Maximum cost of a path (1)

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 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 ≤ 11,
0 ≤ x < n, that the diagonal has only zeros, and that the rest of
numbers are between −10⁶ and 10⁶.

Output

Print the maximum cost of all the paths without repeated vertices that
begin at x.

Problem information

Author: Unknown
Translator: Salvador Roura

Generation: 2026-01-25T11:22:32.339Z

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