{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# TP 4 : Programmation dynamique"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"readKnapInstance"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\"\"\"Open and read a KnapFile.\n",
"\n",
"Args: \\\\\n",
" - filename (String): the name of the file to read.\n",
"\n",
"Returns: \\\\\n",
" - price (Vector{Integer}): prices of items to put in the KnapSack. \\\\\n",
" - weight (Vector{Integer}): weights of items to put in the KnapSack. \\\\\n",
" - capacity (Integer): the maximum capacity of the KnapSack.\n",
"\"\"\"\n",
"function readKnapInstance(filename)\n",
" price = []\n",
" weight = []\n",
" capacity = -1\n",
" open(filename) do f\n",
" for i = 1:3\n",
" tok = split(readline(f))\n",
" if (tok[1] == \"ListPrices=\")\n",
" for i = 2:(length(tok)-1)\n",
" push!(price, parse(Int64, tok[i]))\n",
" end\n",
" elseif (tok[1] == \"ListWeights=\")\n",
" for i = 2:(length(tok)-1)\n",
" push!(weight, parse(Int64, tok[i]))\n",
" end\n",
" elseif (tok[1] == \"Capacity=\")\n",
" capacity = parse(Int64, tok[2])\n",
" else\n",
" println(\"Unknown read :\", tok)\n",
" end\n",
" end\n",
" end\n",
" return price, weight, capacity\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"analyseDynamique (generic function with 1 method)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"function analyseDynamique(price, weight, i, j)\n",
" if i > 0\n",
" C1, sol1 = analyseDynamique(price, weight, i - 1, j)\n",
" if j - weight[i] >= 0\n",
" C2, sol2 = analyseDynamique(price, weight, i - 1, j - weight[i])\n",
" C2 += price[i]\n",
" if C1 >= C2\n",
" res = C1\n",
" sol = push!(sol1, 0)\n",
" else\n",
" res = C2\n",
" sol = push!(sol2, 1)\n",
" end\n",
" else\n",
" res = C1\n",
" sol = push!(sol1, 0)\n",
" end\n",
" else\n",
" res = 0\n",
" sol = Vector{Int8}()\n",
" end\n",
" \n",
" return res, sol\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"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(\"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": [
{
"data": {
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
],
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0.6926427062042235cy), (0.3845562161328376cx, -0.27520393020637507cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(0.04598844997483381cx, 0.8908951380516595cy), (0.3041860503910396cx, -0.26289319997381244cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(-0.07735325117145776cx, 0.9479072249973377cy), (-0.901074053997336cx, 0.5141494073519517cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(0.3041860503910396cx, -0.26289319997381244cy), (0.045988449974833784cx, 0.8908951380516595cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(0.23388272856129344cx, -0.43139752704863454cy), (-0.5780983017482865cx, -0.9406005348735184cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(-0.5780983017482865cx, -0.9406005348735184cy), (0.2338827285612934cx, -0.43139752704863454cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(-0.6972331325527618cx, -0.8908951377579393cy), (-0.9755842461688985cx, 0.35295177010722867cy)])], Symbol(\"\"))]), List([Compose.Property{Compose.LineWidthPrimitive}(Compose.LineWidthPrimitive[Compose.LineWidthPrimitive(1.3416407864998738mm)]), Compose.Property{Compose.FillPrimitive}(Compose.FillPrimitive[Compose.FillPrimitive(RGBA{Float64}(0.0,0.0,0.0,0.0))]), Compose.Property{Compose.StrokePrimitive}(Compose.StrokePrimitive[Compose.StrokePrimitive(RGBA{Float64}(0.8274509803921568,0.8274509803921568,0.8274509803921568,1.0))])]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\")), Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([]), List([Compose.Form{Compose.LinePrimitive}(Compose.LinePrimitive[Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(0.22993542917571522cx, 0.9901442038981201cy), (0.13087368362935287cx, 0.9764778009585108cy), (0.21554397780937445cx, 0.9232712103567009cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(0.40197465254261655cx, -0.17673262437041853cy), (0.3845562161328376cx, -0.27520393020637507cy), (0.46119564785337674cx, -0.21096688866839003cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(0.2502884354107841cx, -0.17866109742709843cy), (0.3041860503910396cx, -0.26289319997381244cy), (0.3170414337929225cx, -0.16372294678471044cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(-0.8338639299345193cx, 0.588195333799399cy), (-0.901074053997336cx, 0.5141494073519517cy), (-0.8019923078694982cx, 0.5276700428495417cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(0.09988606495508923cx, 0.8066630355049456cy), (0.045988449974833784cx, 0.8908951380516595cy), (0.03313306657295091cx, 0.7917248848625575cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(-0.5166591999010254cx, -0.8617003652653238cy), (-0.5780983017482865cx, -0.9406005348735184cy), (-0.4803171677616572cx, -0.9196517918017049cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(0.1724436267140323cx, -0.5102976966568291cy), (0.2338827285612934cx, -0.43139752704863454cy), (0.13610159457466414cx, -0.4523462701204481cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, 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]
},
"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)"
]
}
],
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}