FloydWarshall

FloydWarshall.ipynb

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      "   x   y   u   v   s   \n",
      "x [0, 2, 3, 4, 9]\n",
      "y [12, 0, 15, 6, 7]\n",
      "u [2, 4, 0, 1, 11]\n",
      "v [16, 4, 19, 0, 11]\n",
      "s [5, 7, 8, 9, 0]\n"
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   "source": [
    "def FloydWarshall(G):\n",
    "    A=[]    # A= (a_{ij}) n×n adjacency matrix of the digraph G\n",
    "    \n",
    "    for u in G:\n",
    "        Au = []  # row of A correponding to vertex u \n",
    "        for v in G:\n",
    "            if  v in G[u]:Au.append(G[u][v])\n",
    "            elif u == v : Au.append(0)\n",
    "            else: Au.append(float(\"inf\"))     \n",
    "        A.append(Au)\n",
    "    \n",
    "    Cnext = A\n",
    "    \n",
    "    for k in range(len(G)):\n",
    "        C = Cnext\n",
    "        for i in range(len(G)):\n",
    "            for j in range(len(G)):\n",
    "                if C[i][j] > C[i][k]+ C[k][j]:\n",
    "                        Cnext[i][j] = C[i][k]+ C[k][j]\n",
    "    return Cnext\n",
    "            \n",
    "G = {'s': {'u':10, 'x':5},\n",
    "    'u': {'v':1, 'x':2},\n",
    "    'v': {'y':4},\n",
    "    'x':{'u':3,'v':9,'y':2},\n",
    "    'y':{'s':7,'v':6}}\n",
    "\n",
    "F = FloydWarshall(G)\n",
    "\n",
    "V = \"   \"\n",
    "for u in G:\n",
    "    V = V + u + \"   \"\n",
    "print(V)\n",
    "\n",
    "i  = 0\n",
    "for u in G:\n",
    "    print(u,F[:][i])\n",
    "    i = i + 1\n"
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