From 08498fea68d07e02db83dde4d66f4dc716d62a89 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Laure=CE=B7t?= <laurentfainsin@protonmail.com>
Date: Fri, 17 Dec 2021 22:50:48 +0100
Subject: [PATCH] feat: ajout de bellman ford

---
 tp4.ipynb | 417 ++++++++++++++++++++++++++++++++++++++++++++++++++++--
 1 file changed, 408 insertions(+), 9 deletions(-)

diff --git a/tp4.ipynb b/tp4.ipynb
index 397fdd1..162ebaf 100644
--- a/tp4.ipynb
+++ b/tp4.ipynb
@@ -9,7 +9,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [
     {
@@ -61,7 +61,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
@@ -103,39 +103,438 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "3906\n",
-      "Int8[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0]\n"
+      "2291\n",
+      "Int8[0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0]\n"
      ]
     }
    ],
    "source": [
-    "price, weight, capacity = readKnapInstance(\"test4.opb\")\n",
+    "price, weight, capacity = readKnapInstance(\"test2.opb\")\n",
     "\n",
     "res, sol = analyseDynamique(price, weight, length(price), capacity)\n",
     "\n",
     "println(res)\n",
     "println(sol)"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "using Pkg\n",
+    "Pkg.add(\"GraphPlot\")\n",
+    "Pkg.add(\"Graphs\")\n",
+    "Pkg.add(\"SimpleWeightedGraphs\")\n",
+    "using Graphs\n",
+    "using GraphPlot\n",
+    "using SimpleWeightedGraphs"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 126,
+   "metadata": {},
+   "outputs": [
+    {
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Compose.Rotation{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}, Tuple{Measures.AbsoluteLength, Measures.AbsoluteLength}}((0.3286018055346671cx, -0.3719980619221529cy), \"3\", Compose.HCenter(), Compose.VCenter(), Compose.Rotation{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}(0.0, (0.5w, 0.5h)), (0.0mm, 0.0mm)), Compose.TextPrimitive{Tuple{Measures.Length{:cx, Float64}, Measures.Length{:cy, Float64}}, Compose.Rotation{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}, Tuple{Measures.AbsoluteLength, Measures.AbsoluteLength}}((-0.6728173787216601cx, -1.0cy), \"4\", Compose.HCenter(), Compose.VCenter(), Compose.Rotation{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}(0.0, (0.5w, 0.5h)), (0.0mm, 0.0mm)), Compose.TextPrimitive{Tuple{Measures.Length{:cx, Float64}, Measures.Length{:cy, Float64}}, Compose.Rotation{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}, Tuple{Measures.AbsoluteLength, Measures.AbsoluteLength}}((-1.0cx, 0.4620566323492894cy), \"5\", Compose.HCenter(), Compose.VCenter(), Compose.Rotation{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}(0.0, (0.5w, 0.5h)), (0.0mm, 0.0mm))], Symbol(\"\"))]), List([Compose.Property{Compose.FontSizePrimitive}(Compose.FontSizePrimitive[Compose.FontSizePrimitive(4.0mm)]), Compose.Property{Compose.StrokePrimitive}(Compose.StrokePrimitive[Compose.StrokePrimitive(RGBA{Float64}(0.0,0.0,0.0,0.0))]), Compose.Property{Compose.FillPrimitive}(Compose.FillPrimitive[Compose.FillPrimitive(RGBA{Float64}(0.0,0.0,0.0,1.0))])]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\"))]), List([]), List([]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\"))"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "g = SimpleWeightedDiGraph(5)\n",
+    "\n",
+    "add_edge!(g, 1, 2, 9)\n",
+    "add_edge!(g, 1, 3, 3)\n",
+    "add_edge!(g, 2, 3, 6)\n",
+    "add_edge!(g, 2, 5, 2)\n",
+    "add_edge!(g, 3, 4, 1)\n",
+    "add_edge!(g, 3, 2, 2)\n",
+    "add_edge!(g, 4, 3, 2)\n",
+    "add_edge!(g, 4, 5, 2)\n",
+    "\n",
+    "nodelabel = 1:nv(g)\n",
+    "edgelabel = edges(g).iter.is[3]\n",
+    "gplot(g, nodelabel=nodelabel, edgelabel=edgelabel)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 136,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "([0.0, 5.0, 3.0, 4.0, 6.0], [0, 3, 1, 3, 4])"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# https://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm\n",
+    "function bellmanFord(graph, source)\n",
+    "\n",
+    "    # Step 1: initialize graph\n",
+    "    d = fill(Inf, nv(graph)); # distance array\n",
+    "    p = fill(0, nv(graph)); # predecessor array\n",
+    "    d[source] = 0; # source's distance to source is null\n",
+    "\n",
+    "    # Step 2: relax edges repeatedly\n",
+    "    for _ in 2:nv(graph)\n",
+    "        # println(\"test: \", k)\n",
+    "        for (v, u, w) in edges(graph).iter\n",
+    "            # println(u, \" \", v, \" \", w)\n",
+    "            if d[u] + w < d[v]\n",
+    "                d[v] = d[u] + w\n",
+    "                p[v] = u\n",
+    "            end\n",
+    "        end\n",
+    "    end\n",
+    "\n",
+    "    # Step 3: check for negative-weight cycles\n",
+    "    for (v, u, w) in edges(graph).iter\n",
+    "        if d[u] + w < d[v]\n",
+    "            error(\"Graph contains a negative-weight cycle\")\n",
+    "        end\n",
+    "    end\n",
+    "\n",
+    "    return d, p\n",
+    "end\n",
+    "bellmanFord(g, 1)"
+   ]
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Julia 1.6.4",
+   "display_name": "Julia 1.7.0",
    "language": "julia",
-   "name": "julia-1.6"
+   "name": "julia-1.7"
   },
   "language_info": {
    "file_extension": ".jl",
    "mimetype": "application/julia",
    "name": "julia",
-   "version": "1.6.4"
+   "version": "1.7.0"
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   "orig_nbformat": 4
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