[Need help] Shortest path, but edge has 2 cost Ai and Bi, and cost of path is prod of sum Ai and Bi

Revision en3, by 3509, 2022-10-10 08:48:11
Source

My school hosted a local ICPC format contest yesterday, this problem appeared in it. Since it was for local only, I cannot provide link for submission (sorry!)

Statement

Given a weighted undirected graph $$$G$$$ with $$$n$$$ vertices and $$$m$$$ edges. Edge $$$e_i$$$ is a tuple $$$(u_i, v_i, A_i, B_i)$$$ denotes there is an edge connects $$$u_i$$$ with $$$v_i$$$, with cost $$$A_i$$$ and $$$B_i$$$. Consider path $$$u \rightarrow v$$$ is a sequence of edges $$$E: \{e_1, e_2,... e_k\}$$$, cost of $$$E$$$ is defined as product of (sum of all $$$A_x$$$) and (sum of all $$$B_x$$$) with $$$x$$$ is an edge in $$$E$$$. Calculate shortest path from node $$$1$$$ to all other nodes.

Sample Tests
Input 1
4 4
1 2 2 4
3 4 4 1
4 2 1 1
1 3 3 1
Output 1
8
3
14
Input 2
3 2
1 2 2 5
2 1 3 3
Output 2
9
-1

History

 
 
 
 
Revisions
 
 
  Rev. Lang. By When Δ Comment
en6 English 3509 2022-10-10 09:07:32 37 Tiny change: ' 2000$\n\n##### ' -> ' 2000$\n\nThere is no additional guarantees\n\n##### '
en5 English 3509 2022-10-10 09:01:12 0 (published)
en4 English 3509 2022-10-10 08:57:58 628
en3 English 3509 2022-10-10 08:48:11 560 Tiny change: 'edges $E: {e_1, e_2,... e_k}$, cost o' -> 'edges $E: \{e_1, e_2,... e_k\}$, cost o'
en2 English 3509 2022-10-10 08:28:54 6
en1 English 3509 2022-10-10 08:28:17 617 Initial revision (saved to drafts)