Merge branch 'main' of https://github.com/cpge-itc/itc2

_toc.yml

@@ -38,7 +38,7 @@ parts:
     - td: 'Exercice : Chemin dans une matrice'
       file: algo/prog_dyn/td/matrice_prog_dyn.pdf
     - cor: algo/prog_dyn/tp/tp1/tp_prog_dyn.ipynb
-    - cor: algo/prog_dyn/tp/tp2/tp_sac_dos.ipynb
+    - tp: algo/prog_dyn/tp/tp2/tp_sac_dos.ipynb
     - cor: algo/prog_dyn/seam_carving/seam_carving.ipynb
 - caption: Apprentissage automatique
   chapters:
@@ -48,4 +48,4 @@ parts:
       file: apprentissage/cours/science_donnees/science_donnees.pdf
     - slides_ipynb: apprentissage/cours/knn/knn.ipynb
     - tp: apprentissage/cours/knn/exemple/knn_iris.ipynb
-root: intro
+root: intro

files/dl/algo/prog_dyn/cours/prog_dyn.ipynb

@@ -1 +1 @@
-{"cells": [{"cell_type": "markdown", "metadata": {}, "source": ["# Programmation dynamique\n\n<iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe>", "\n", "<iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe>\n", "<iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe>\n", "<iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe>\n", "<iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe>\n", "<iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe>\n", "<iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe>\n", "<iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe>\n", "<iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe><iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe>"]}, {"cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": ["def knapsack(c, w, v):\n", "    \"\"\" \n", "    Renvoie la valeur maximum que l'on peut mettre\n", "    dans un sac \u00e0 dos de capacit\u00e9 c.\n", "    Le i\u00e8me objet a pour poids w[i] et valeur v[i].\n", "    \"\"\"\n", "    n = len(w) # nombre d'objets\n", "    dp = [[0]*(n + 1) for i in range(c + 1)]\n", "    # dp[i][j] = valeur max dans un sac de capacit\u00e9 i\n", "    # o\u00f9 j est le nombre d'objets autoris\u00e9s\n", "    for i in range(1, c + 1):\n", "        for j in range(1, n + 1):\n", "            if w[j - 1] <= i:\n", "                x = v[j - 1] + dp[i - w[j - 1]][j - 1]\n", "                dp[i][j] = max(dp[i][j - 1], x)\n", "            else:\n", "                dp[i][j] = dp[i][j - 1]\n", "    return dp[c][n]"]}, {"cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [{"data": {"text/plain": ["19"]}, "execution_count": 6, "metadata": {}, "output_type": "execute_result"}], "source": ["w = [2, 2, 2, 3, 5, 6, 8]\n", "v = [1, 1, 1, 7, 10, 10, 18]\n", "knapsack(10, w, v)"]}, {"cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [{"data": {"text/plain": ["19"]}, "execution_count": 38, "metadata": {}, "output_type": "execute_result"}], "source": ["def knapsack2(c, w, v):\n", "    n = len(w)\n", "    dp = [0]*(c + 1)\n", "    for j in range(n):\n", "        dp_ = dp[:] # copie de dp\n", "        for i in range(c + 1):\n", "            if w[j] <= i:\n", "                dp[i] = max(dp_[i], v[j] + dp_[i - w[j]])\n", "    return dp[-1]\n", "\n", "knapsack2(10, w, v)"]}, {"cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [{"ename": "NameError", "evalue": "name 'w' is not defined", "output_type": "error", "traceback": ["\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)", "Cell \u001b[0;32mIn [2], line 13\u001b[0m\n\u001b[1;32m     10\u001b[0m         \u001b[39mreturn\u001b[39;00m dp[(i, j)]\n\u001b[1;32m     11\u001b[0m     \u001b[39mreturn\u001b[39;00m aux(c, \u001b[39mlen\u001b[39m(w))\n\u001b[0;32m---> 13\u001b[0m knapsack_memo(\u001b[39m10\u001b[39m, w, v)\n", "\u001b[0;31mNameError\u001b[0m: name 'w' is not defined"]}], "source": ["def knapsack_memo(c, w, v):\n", "    dp = {}\n", "    def aux(i, j):\n", "        if i == 0 or j == 0:\n", "            return 0\n", "        if (i, j) not in dp:\n", "            dp[(i, j)] = aux(i, j - 1)\n", "            if w[j - 1] <= i:\n", "                dp[(i, j)] = max(dp[(i, j)], v[j - 1] + aux(i - w[j - 1], j - 1))\n", "        return dp[(i, j)]\n", "    return aux(c, len(w))\n", "\n", "knapsack_memo(10, w, v)"]}, {"cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [{"ename": "NameError", "evalue": "name 'w' is not defined", "output_type": "error", "traceback": ["\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)", "Cell \u001b[0;32mIn [1], line 14\u001b[0m\n\u001b[1;32m     11\u001b[0m         \u001b[39mreturn\u001b[39;00m v\n\u001b[1;32m     12\u001b[0m     \u001b[39mreturn\u001b[39;00m aux(c, \u001b[39mlen\u001b[39m(w))\n\u001b[0;32m---> 14\u001b[0m knapsack_memo2(\u001b[39m10\u001b[39m, w, v)\n", "\u001b[0;31mNameError\u001b[0m: name 'w' is not defined"]}], "source": ["from functools import cache\n", "\n", "def knapsack_memo2(c, w, v):\n", "    @cache\n", "    def aux(i, j):\n", "        if i == 0 or j == 0:\n", "            return 0\n", "        v = aux(i, j - 1)\n", "        if w[j - 1] <= i:\n", "            v = max(v, v[j - 1] + aux(i - w[j - 1], j - 1))\n", "        return v\n", "    return aux(c, len(w))\n", "\n", "knapsack_memo2(10, w, v)"]}, {"cell_type": "markdown", "metadata": {}, "source": ["## Plus courts chemins\n", "\n", "$$M = \n", "\\begin{pmatrix}\n", "0 & 3 & 8 & \\infty & -4\\\\\n", "\\infty & 0 & \\infty & 1 & 7\\\\\n", "\\infty & 4 & 0 & \\infty & \\infty\\\\\n", "2 & \\infty & -5 & 0 & \\infty\\\\\n", "\\infty & \\infty & \\infty & 6 & 0\\\\\n", "\\end{pmatrix} \n", "$$"]}, {"cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [{"data": {"text/plain": ["[[0, 3, 8, inf, -4],\n", " [inf, 0, inf, 1, 7],\n", " [inf, 4, 0, inf, inf],\n", " [2, inf, -5, 0, inf],\n", " [inf, inf, inf, 6, 0]]"]}, "execution_count": 8, "metadata": {}, "output_type": "execute_result"}], "source": ["g = [\n", "    [0, 3, 8, float(\"inf\"), -4],\n", "    [float(\"inf\"), 0, float(\"inf\"), 1, 7],\n", "    [float(\"inf\"), 4, 0, float(\"inf\"), float(\"inf\")],\n", "    [2, float(\"inf\"), -5, 0, float(\"inf\")],\n", "    [float(\"inf\"), float(\"inf\"), float(\"inf\"), 6, 0]\n", "]\n", "\n", "g"]}, {"cell_type": "markdown", "metadata": {}, "source": ["\n", "### Bellman-Ford"]}, {"cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": ["def bellman(g, r):\n", "    n = len(g)\n", "    dist = [float(\"inf\") for i in range(n)]\n", "    dist[r] = 0\n", "    for k in range(n - 2):\n", "        for u in range(n):\n", "            for v in range(len(g[u])):\n", "                if g[u][v] != 0:\n", "                    dist[v] = min(dist[v], dist[u] + g[u][v])\n", "    return dist"]}, {"cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [{"data": {"text/plain": ["[0, 1, -3, 2, -4]"]}, "execution_count": 10, "metadata": {}, "output_type": "execute_result"}], "source": ["bellman(g, 0)"]}, {"cell_type": "markdown", "metadata": {}, "source": ["### Floyd-Warshall"]}, {"cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [{"data": {"text/plain": ["[[0, 1, -3, 2, -4],\n", " [3, 0, -4, 1, -1],\n", " [7, 4, 0, 5, 3],\n", " [2, -1, -5, 0, -2],\n", " [8, 5, 1, 6, 0]]"]}, "execution_count": 12, "metadata": {}, "output_type": "execute_result"}], "source": ["import copy\n", "\n", "def floydwarshall(g):\n", "    n = len(g)\n", "    dist = copy.deepcopy(g)\n", "    for k in range(n):\n", "        for u in range(n):\n", "            for v in range(n):\n", "                dist[u][v] = min(dist[u][v], dist[u][k] + dist[k][v])\n", "    return dist\n", "\n", "floydwarshall(g)"]}], "metadata": {"kernelspec": {"display_name": "Python 3.10.6 64-bit", "language": "python", "name": "python3"}, "language_info": {"codemirror_mode": {"name": "ipython", "version": 3}, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.6"}, "vscode": {"interpreter": {"hash": "916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1"}}}, "nbformat": 4, "nbformat_minor": 2}
+{"cells": [{"cell_type": "markdown", "metadata": {}, "source": ["# Programmation dynamique\n\n<iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe>", "\n", "<iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe>\n", "<iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe>\n", "<iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe>\n", "<iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe>\n", "<iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe>\n", "<iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe>\n", "<iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe>\n", "<iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe>\n", "<iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe>\n", "<iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe><iframe src=https://mozilla.github.io/pdf.js/web/viewer.html?file=https://raw.githubusercontent.com/fortierq/cours/main/algo/prog_dyn/cours/prog_dyn.pdf#zoom=page-fit&pagemode=none height=500 width=100% allowfullscreen></iframe>"]}, {"cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": ["def knapsack(c, w, v):\n", "    \"\"\" \n", "    Renvoie la valeur maximum que l'on peut mettre\n", "    dans un sac \u00e0 dos de capacit\u00e9 c.\n", "    Le i\u00e8me objet a pour poids w[i] et valeur v[i].\n", "    \"\"\"\n", "    n = len(w) # nombre d'objets\n", "    dp = [[0]*(n + 1) for i in range(c + 1)]\n", "    # dp[i][j] = valeur max dans un sac de capacit\u00e9 i\n", "    # o\u00f9 j est le nombre d'objets autoris\u00e9s\n", "    for i in range(1, c + 1):\n", "        for j in range(1, n + 1):\n", "            if w[j - 1] <= i:\n", "                x = v[j - 1] + dp[i - w[j - 1]][j - 1]\n", "                dp[i][j] = max(dp[i][j - 1], x)\n", "            else:\n", "                dp[i][j] = dp[i][j - 1]\n", "    return dp[c][n]"]}, {"cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [{"data": {"text/plain": ["19"]}, "execution_count": 6, "metadata": {}, "output_type": "execute_result"}], "source": ["w = [2, 2, 2, 3, 5, 6, 8]\n", "v = [1, 1, 1, 7, 10, 10, 18]\n", "knapsack(10, w, v)"]}, {"cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [{"data": {"text/plain": ["19"]}, "execution_count": 38, "metadata": {}, "output_type": "execute_result"}], "source": ["def knapsack2(c, w, v):\n", "    n = len(w)\n", "    dp = [0]*(c + 1)\n", "    for j in range(n):\n", "        dp_ = dp[:] # copie de dp\n", "        for i in range(c + 1):\n", "            if w[j] <= i:\n", "                dp[i] = max(dp_[i], v[j] + dp_[i - w[j]])\n", "    return dp[-1]\n", "\n", "knapsack2(10, w, v)"]}, {"cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [{"ename": "NameError", "evalue": "name 'w' is not defined", "output_type": "error", "traceback": ["\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)", "Cell \u001b[0;32mIn [2], line 13\u001b[0m\n\u001b[1;32m     10\u001b[0m         \u001b[39mreturn\u001b[39;00m dp[(i, j)]\n\u001b[1;32m     11\u001b[0m     \u001b[39mreturn\u001b[39;00m aux(c, \u001b[39mlen\u001b[39m(w))\n\u001b[0;32m---> 13\u001b[0m knapsack_memo(\u001b[39m10\u001b[39m, w, v)\n", "\u001b[0;31mNameError\u001b[0m: name 'w' is not defined"]}], "source": ["def knapsack_memo(c, w, v):\n", "    dp = {}\n", "    def aux(i, j):\n", "        if i == 0 or j == 0:\n", "            return 0\n", "        if (i, j) not in dp:\n", "            dp[(i, j)] = aux(i, j - 1)\n", "            if w[j - 1] <= i:\n", "                dp[(i, j)] = max(dp[(i, j)], v[j - 1] + aux(i - w[j - 1], j - 1))\n", "        return dp[(i, j)]\n", "    return aux(c, len(w))\n", "\n", "knapsack_memo(10, w, v)"]}, {"cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [{"ename": "NameError", "evalue": "name 'w' is not defined", "output_type": "error", "traceback": ["\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)", "Cell \u001b[0;32mIn [1], line 14\u001b[0m\n\u001b[1;32m     11\u001b[0m         \u001b[39mreturn\u001b[39;00m v\n\u001b[1;32m     12\u001b[0m     \u001b[39mreturn\u001b[39;00m aux(c, \u001b[39mlen\u001b[39m(w))\n\u001b[0;32m---> 14\u001b[0m knapsack_memo2(\u001b[39m10\u001b[39m, w, v)\n", "\u001b[0;31mNameError\u001b[0m: name 'w' is not defined"]}], "source": ["from functools import cache\n", "\n", "def knapsack_memo2(c, w, v):\n", "    @cache\n", "    def aux(i, j):\n", "        if i == 0 or j == 0:\n", "            return 0\n", "        v = aux(i, j - 1)\n", "        if w[j - 1] <= i:\n", "            v = max(v, v[j - 1] + aux(i - w[j - 1], j - 1))\n", "        return v\n", "    return aux(c, len(w))\n", "\n", "knapsack_memo2(10, w, v)"]}, {"cell_type": "markdown", "metadata": {}, "source": ["## Plus courts chemins\n", "\n", "$$M = \n", "\\begin{pmatrix}\n", "0 & 3 & 8 & \\infty & -4\\\\\n", "\\infty & 0 & \\infty & 1 & 7\\\\\n", "\\infty & 4 & 0 & \\infty & \\infty\\\\\n", "2 & \\infty & -5 & 0 & \\infty\\\\\n", "\\infty & \\infty & \\infty & 6 & 0\\\\\n", "\\end{pmatrix} \n", "$$"]}, {"cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [{"data": {"text/plain": ["[[0, 3, 8, inf, -4],\n", " [inf, 0, inf, 1, 7],\n", " [inf, 4, 0, inf, inf],\n", " [2, inf, -5, 0, inf],\n", " [inf, inf, inf, 6, 0]]"]}, "execution_count": 8, "metadata": {}, "output_type": "execute_result"}], "source": ["g = [\n", "    [0, 3, 8, float(\"inf\"), -4],\n", "    [float(\"inf\"), 0, float(\"inf\"), 1, 7],\n", "    [float(\"inf\"), 4, 0, float(\"inf\"), float(\"inf\")],\n", "    [2, float(\"inf\"), -5, 0, float(\"inf\")],\n", "    [float(\"inf\"), float(\"inf\"), float(\"inf\"), 6, 0]\n", "]\n", "\n", "g"]}, {"cell_type": "markdown", "metadata": {}, "source": ["\n", "### Bellman-Ford"]}, {"cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": ["def bellman(g, r):\n", "    n = len(g)\n", "    dist = [float(\"inf\") for i in range(n)]\n", "    dist[r] = 0\n", "    for k in range(n - 2):\n", "        for u in range(n):\n", "            for v in range(len(g[u])):\n", "                if g[u][v] != 0:\n", "                    dist[v] = min(dist[v], dist[u] + g[u][v])\n", "    return dist"]}, {"cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [{"data": {"text/plain": ["[0, 1, -3, 2, -4]"]}, "execution_count": 10, "metadata": {}, "output_type": "execute_result"}], "source": ["bellman(g, 0)"]}, {"cell_type": "markdown", "metadata": {}, "source": ["### Floyd-Warshall"]}, {"cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [{"data": {"text/plain": ["[[0, 1, -3, 2, -4],\n", " [3, 0, -4, 1, -1],\n", " [7, 4, 0, 5, 3],\n", " [2, -1, -5, 0, -2],\n", " [8, 5, 1, 6, 0]]"]}, "execution_count": 12, "metadata": {}, "output_type": "execute_result"}], "source": ["import copy\n", "\n", "def floydwarshall(g):\n", "    n = len(g)\n", "    dist = copy.deepcopy(g)\n", "    for k in range(n):\n", "        for u in range(n):\n", "            for v in range(n):\n", "                dist[u][v] = min(dist[u][v], dist[u][k] + dist[k][v])\n", "    return dist\n", "\n", "floydwarshall(g)"]}], "metadata": {"kernelspec": {"display_name": "Python 3.10.6 64-bit", "language": "python", "name": "python3"}, "language_info": {"codemirror_mode": {"name": "ipython", "version": 3}, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.6"}, "vscode": {"interpreter": {"hash": "916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1"}}}, "nbformat": 4, "nbformat_minor": 2}