<p>You are given an undirected weighted graph of&nbsp;<code>n</code>&nbsp;nodes (0-indexed), represented by an edge list where&nbsp;<code>edges[i] = [a, b]</code>&nbsp;is an undirected edge connecting the nodes&nbsp;<code>a</code>&nbsp;and&nbsp;<code>b</code>&nbsp;with a probability of success of traversing that edge&nbsp;<code>succProb[i]</code>.</p>

<p>Given two nodes&nbsp;<code>start</code>&nbsp;and&nbsp;<code>end</code>, find the path with the maximum probability of success to go from&nbsp;<code>start</code>&nbsp;to&nbsp;<code>end</code>&nbsp;and return its success probability.</p>

<p>If there is no path from&nbsp;<code>start</code>&nbsp;to&nbsp;<code>end</code>, <strong>return&nbsp;0</strong>. Your answer will be accepted if it differs from the correct answer by at most <strong>1e-5</strong>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2019/09/20/1558_ex1.png" style="width: 187px; height: 186px;" /></strong></p>

<pre>
<strong>Input:</strong> n = 3, edges = [[0,1],[1,2],[0,2]], succProb = [0.5,0.5,0.2], start = 0, end = 2
<strong>Output:</strong> 0.25000
<strong>Explanation:</strong>&nbsp;There are two paths from start to end, one having a probability of success = 0.2 and the other has 0.5 * 0.5 = 0.25.
</pre>

<p><strong class="example">Example 2:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2019/09/20/1558_ex2.png" style="width: 189px; height: 186px;" /></strong></p>

<pre>
<strong>Input:</strong> n = 3, edges = [[0,1],[1,2],[0,2]], succProb = [0.5,0.5,0.3], start = 0, end = 2
<strong>Output:</strong> 0.30000
</pre>

<p><strong class="example">Example 3:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2019/09/20/1558_ex3.png" style="width: 215px; height: 191px;" /></strong></p>

<pre>
<strong>Input:</strong> n = 3, edges = [[0,1]], succProb = [0.5], start = 0, end = 2
<strong>Output:</strong> 0.00000
<strong>Explanation:</strong>&nbsp;There is no path between 0 and 2.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= n &lt;= 10^4</code></li>
	<li><code>0 &lt;= start, end &lt; n</code></li>
	<li><code>start != end</code></li>
	<li><code>0 &lt;= a, b &lt; n</code></li>
	<li><code>a != b</code></li>
	<li><code>0 &lt;= succProb.length == edges.length &lt;= 2*10^4</code></li>
	<li><code>0 &lt;= succProb[i] &lt;= 1</code></li>
	<li>There is at most one edge between every two nodes.</li>
</ul>

#define MAX_ARR 10020
#define MIN_VAL -999999999999

double ret;
int N;
int st;
int en;

int q[MAX_ARR*100];
int qw;
int qr;

struct p {
    double prob;
    int no;
};

vector<p> ne[MAX_ARR];

double pro[MAX_ARR];

void Find () {
    int i;
    for ( i = 0; i < N; i++ ) {
        pro[i] = MIN_VAL;
    }

    qw = 0;
    qr = 0;
    q[qw++] = st;
    pro[st] = 0.0;

    while ( qr < qw ) {
        int cu = q[qr++];
        double cupro = pro[cu];
        for ( i = 0; i < ne[cu].size(); i++ ) {
            int nex = ne[cu][i].no;

            double prob = log ( ne[cu][i].prob );
            double totprob = prob + cupro;

            if ( pro[nex] < totprob ) {
                q[qw++] = nex;
                pro[nex] = totprob;
            }
        }
    }
}


class Solution {
public:
    double maxProbability(int n, vector<vector<int>>& edges, vector<double>& succProb, int start_node, int end_node) {
        int i;

        N = n;

        st = start_node;
        en = end_node;

        for ( i = 0; i <= N; i++ ) {
            ne[i].clear();
        }
        for ( i = 0; i < edges.size(); i++ ) {
            int n1 = edges[i][0];
            int n2 = edges[i][1];
            struct p ps;

            ps.prob = succProb[i];
            ps.no = n2;
            ne[n1].push_back(ps);
            ps.no = n1;
            ne[n2].push_back(ps);
        }

        Find ();

        if ( pro[en] == MIN_VAL ) {
            return 0;
        }

        ret = exp ( pro[en] );

        return ret;
    }
};
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