Sem_2_Task_6

#include <iostream>
#include <vector>
#include <algorithm>
#include <set>

struct Edge;

const size_t INF = size_t(1e12);

namespace {
    using NumsVec = std::vector<size_t>;
    using VecNumsVec = std::vector<NumsVec>;
    using DoubleVec = std::vector<long double>;
    using VecDoubleVec = std::vector<DoubleVec>;
    using BoolVec = std::vector<bool>;
    using EdgeVec = std::vector<Edge>;
}

struct Edge {
    Edge() = default;
    Edge(std::pair<size_t, size_t> edge) : from(edge.first), to(edge.second) {};
    Edge(size_t i, size_t j, size_t w, size_t u) : from(i), to(j) {};

    bool operator==(const Edge& other) const {
        return from == other.from && to == other.to;
    }

    size_t from = 0;
    size_t to = 0;
    long double risk = 1;
};

std::istream& operator>>(std::istream& input, Edge& p) {
    input >> p.from >> p.to >> p.risk;
    --p.from;
    --p.to;
    p.risk /= 100;
    return input;
}

void InputEdges(std::vector<Edge>& edges) {
    for (auto& edge : edges) {
        std::cin >> edge;
    }
}

template<>
struct std::hash<Edge> {
    size_t operator()(const Edge& p) const {
        return p.from * p.to;
    }
};

std::ostream& operator<<(std::ostream& output, NumsVec& vec) {
    for (auto elem : vec) {
        std::cout << elem + 1 << " ";
    }
    return output;
}

struct Graph {
    Graph(size_t n) : size(n), visited(n, false), color(n, 0),
    top_sort(n, 0), top_sort_pos(n - 1), d(n, INF) {};

    Graph(size_t n, EdgeVec& edges) : size(n), visited(n, false), color(n, 0),
    top_sort(n, 0), top_sort_pos(n - 1), d(n, INF), matrix(n, DoubleVec(n, 1)), neighbours(n) {
        for (auto edge : edges) {
            matrix[edge.from][edge.to] = edge.risk;
            matrix[edge.to][edge.from] = edge.risk;
            neighbours[edge.from].push_back(edge.to);
            neighbours[edge.to].push_back(edge.from);
        }
        for (size_t v = 0; v < n; ++v) {
            matrix[v][v] = 0;
        }
    };

    size_t size = 0;
    bool cycle = false;

    VecDoubleVec matrix;
    VecNumsVec neighbours;
    BoolVec visited;
    NumsVec color;
    NumsVec top_sort;
    NumsVec d;
    size_t top_sort_pos = 0;
};

void Floyd(Graph& g) {
    for (size_t k = 0; k < g.size; ++k) {
        for (size_t u = 0; u < g.size; ++u) {
            for (size_t v = 0; v < g.size; ++v) {
                g.matrix[u][v] = std::min(g.matrix[u][v], 1 - (1 - g.matrix[u][k]) * (1 - g.matrix[k][v]));
            }
        }
    }
}

int main() {
    size_t n, m, s, t;
    std::cin >> n >> m >> s >> t;
    EdgeVec edges(m);
    InputEdges(edges);
    Graph g(n, edges);
    Floyd(g);
    std::cout << g.matrix[s - 1][t - 1];
}