Problem:
Network Reliability

An undirected graph is given.
Each edge of the graph disappears with a constant probability.
Calculate the probability with which the remained graph is connected.

Input

The first line contains three integers N (1 \leq N \leq 14), M (0 \leq M \leq 100) and P (0 \leq P \leq 100), separated by a single space.
N is the number of the vertices and M is the number of the edges. P is the probability represented by a percentage.

The following M lines describe the edges.
Each line contains two integers v_i and u_i (1 \leq u_i, v_i \leq N).
(u_i, v_i) indicates the edge that connects the two vertices u_i and v_i.

Output

Output a line containing the probability with which the remained graph is connected.
Your program may output an arbitrary number of digits after the decimal point. However, the absolute error should be 10^{-9} or less.

Sample Input 1

3 3 50
1 2
2 3
3 1

Output for the Sample Input 1

0.500000000000

Sample Input 2

3 3 10
1 2
2 3
3 1

Output for the Sample Input 2

0.972000000000

Sample Input 3

4 5 50
1 2
2 3
3 4
4 1
1 3

Output for the Sample Input 3

0.437500000000

Solution in Ruby (judge verdict: Time Limit Exceeded)

n, m, q = gets.split.map(&:to_i)

prob = {}
(1..m).each do
    i, j = gets.split.map(&:to_i) 
    i, j = [i, j].sort
    prob[(i << 4) + j] = q / 100.0
end

def f(n, prob)
    return 1.0 if n == 1
    return 0.0 if disconnected?(n, prob)
    return 1.0 - prob.values[0] if n == 2

    key = prob.keys[0]
    i, j = key >> 4, key & 15

    ans = 0

    if prob[key] >= 1e-11
        new_prob = prob.dup
        new_prob.delete(key)
        ans += prob[key] * f(n, new_prob)
    end

    if 1.0 - prob[key] >= 1e-11
        new_prob = Hash.new(1.0)
        prob.each do |k, q|
            u, v = k >> 4, k & 15
            next if k == key
            u = j if k >> 4 == i
            v = j if k & 15 == i
            u, v = [u, v].sort
            new_prob[(u << 4) + v] *= prob[k]
        end
        ans += (1.0 - prob[key]) * f(n-1, new_prob)
    end
    ans
end

require 'set'
def disconnected?(n, prob)
    return true if n > prob.size + 1
    neighbour = {}
    prob.each_key do |key|
        i, j = key >> 4, key & 15
        (neighbour[i] ||= []) << j
        (neighbour[j] ||= []) << i
    end
    i = neighbour.keys.min
    reached = Set[i]
    queue = [i]
    until queue.empty?
        i = queue.shift
        neighbour[i].each do |j|
            next if reached.include?(j)
            reached << j
            queue << j
        end
    end
    reached.size != n
end

printf("%.12f\n", f(n, prob))