2402 -> 4294 -> 8650 -> 8522 -> 1453 -> 7635 -> 8208 -> 5653.

I'll re-read edges to be sure: Actually, the provided edges: There's (8287,7850) is present: "8287, 7850" is in the list: it is the 23rd pair in the list? Let's check: The list: 
1. (8287, 6251)
2. (6251, 7840)
3. (7840, 4271)
4. (4271, 4805)
5. (4805, 1220)
6. (1220, 5263)
7. (5263, 3133)
8. (3133, 5113)
9. (5113, 3626)
10. (3626, 5362)
11. (8287, 5593)
12. (5593, 5505)
13. (5505, 7283)
14. (7283, 4825)
15. (4825, 6692)
16. (6692, 9255)
17. (9255, 9859)
18. (9859, 4919)
19. (4919, 3180)
20. (3180, 9508)
21. (8287, 3463)
22. (3463, 2112)
23. (2112, 4304)
24. (4304, 4385)
25. (4385, 9595)
26. (9595, 7740)
27. (7740, 9235)