Worst path

Given a directed and complete graph with n vertices, and an initial
vertex x, compute the maximum cost of all the paths without repeated
vertices that begin at x. The given graph is represented by an n × n
matrix M, where for every pair (i, j) with i ≠ j, m_(ij) is the (perhaps
negative) cost of the arc from i to j.

For instance, the maximum cost of the first test is 80, corresponding to
the path 1 → 0 → 3, with cost −10 + 90 = 80.

Input

Input consists of several cases, each one with the number of vertices n,
followed by the matrix M (n lines, each one with n integer numbers),
followed by the initial vertex x. Vertices are numbered from 0 to n − 1.
You can assume 1 ≤ n ≤ 18, 0 ≤ x < n, that the diagonal has only zeros,
and that the rest of numbers are between −10⁶ and 10⁶.

Output

For every case, print the cost of the worst path without repeated
vertices that begins at x.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T09:54:43.549Z

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