Quantitative Group Testing - zero/one vs n/2 choose random matrix

quantitative-group-testing-zero-one-vs-n-2-choose-random-matrix.ipynb

{
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  "metadata": {
    "colab": {
      "name": "Quantitative Group Testing - zero/one vs n/2 choose random matrix",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/amirc/0ff609ce900b0847ed003901cffbcf1d/quantitative-group-testing-zero-one-vs-n-2-choose-random-matrix.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ebaj_oyVPOYm",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1IvcdFARPTgQ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def gen_rand_vec(n, k):\n",
        "  v=np.zeros(n)\n",
        "  v[np.random.choice(n, size=k, replace=False)] = 1\n",
        "  return v"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X5Ns6IrvY65b",
        "colab_type": "text"
      },
      "source": [
        "# estimator 1"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EifzSB0_md2g",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def solve_with_zero_one(n, k, m, t_values=False):\n",
        "  if not t_values:\n",
        "    t_values = [k]\n",
        "\n",
        "  x = gen_rand_vec(n,k)\n",
        "  A = np.matrix(np.random.randint(2, size=(m, n)))\n",
        "  y=A.dot(x)\n",
        "  A_c = A.copy()\n",
        "  x_c = x.copy()\n",
        "  \n",
        "  A_rows_items_num = np.sum(A_c, axis=1)\n",
        "  A_rows_items_num_inv = 1. / A_rows_items_num\n",
        "  A_cols_sum = np.sum(A_c, axis=0).tolist()[0]\n",
        "  \n",
        "  # one shot\n",
        "  items_scores = list(map(\n",
        "    lambda i: y.dot(np.multiply(A_c[:,i], A_rows_items_num_inv)) / A_cols_sum[i],\n",
        "    range(A_c.shape[1])\n",
        "  ))\n",
        "  sorted_idx = np.argsort(np.array(items_scores).flatten())\n",
        "  ans = list()\n",
        "  for t_val in t_values: \n",
        "    ans.append(sum(x_c[sorted_idx[-t_val:]]) / min(t_val, k))\n",
        "  return ans"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cNV4fGxNF1Jn",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def solve_with_zero_one_2(n, k, m, t_values=False):\n",
        "  if not t_values:\n",
        "    t_values = [k]\n",
        "\n",
        "  x = gen_rand_vec(n,k)\n",
        "  A = np.matrix(np.random.randint(2, size=(m, n)))\n",
        "  y=A.dot(x)\n",
        "  A_w = np.ones(A.shape) - A\n",
        "  y_w = (np.ones(y.shape) * k) - y\n",
        "  A_c = np.concatenate((A, A_w))\n",
        "  y_c = np.concatenate((y, y_w), axis=1)\n",
        "  x_c = x.copy()\n",
        "  \n",
        "  A_rows_items_num = np.sum(A_c, axis=1)\n",
        "  A_rows_items_num_inv = 1. / A_rows_items_num\n",
        "  A_cols_sum = np.sum(A_c, axis=0).tolist()[0]\n",
        "  \n",
        "  # one shot\n",
        "  items_scores = list(map(\n",
        "    lambda i: y_c.dot(np.multiply(A_c[:,i], A_rows_items_num_inv)),\n",
        "    range(A_c.shape[1])\n",
        "  ))\n",
        "  sorted_idx = np.argsort(np.array(items_scores).flatten())\n",
        "  ans = list()\n",
        "  for t_val in t_values: \n",
        "    ans.append(sum(x_c[sorted_idx[-t_val:]]) / min(t_val, k))\n",
        "  return ans"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OFJ_0VZdnch5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def solve_with_choose(n, k, m, t_values=False):\n",
        "  if not t_values:\n",
        "    t_values = [k]\n",
        "\n",
        "  x = gen_rand_vec(n,k)\n",
        "  a=[np.random.choice(range(n), int(n/2)) for i in range(m)]\n",
        "  A = np.matrix([np.histogram(l, range(n+1))[0] for l in a])\n",
        "  y=A.dot(x)\n",
        "  A_c = A.copy()\n",
        "  x_c = x.copy()\n",
        "  \n",
        "  A_rows_items_num = np.sum(A_c, axis=1)\n",
        "  A_rows_items_num_inv = 1. / A_rows_items_num\n",
        "  A_cols_sum = np.sum(A_c, axis=0).tolist()[0]\n",
        "  \n",
        "  # one shot\n",
        "  items_scores = list(map(\n",
        "    lambda i: y.dot(np.multiply(A_c[:,i], A_rows_items_num_inv)) / A_cols_sum[i],\n",
        "    range(A_c.shape[1])\n",
        "  ))\n",
        "  sorted_idx = np.argsort(np.array(items_scores).flatten())\n",
        "  ans = list()\n",
        "  for t_val in t_values: \n",
        "    ans.append(sum(x_c[sorted_idx[-t_val:]]) / min(t_val, k))\n",
        "  return ans"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "outputId": "4855e5fa-673f-4535-9e00-77ba1cf5be20",
        "id": "npPjHar5KNGZ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 126
        }
      },
      "source": [
        "n = 2000\n",
        "theta = 0.5\n",
        "r = 100\n",
        "\n",
        "k = int(n**theta)\n",
        "print(n,k)\n",
        "\n",
        "c = np.log(k)\n",
        "m_base = int(k*(1-theta)/theta)\n",
        "r_20per = int(r/5)\n",
        "\n",
        "ans_01 = list()\n",
        "ans_01_2 = list()\n",
        "ans_c = list()\n",
        "print()\n",
        "for alpha in range(1,r):\n",
        "  if alpha % r_20per == 0:\n",
        "    print(alpha/r)\n",
        "    \n",
        "  m = int((1+3 * (alpha/r)) * c * m_base)\n",
        "  \n",
        "  tmp = list()\n",
        "  for i in range(4):\n",
        "    tmp.append(solve_with_zero_one(n, k, m, t_values=[m, k]))\n",
        "  ans_01.append(np.average(tmp, axis=0))\n",
        "\n",
        "  tmp = list()\n",
        "  for i in range(4):\n",
        "    tmp.append(solve_with_zero_one_2(n, k, m, t_values=[m, k]))\n",
        "  ans_01_2.append(np.average(tmp, axis=0))\n",
        "\n",
        "\n",
        "  tmp = list()\n",
        "  for i in range(4):\n",
        "    tmp.append(solve_with_choose(n, k, m, t_values=[m, k]))\n",
        "  ans_c.append(np.average(tmp, axis=0))"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "2000 44\n",
            "\n",
            "0.2\n",
            "0.4\n",
            "0.6\n",
            "0.8\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sFMukbRPE40S",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "h_01=np.array(ans_01)\n",
        "h_01_2=np.array(ans_01_2)\n",
        "h_c=np.array(ans_c)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fKFpqQT2E5f4",
        "colab_type": "code",
        "outputId": "0056d73b-df56-45c2-9acf-48273d724a44",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 521
        }
      },
      "source": [
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01[:,0], c='r', s=20)\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_c[:,0], s=20)\n",
        "plt.show()\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01[:,0], c='r', s=20)\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01_2[:,0], c='g', s=20)\n",
        "plt.show()"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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UbX57CIx4LSyVLDaKttS5tbSMLU71Hgwf8apyR5nHlN6RaKKWL0YpR1xwAju/fAfJp44z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\nRURiREFfRCRG/j+v680mHEhNRAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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eKL1Ti9IwItKmdKVfj9IwItKGFPSnEknDxKlwVd1GVbFEZKFR0I+h7/E+8ofy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\nAx1vLBXxj3vkAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "31udjlISzKoH",
        "outputId": "61e3c974-60b8-474a-be67-befc46f344b9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 521
        }
      },
      "source": [
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01[:,1], c='r', s=20)\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_c[:,1], s=20)\n",
        "plt.show()\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01[:,1], c='r', s=20)\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01_2[:,1], c='g', s=20)\n",
        "plt.show()"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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GkCWANZYhMjZaaCWw6vrbYUUUsnaGOzpyiP7Nd7Pho1/Aao+QEaH/2jM4smePr0VCRfdz\n80Z7gdLQVjstMz4On/xkIf8eXbeO/mvPmJhczd1//p7ruow/9+ehbFWrZUTkOuAqY8yf5h7/X8D5\nxpj1jnP+79x7fV1ELgAeAn7LGOO5LbhWy6hWUJfFMxUWGLm9fziT4sHH/pbT33ljojkWlFWUJI9b\nQvzp54itXEq0I+zaRKx0kZDr/YQCbPlwgOgnf69qBU8rlCBOt3ouYtoHLHc8juWOOfUC3wMwxjwH\nRIDF/i5VqebllXOOHxjxeEWJKhtMuL1/23iWRSHsgT2fe3bJS0fvvYu1H1pZFEVXXCTkdT/BAHFr\nQcX8e7QjzNrlx+jAPoP8pGW2AqtFZCX2oH498Icl5/w78LvA34vIB7EH98rL5pRqAVOqinFWo+Qj\n4t5eO7eci+Bd33/+AmJ//y049eTiSN9HXtpzkVC1+1nTpRUrc0zVyN0YMwasBx4HdmJXxbwiIl8V\nkZ7caX8O3CQig8AjwKfMbK2OUmoOcauK+fJ/PI34gZGylgNlrQh8VKMU3j8UYEFIiIQC9F93BtEL\nz3cdvJPtCxk8YTXJ9oWey/WjK5ay9iO/45oL97yfwDyS336Y5HFLGDzlTJLHLdGKlVmmK1SVmgH5\nnPMv9x3k9h+/Wja56jrpuqzN38rLRx4huf424sctJfbefqL33uXeisCrU+MkdnVyu5+RzBiCEAlg\nL1a6roZ2Cso3vzl3HdyVmiFek6s/Wn8h19z7rPuk6w9/UN7m1zkI+1x6X7VTo4/l+qWTom7v6dSo\nXRfnOm0/oNQc49VyYPve971bEVTLk/tceu/62blOjdGRQ1WX67v9ZrEiOr/sPZ2avV/6XKctf5Wa\nIV6TkWcuP6b8eHac2J7XCouBXNvxgu+l9347NbpJDqeL2hrk2xXMbwuWvWfpvfmaOFbTQgd3pWaI\nV8uBVUsWFB8XQ/8Pv070mo+4lj8W8bn0vuyzxdD/xP1ELaou1/dsITCaLXrPUACsoLRMv/S5TnPu\nSs0wrwU9yeE08Tf3E7vkAhgZKd7TtFr7Wp87NJXta+rzNZUWYjnfE9DFStNMc+5KzVFeLQeiHWGi\nqXcZWHlmcavdpx6kp1r7Wp9L74s+u8P/ayq2ECi5Hx3U5wYd3JWaCV6Rdcnx5PHL6Lv4ZlJWmJRl\nn7Lh0pvpPn4Z0Zm/6oJW28WoGWjOXanp5tVCwOV4PDAPK1yl1e4s0RYCjUUHd6XqqXTVp9eGFjt3\nuh6PjR8lEyxpx+totetU8+baqqXo4K5UvbhF6F4tBH7xC9fj0Xf2+drEY2D7PrrveJIbNr5A9x1P\nsml7aS8/1eo0565UPXg1+XrxRfc69PPO86xP7+nsrJjfdtad5xcQbXhsB92rFmvKRBVo5K6URwOt\nml6/eTOEQsWNuSwLhofd69A/+MGK9enO/HZp+mXKbYRVS9DIXbW2Rx6xI+y2tkk10Cq8PhRiIHYW\nfVd/fqKE8Yn76enqsleXurUQ8NGC123Zf/eqxZNvI6xahi5iUi2jbPGQz6ZbrhIJePll+PjHSWLx\nyvEnc9O1Xybt3MUIw4M3nsfpSxf5S5eUlkVWWDy0Zfe7ZXXn2oGxNegiJqUcXFvqZvb7arpVJh+t\nBwIMdJ1L39WfJzBuSIeKJ0jTCJ/9zkuMG1N98HX5DSJ+4dWeDcW07lxVozl31bC8SgFLj3s1vkoe\nv6xq062i90ok4Kc/hd5eklg8s3g1G66+lZQV4Wi4HUTKrvHoaHbi8/LX6bNcMjZ+tCz9MprNcnBk\nlORwWuvOVUUauauG5BqJe2x64daa1goEiAfmEX3oofJ+6bmo3XVzi9efrxitgyEcCpIeKx6UC+1v\n8/3ZnTn+Vatcf4PIl0Xm0y8jmTHGDfzZ/35ZUzGqKo3cVcPxisR3v33Yd2vawgTkunV2jv2JJ+zv\nucnUss8wwobLb2F3+Bj6rv68Z7QeDgX4+ifOIBwKlH/e+FH3BU0dHd5lkWcuY0vfZdz3R2cTDATI\nZE3xbx+6gEl50MFdNRyvUsD8phelx0tb05YtDHLplx4/MIKVzRa/VzbL9hNPLTsOhnltQSJWgDuv\nW8s1a5dx59JhIpk0C9JHiWTS9J84TPSdfe4LmrzKJR1lkYvaLdqCWv6o/NO0jGo4NW16kYvQ1y4/\npmgCEmBw7/uek5Gx8aNk0qPgqH7JBIOc+dZrZe0BwqEA37rh7ImqmESCnr/4E7qxitv2ei1oqlQu\nWeWetfxRedHIXTUc35telETo+QnIZ3e/W3XpfvSdffQ//QCRTIoFqSNEMin6N9/NqvT79D9xPxEx\nhc+487q1XPSB4yf+kci1HIiOHGLtb349sY1dlQi90o5LXvesk6nKi9a5q4aV3LOf+K4hYmu6iK5Y\nOnHcYzOM/HOVNp4oyNXAJ53RtxmFgQE46yyS7Qu9yxCr1c/73FjD9Z4r3JtqDVrnrprbI48Q7e0l\n6rKy1GszDJjIpaeYmAi1stnyjZxz29dFe3uJHn0byMDDD8OVV9qfQYVNKfJb33lU4fjdWMNNpXtT\nykkjd9V4prCyNLlnP933PE/KkUuPZNJs+fyHi6L/os+aZJQ9pdcq5cFv5K45d9V4vNroDg1Vfalr\nLv2pB+xKFihfYOTIg9fcP71CDl2p6aZpGdV4urqqriyt9Nqenc/QvfO54kqWrq6KTcS8Fk0pNVdp\n5K7mJGeUXBYx53PajqqT5LcfZjBlVY+q87l0Mqw9mhvYH3rIfs5tgVEi4d2+QBcQqTlMI3c15zij\n5JHMGCJCJBQsjpgd7XIHRjro+9kQ1u4X/EXVbq12t271bCIWP2G1ZwMvndxUc5VG7mpOKY2Sx8bx\nXnLf2Unyg2fQ97Mh76jaayOO0nx4hVSPLiBSjcjX4C4iV4nIayKyW0S+6PL8XSKyPff1KxF5v/6X\nqlqBW2sBp9Il9xV3JXLb09SLS6onX76oC4hUI6qalhGRIHAfcAUQB7aKyCZjzKv5c4wxtznO/8/A\nWdNwraoFuEXJTqURs2dU7WzS5dzT9PLLvatXKuyMpP3TVaPxE7mfB+w2xrxhjBkFvgt8rML564AK\nIZJS3kqj5FAArKB4RszRjjD9J9bQpKtauWSVFgDaP101Cj8TqsuAvY7HceB8txNFZAWwEnhy6pem\nmlaVxT2lUTJQcal/zU26lGoB9Z5QvR541BhT2hMVABG5WUS2ici2xGR3mleNzWce3BklV4yYJ9uk\nS6kmV7X9gIhcAHzFGPOR3OMvARhjvuZy7svAnxlj/rXaB2v7gRY0lQ2pJ/ue2gJANZl6th/YCqwW\nkZUi0oYdnW9y+cA1wLHAc7VerGoRU2gbkOdnQRN33WW/ZyJBsn0hgyesJtm+cHLvr1SDqppzN8aM\nich64HEgCDxsjHlFRL4KbDPG5Af664HvmtnqRKbmvqm0DaBCCwBnlctLL8Ftt0FbW26v01ux2ixf\ni5u0xYBqJtoVUhWb7jRGvn+LsxVurn+L52cnEiRfe4Pun7xHaqxCH3ZHiibZvpDuWx4mZUUmzg8F\n2HLVcURPPbno/ZPDaV7Zf4ib/nFb0cbWrn3elZpl2hVS1a6WRT+T5bEhtedn547HP30L1pHDRW9V\ntoeoI+0TX7SkfA/UI4eJf/qWovcf2L6P7jue5LP/68Wigd31/ZVqIDq4K1si4dk4q+rr3Jb3V1La\nRvff3iS5/jaSWAy2H08Sy/7snTsL1xTb9zqZQPHepWUtABxpn9jBt8v2Os0EgsT2vV64t+Se/YVW\nB0cz5QVe2mJANTId3JVtMpOdU4z081HzDf+0k/M//S0+/Ll/4IY/+Fu6b3mYTWsugl/8onBN0ZFD\n9G++216sFBL3FgCOydWoxcRepyGxFzdtvtsulczdW3zXkGurg3ltQW0xoBqe5tyVrdYyxSmWNbrt\nZeoUyaTZcsMHiHafV/QZyeOWEH/6OWIrl3oPvI7cfbJ9IfE39xO75AKi771ddK3Jnbvp3jhYdA3h\nkPDgH5/D6UsX6cCu5iTNuavaVGic5WqKZY1VG4SF24gvjpVdU/Teu1j7oZWVB15H2ifaEbbPv/eu\nsnuLrlha1hDszuvWctEHjteBXTU8jdxVMb/VMtMduTsrVepVwePxPsnhtDYEUw3Db+Sum3WoYp2d\n/gbQfKRfWtboc/DNNwjbUGFTjsJA6/ea/FyzR0MwHdRVs9HIXU1Jcs9+4ruGiK3pIrpiadFjotGq\nzb+cUXPROSOHtG2AUi40clfTrmhF57ODfHLh83zvN2CNZxn52TuIFSLSZnlvlUd51BztCFfcqFop\n5Y9G7mpSXHPmxoBI1ddWXPk5Hc3FlGoiWi2jplW1apdKKq78rFaFM5lFU0q1IB3c1aRU2w6vkoor\nPys1F5uJ9ghKNQkd3NWkuG0a/ceLRwvb3YXGMlhiqm+VVxqJe9Xbw+TaIyjVonRCVU2a26bRt9ZS\nLeM1ceq2UfXWrfZ5zlx8Pl2juXilyuiEqpodM9zuQKlmoROqam6rtX1Bre0RlGpxmpZRtaulRYHX\neZPZlcktXaOUcqWRu6qN34qVaudNNhJ3NAVTSnnTnLvyJblnP/GtO4h95lNlrXPL8t615Mene1s/\npZqM5txV3Qx88/t03/M8N2w5RPen7mPTmv8w8aRbnryWfLpG4kpNCx3cW1RyOM3g3vdJDqcrrvpM\n7tlP3+tBUlaYw+H5pKwIGz56K8n2hfYJbnnyKvn0os9WSk0LnVBtQUUNv0Yz9G/+Bj17trk26Yrv\nGsIaz5JyvN7KZomf0EX0N792z5NXaAdc9NklTcSUUvWjOfcW49bwK5JJseX+G+02uyW58eSe/XTf\n8zwpK+w4P82WS+cTPf/smqplXD+7UhMxpVQZzbkrV24Nv6xslviiJbkHxbnx6Iql9J+SLbQViGTS\nfLkrS3zt+ROpGS8l+XTXz67UREwpNWmalmkxbg2/MsEgsYO5ChiXHHrP5z5Bd66twC8DC7n9mb1Y\nG1+oOa3i+tmVmogppSZNI/cWU2j4FQqwICREZJz+J+4nagHt7SS//TCDKatssjO6Yimx7t/m9mf2\nksqMczg9RiozzobHdvieGHVrNlbUREwpVTcaubegnp3P0H3/bcSPW0rsvf1E/5+/gbO/xsBIB30/\nG8La7R6V59MqKSai73xaxe8A7dZsTClVfzq4t5pEAnp7iY6MTCxGuu02kjt307dxkFRmvDB4b3h0\nB93DcaKnngydnVNLqzgmV6OdnTqoKzXNNC3TajwWGMV3DZVPdh45TPzTtxTaB0w6raKbbCg143xF\n7iJyFXA3EAQ2GmP+u8s5nwS+Ahhg0Bjzh3W8TlWNIzJOti/0Tnu4LDBKhto5eFwno9mDRcczgSCx\nfa9PbIxx+eW1p1VyvykwMjLRjiD3XroqVanpU3VwF5EgcB9wBRAHtorIJmPMq45zVgNfArqNMQdE\n5PjpumDlwrHpxUDXufRdfStWm+VezVKywGhg5Xn2+T96g+z4OFZQiAhkRlL0b77brn2Hoo0xoh1h\n/2mV/G8KusmGUjPKT+R+HrDbGPMGgIh8F/gY8KrjnJuA+4wxBwCMMe/U+0KVB0dknMSi73c/S8oI\nqfQYABse20H3qsXFg3GudW7ytTfo+8l7pMbGC+eHQ3Dfx1Zz+lX/AUZGGDxhNbGDbxOt1o7Xy2Ra\n+yqlpszP4L4M2Ot4HAfOLznnAwAisgU7dfMVY8xP6nKFqjJHZBxftAQrmyVlTTztWc3S2Uk8ZWEF\nXyA1NjFJ2hYMsuiETp69/f+l7/Ug1niWTCBI/ylZeiYTaVdoRaCUmj71qpYJAauBS4AY8IyIfMgY\n877zJBG5GbgZ4KSTTqrTR7c4R2QcO/g2mWCw6OlK1Sxe1S/z24L0vdVByhov9JTZ8FaA7uH05Kpc\ndJMNpWacn2qZfcByx+NY7phTHNhkjMkYY94EfoU92BcxxjxgjDnHGHNOp/4PXh+OTS+iFvQ/cT8R\nMb6qWbyqX46MZuvfJkBb+yo1o/xE7luB1SKyEntQvx4orYT5Z2Ad8D9FZDF2muaNel6oqsARGfd0\nddFdqVqmhFv1S3I4rW0ClGpwVQd3Y8yYiKwHHsfOpz9sjHlFRL4KbDPGbMo9d6WIvApkgb80xiSn\n88JVic7OQlQchZrSJ6XVL/mIfkNJa15deKRU49CWv8pTcjitbQKUmmP8tvzV9gPKU0317EqpOUXb\nDyilVBPSwX2a6D6hSqnZpGmL3B3JAAARjklEQVSZaaD7hCqlZptG7nWWHE7T99iOSW9oUVUiAVu3\n2t9n8rVKqYaig3udTes+oVNpnattd5VqKTq419m07ROaaxCWxGKw/XiSWCTX38bgv71Z/luBI0JP\nDqftc9bfZndmPHhwooWvRvBKNS3NudfZtC0AGhpi4LSL6Lv4JqxslpGQhYgQ+aedZGTXRF7frf1v\nMEDmU9+kf/M36Nn1L/b7adtdpZqaLmKaJvVeAJTcs5/ue54nZbm/V8QKsOVP1xL94Cq7/W/7Qrpv\neZiUFZk4J5Niy/032j3a29thzx4d3JVqMH4XMWlaZppEO8KsXX5M5YG9hgnOeGAeVrjN83krECC+\na6iwhV6+/W/ROeNZ4ktPtgd2bburVFPTwX221DjBGTu2vaydr1NmNENsTVfl9r/zFxD7+2/ZEfu6\ndVO+BaXU3KWD+2xw7ivqZ4IzkSC6cwf9V3bZ7XnbgoTGMlhjGRakjhDJpOjf/A2i8yyX9r/jLAgJ\nkVCAL19zGvEVp5JsXziz96uUmnE6oTobatlX1DFB2jM6Sve3HyZ+/EnE/uQmOHSI+KIl9jZ4Vu59\nne1/X3qJ7v9yE/HjlvLLY2Pcnr3Ze29VpVRT0cG9nhIJf7sN+d1X1Bnh5/4hiH7mRqIvvgiHkjAy\nUtjAOtm+hHhkMbHhNNH8Z198MdHca/+g56+q762qlGoampapl1py6I7dk1i40HuCMx/hO1kWDA8X\nvX5g7eV037yRGx79Fd13PMmm7fuKXus6uVqvhVVKqTlJSyHrIZGwB3RnmsVZaugV0VeL9H28b/K1\nN+j+yXtFm1z7Kou0Amzpu0wjd6UajJZCziSvCHtoqHJEX21f0WoRfmcn8RWnYgVd2h0E5k16b1Wl\nVOPTnHs9eOXQOzrKcub09toTni4DuuvCp3XrSP7OxcR3DRFb00V0xdKi11RsdzCFvVWVUo1NB/d6\nyEfYvb12xJ7J2I+Hh31XxXi1CS46/uwg/deaoiqXqu0OprC3qlKqcWnOfRI8WwuU5tBzOfMk1kTJ\nIpmyZf/J4TTddzxJKlOcN//R+gu55t5ny4675cp1v1OlWoPuoTpNKm7E4YiS848H/u4f6Hs9iDWe\nJRMI0n9Klp6SqD3fJjjFxCBuBQJs3/u+6/H4gZGyAVz3O1VKOemEag1q3YgjOZym760OUlaYw+F5\npKwwG97qKDvfK29+5vJjpqd9sFKq6engXoNaN+JwOz8owlO73ika4PN584gVmKhmubKLVf++a6Ll\ngFa5KKVqoGmZGtS6EYfb+UdGs3zlh6/wXwd+WZTS6TlzGd2rFtt586d/QvQjv13ccuCSqzSfrpTy\nTSP3GrhG2BUiaef589smOjQOp7OuKZ1oR5i1kQzRz9xY1FQs+pkb7eM6sCulfNLIvUZFEbaPSDp/\n/lO73uErPxhkeFwKz1nZbPnkaC1NxZRSyoNG7n45NtZwbsSRHE4zuPd9z0lVsCPySzuDjKWLFzpl\n0qPExo8Wn5xbEJVsX8jgCavt9rxuTcWUUqoCjdz9cLTdZXTUXqC0bl3lssgS0Xf20f/0A2y4xN4D\nNRMM0v/Ug0SvXw7OVac+yyeVUqoSXcRUjUfzruTO3XRvHCxaYBQOCQ/+8TmcvnRRebpmiguatMmX\nUgq0cVj9eDQFi+8aKitzTI8ZPvudlyba7jrlWhREybD2aG5gd2nzW2u5pVJKufE1uIvIVSLymojs\nFpEvujz/KRFJiMj23Nef1v9SZ0EiAQcOuDYFi63pKitzBDg6mquEeXQHyWdfKN46b906O1J/4gn3\nfUwTCWJ7XiOT1YVLSqmpqTq4i0gQuA+4GjgNWCcip7mc+k/GmDNzXxvrfJ0zL9+q95OfhLExO3p3\ntN2NrlhaKHOcZ5VvXG0dOUz807f4b/Ob+7zoNR+h/4df1/a8SqkpqZpzF5ELgK8YYz6Se/wlAGPM\n1xznfAo4xxiz3u8Hz+mcu1uePRKBgQE466yyHPkr+w9x0z9uI+3cMCOTYsv9N9rb4Dk32PD5ecnj\nlhB/+jliK5fqwK6UKqhnzn0ZsNfxOJ47VupaEdkhIo+KyHKPi7pZRLaJyLaEM10xlyQSsHkzhIoL\niZILowyaDrs00SHaEeaiD3Ry53W5xU0hIZJJ07/57sL+poU69RKFMsrX3ijL60fHRlibelcHdqXU\npNSrFPKHwCPGmLSIfAb4B+Cy0pOMMQ8AD4Adudfps+snX/IYCsHhw4XDAx+8iL6rb8XacojMs0+6\nljwWFje9uZ/YJRcQfe/tiSdd6tSLyiiz4/SvOIeeHT+v+BqllPLLT+S+D3BG4rHcsQJjTNIYk1/F\nsxH47fpc3gxKJCZ2TXIM7MnOpfRdfavd2XHUvW1AXrQjzNoPrSR6710VN78u6y45Ns6Gj36B5HFL\nKm+YrZRSPvmJ3LcCq0VkJfagfj3wh84TROREY8xbuYc9wM66XuVMcFv239FB/Kv9WPvnkRrNFg57\n9VQvcGxv57b5tWv/9jaL+NPPEU29671htlJK+VR1cDfGjInIeuBxIAg8bIx5RUS+CmwzxmwCPi8i\nPcAY8B7wqWm85unhtg9qNkvs6kvJbBwsOpzJjhPb8xpETq68ubXHc57dJVcuhY6Vk70DpZQq8FXn\nbozZbIz5gDHmFGPMf8sd++vcwI4x5kvGmNONMWuNMZcaY3ZN50VPi/w+qCXpFGfJ44JwiIgY+n/4\ndaLXfKS8zNGnWrtLKqVUrVq3/UDpfqc5yT37ie8aIrami6ij50tyOO0+WVqtzLEC3fdUKVUrbT9Q\nSX6B0hVXFEXfA9v30b1xkBv+9TDdGweLWghEO8J2aWI2VfxeHmWOfji7SyqlVD21XldIZ1VMfvL0\nxhtJLjiOvufHSY2NFyY6Nzy2g+5ViycGX7e8vJYsKqXmoNaL3N0agaVSxD+/AevI4aLDZQ27PPLy\nWtmilJprWi9yd4u+gdhvhsgEinvEuDbsqlLmqJRSc0HrRe7O6Hv+/MLh6Mgh+jffTSSTtlsIVKpg\n8Wr+pZRSc0RrV8u8/DJ8/OPasEsp1TC0WsZF0X6nnZ1w5ZVlOfTovXfZLQR0YFdKNbCWybl77neq\nOXSlVBNqici9rFFXSfOvZPtCBk9YXdbO15dEArZuLd5xSSmlZllLRO6ujbpyZY7P7n7XPaL3I98i\nuK3NrsB56KHyrfOUUmoWNE/kXiGC9mrUNb8tWDGir/p5+cVQBw/a33t7NYJXSs0JzTG4e7QTyPNq\n1HVkNIsVKP4jKFu45MVtMdQUWhEopVQ9NX5axq2dQG+vPUnqmBwt7JTkaNSVHE67t94tXbjkRlsR\nKKXmsMaP3GuIoEsbdU2p9a62IlBKzWGNG7nnW/Z2dFSMoKu11XWL6POqtuTVMkql1BzVmIN7aZVK\nb68dNVuWPbDnImjP2vYS0Y5w2eDt97WVdlxSSqnZ0njtBxIJe9LUuddpezu8+CIMDxci6ORwmu47\nniSVmcipR0IBtlx1HNFTK2yPB+6vtQJs6btMV64qpWZV87Yf8MqxDw8XNfPK17YXnXbkMPFP31J1\nezzX1/qtolFKqTmg8QZ3n1UqrrXtgSCxfa9XrUn33MDaTxWNUkrNAY03uPusUimqhAkJkUya/s13\nEx05ZJ9QoSZdN7BWSjW6xsu553lscF1qKhtb6wbWSqm5xm/OvTGrZcB3lUq0I0z0Qyvh3rvsVExJ\nRU3V1+qgrpRqQI07uNdKa9KVUi2k+Qf30vSNDupKqRbQeBOqtajSUEwppZpVcw7uiQT89Kfaklcp\n1bKab3DPR+u///vFq1hBW/IqpVpGcw3uufa/SSwGFywt3zavpKFYYbNspZRqMr4mVEXkKuBuIAhs\nNMb8d4/zrgUeBc41xkyhiH2ShoYYOO0i+i6+CSubJRMM0r/5bnr2vgTj4zU3FFNKqUZVdRGTiASB\nXwFXAHFgK7DOGPNqyXkLgB8DbcD6aoP7lBcxuUju2U/3Pc+TsiZq0yOZNFsunU/0/LO9G4ppUzCl\nVIOoZ+Ow84Ddxpg3jDGjwHeBj7mcdztwB5Cq6UrrJDmc5qlEllC4uKmYFW4jvvb8yg3FtCmYUqrJ\n+EnLLAP2Oh7HgfOdJ4jI2cByY8yPReQv63h9vuTTLEERjoxL0XOZYLCo4Zc2BVNKtYIpT6iKSAD4\nH8Cf+zj3ZhHZJiLbElMsScxPiO5++zB9j+0glRnnyGi28Pz8cNC14Zc2BVNKtQI/kfs+YLnjcSx3\nLG8B8FvA0yICcAKwSUR6SvPuxpgHgAfAzrlP9qKdE6LpsSyBQHG0Pr8tyN/8p9O5dM3xNW+tp5RS\nzcDP4L4VWC0iK7EH9euBP8w/aYw5CCzOPxaRp4G/mK5qmeRwuhCpp8ilV7LF/05kjfEc2PO0KZhS\nqplVTcsYY8aA9cDjwE7ge8aYV0TkqyLSM90XWMptQjQcFNpCmmZRSqk8X3XuxpjNwOaSY3/tce4l\nU78sb24TohIQfrz+Qo6MZjXNopRSNOAKVa8J0VVLFrB2+TE6sCulFA3a8lcnRJVSqrKGHNxBJ0SV\nUqqShkvLKKWUqk4Hd6WUakI6uCulVBPSwV0ppZqQDu5KKdWEdHBXSqkmpIO7Uko1oao7MU3bB4sk\ngD2z8uHlFgPvzvZFzLBWvGdozfvWe24uK4wxndVOmrXBfS4RkW1+tq1qJq14z9Ca96333Jo0LaOU\nUk1IB3ellGpCOrjbHpjtC5gFrXjP0Jr3rffcgjTnrpRSTUgjd6WUakItMbiLyHIReUpEXhWRV0Tk\n1tzx40TkZyLy69z3Y3PHRUTuEZHdIrJDRM6e3TuonYhEROQXIjKYu+e/yR1fKSIv5O7tn0SkLXc8\nnHu8O/d812xe/1SISFBEXhaRH+UeN/U9i8iQiPybiGwXkW25Y037dxtARI4RkUdFZJeI7BSRC5r9\nnmvVEoM7MAb8uTHmNODDwJ+JyGnAF4GfG2NWAz/PPQa4Glid+7oZuH/mL3nK0sBlxpi1wJnAVSLy\nYeAO4C5jzCrgANCbO78XOJA7flfuvEZ1K/Z+v3mtcM+XGmPOdJT/NfPfbYC7gZ8YY9YAa7H/ezf7\nPdfGGNNyX8AAcAXwGnBi7tiJwGu5n78NrHOcXzivEb+AecBLwPnYCztCueMXAI/nfn4cuCD3cyh3\nnsz2tU/iXmPY/2NfBvwIkBa45yFgccmxpv27DSwC3iz9b9XM9zyZr1aJ3Atyv3qfBbwALDHGvJV7\n6jfAktzPy4C9jpfFc8caSi49sR14B/gZ8DrwvjFmLHeK874K95x7/iAQndkrrotvABuA/C7qUZr/\nng3wUxF5UURuzh1r5r/bK4EE8D9z6beNIjKf5r7nmrXU4C4iHcBjwBeMMYeczxn7n/SmKh0yxmSN\nMWdiR7PnAWtm+ZKmlYhcA7xjjHlxtq9lhl1ojDkbO/3wZyJykfPJJvy7HQLOBu43xpwFHGEiBQM0\n5T3XrGUGdxGxsAf2/22M+UHu8NsicmLu+ROxI1yAfcByx8tjuWMNyRjzPvAUdkriGBHJ753rvK/C\nPeeeXwQkZ/hSp6ob6BGRIeC72KmZu2nue8YYsy/3/R3g/2D/Q97Mf7fjQNwY80Lu8aPYg30z33PN\nWmJwFxEBHgJ2GmP+h+OpTcCf5H7+E+xcfP74H+dm2T8MHHT8utcQRKRTRI7J/dyOPcewE3uQvy53\nWuk95/8srgOezEU/DcMY8yVjTMwY0wVcj30Pf0QT37OIzBeRBfmfgSuBX9LEf7eNMb8B9orIqblD\nvwu8ShPf86TMdtJ/Jr6AC7F/RdsBbM99fRQ7v/pz4NfAE8BxufMFuA87R/1vwDmzfQ+TuOczgJdz\n9/xL4K9zx08GfgHsBr4PhHPHI7nHu3PPnzzb9zDF+78E+FGz33Pu3gZzX68Af5U73rR/t3P3cSaw\nLff3+5+BY5v9nmv90hWqSinVhFoiLaOUUq1GB3ellGpCOrgrpVQT0sFdKaWakA7uSinVhHRwV0qp\nJqSDu1JKNSEd3JVSqgn9/3SpCo2z4jjPAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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nTxCdLn0uMg3ZaA4sq6K2PZvaT3SstFLGO94usJWvl8/YPKXUwtLFvcUkr9pD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\n6eKulFIhpIu7UkqFkC7uSikVQv8fYWrXMnx6xWcAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "outputId": "95b4411d-cdd7-4fbb-928d-f8532490fdd6",
        "id": "GNe3O06y0oIW",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 126
        }
      },
      "source": [
        "n = 20000\n",
        "theta = 0.3\n",
        "r = 30\n",
        "\n",
        "k = int(n**theta)\n",
        "print(n,k)\n",
        "\n",
        "c = np.log(k)\n",
        "m_base = int(k*(1-theta)/theta)\n",
        "r_20per = int(r/5)\n",
        "\n",
        "ans_01 = list()\n",
        "ans_01_2 = list()\n",
        "ans_c = list()\n",
        "print()\n",
        "for alpha in range(1,r):\n",
        "  if alpha % r_20per == 0:\n",
        "    print(alpha/r)\n",
        "    \n",
        "  m = int((1+3 * (alpha/r)) * c * m_base)\n",
        "  \n",
        "  tmp = list()\n",
        "  for i in range(4):\n",
        "    tmp.append(solve_with_zero_one(n, k, m, t_values=[m, k]))\n",
        "  ans_01.append(np.average(tmp, axis=0))\n",
        "\n",
        "  tmp = list()\n",
        "  for i in range(4):\n",
        "    tmp.append(solve_with_zero_one_2(n, k, m, t_values=[m, k]))\n",
        "  ans_01_2.append(np.average(tmp, axis=0))\n",
        "\n",
        "\n",
        "  tmp = list()\n",
        "  for i in range(4):\n",
        "    tmp.append(solve_with_choose(n, k, m, t_values=[m, k]))\n",
        "  ans_c.append(np.average(tmp, axis=0))"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "20000 19\n",
            "\n",
            "0.2\n",
            "0.4\n",
            "0.6\n",
            "0.8\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "LUNNxKEh0oIk",
        "colab": {}
      },
      "source": [
        "h_01=np.array(ans_01)\n",
        "h_01_2=np.array(ans_01_2)\n",
        "h_c=np.array(ans_c)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "outputId": "45f63146-5de2-4fc9-8566-60c6493663ad",
        "id": "HTUGQjfKQUL8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 521
        }
      },
      "source": [
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01[:,0], c='r', s=20)\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_c[:,0], s=20)\n",
        "plt.show()\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01[:,0], c='r', s=20)\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01_2[:,0], c='g', s=20)\n",
        "plt.show()"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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mdiD+e8rMXmh8qSnr6YGTJ+ePlcvRuIhIztQMdzNbA9wKXA1cAuw2s0uq57j7n7r7Dnff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\nVlhiAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "outputId": "3feac48f-70dd-4ccf-8b59-c5088634feee",
        "id": "bDX-ltHMQUMB",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 521
        }
      },
      "source": [
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01[:,1], c='r', s=20)\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_c[:,1], s=20)\n",
        "plt.show()\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01[:,1], c='r', s=20)\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01_2[:,1], c='g', s=20)\n",
        "plt.show()"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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7mbUBrwG7gFHgBNDn7mfK1mwBngbudffLZvbD7v7mUvtVzT1lwrkuE+QZffetdE1+n04K\nC851qaWOrlq2SDzirLnfA5xz9zfCHR8G7gfOlK35D8Cj7n4ZoFJilxQK57p0Tk7SOf2DYNvq1QvO\ndamljq5atkh9RSnLbAAulr0eDbeV+1HgR83sBTN70cx2L7QjM9tnZsNmNjyuWd3pUsVcF9XRRdIv\nrg9UbwK2AB8G+oAvmtkt8xe5++PuvsPdd6zTlL90qWJGu+roIukXpSwzBmwse90Vbis3Crzk7gXg\nu2b2GkGyPxFLlFIffX2wc2ekGe292zfQc8da1dFFUipKcj8BbDGzzQRJfS/wsXlr/jfBGfvvm9la\ngjLNG3EGKnVSxYx21dFF0qtiWcbdrwD7gWPAK8DT7n7azB42s95w2TFgwszOAM8D/8XdJ5IKWkRE\nlqbxAyIiTSRqK6SuUBURySAld6mP8XE4cSJ4FJHEKblL8g4dgk2bYNeu4PHQoUZHJJJ5Su6SrPHx\n4J6o09MwORk89vfrDF4kYUrukqxwrMEc+XywXUQSo+QuyapirIGIxEfJXZJVxVgDEYmP7sQkyati\nrIGIxEPJXeqjirEGIrJ8Kss0M/WOi8gilNyblXrHRWQJSu7NSL3jIlKBknszUu+4iFSg5N6Maugd\nn5ia5dTFt5iYmk00NBFJB3XLNKNS73h/f3DGXigs2Tt+5OQYA0Mj5HM5CsUig3u20bt9/m1wRSRL\nlNybVcTe8YmpWQaGRpgpFJkhuKn1gaEReu5Yq7soiWSYknszi9A7Pnp5mnwudy2xA+RzOUYvTyu5\ni2SYau4Z17Wmg0KxOGdboVika01HgyISkXpQcs+4zpXtDO7Zxop8jlXtN7Ein2NwzzadtYtknMoy\nLaB3+wZ67ljL6OVputZ0KLGLtIBIZ+5mttvMXjWzc2b24ALvf8LMxs3sZPj1C/GHKsvRubKdD2y8\nRYldpEVUPHM3szbgUWAXMAqcMLOj7n5m3tKvuvv+BGIUEZEqRTlzvwc45+5vuPs7wGHg/mTDEhGR\n5YiS3DcAF8tej4bb5ttjZiNm9jUz2xhLdCIiUpO4umX+D9Dt7tuAbwBfXmiRme0zs2EzGx5vpSFX\nCY3m1UgBEVlMlOQ+BpSfiXeF265x9wl3L2WYJ4B/vtCO3P1xd9/h7jvWtcqNGxIazXvk5Bg9B4/z\nwBMv0XPwOEdPjlX+j0SkZURJ7ieALWa22cxuBvYCR8sXmNltZS97gVfiC7GJJTSat3ykwNuzV5gp\nFDkwNKIzeBG5pmJyd/crwH7gGEHSftrdT5vZw2bWGy77lJmdNrNTwKeATyQVcFNJaDRvaaTAnN2G\nIwVERCDiRUzu/izw7Lxtnyl7/hDwULyhZUANo3mj0EgBEalE4weSVBrN29EBq1cHj0uM5o1KIwVE\npBJz94Z84x07dvjw8HBDvnfdjY9XHM1bi4mpWY0UEGkxZvayu++otE6zZeohwmjeWnSubFdSF5EF\nqSwjIpJBSu4iIhmk5C4ikkFK7iIiGaTkvhwJzYxJRDPFKiLLpuReq4RmxiSimWIVkVioz70W4+NB\nkpwuu9y/owMuXEik5XFZmilWEakoap+7ztxrkdDMmEQ0U6wiEhsl91pUOTOmmrnrsc9oT2i+jYik\nm65QrUVpZkx/f3AWXCgsOjPmyMkxBoZGyOdyFIpFBvdso3f7Qjeyqm5tErGKSHao5r4cFWbGTEzN\n0nPwODOF6xMcV+RzvDBw7w1jA6pZm0SsItIcNFumHirMjCnNXZ/hesIuzV2fn7CrWZtErCKSLaq5\nJ6iaueua0S4icVJyT1A1c9c1o11E4qSaex1UM3ddM9pFZCmquadINXPXNaNdROKgskzaaAaMiMQg\nUnI3s91m9qqZnTOzB5dYt8fM3Mwq/skgC9AMGBGJScXkbmZtwKPAR4A7gT4zu3OBdauATwMvxR1k\nSxgfDy40mp6Gycngsb9fZ/AiUpMoZ+73AOfc/Q13fwc4DNy/wLr/BhwEZmKMr3VoBoyIxChKct8A\nXCx7PRpuu8bM7gI2uvv/jTG21qIZMCISo2V/oGpmOeBzwK9GWLvPzIbNbHhc5Ya5SjNgOjpg9erg\nUTNgRKRGUVohx4CNZa+7wm0lq4D3A39pZgDvBY6aWa+7z2lkd/fHgcch6HNfRtzZ1NcHO3dqBoyI\nLFuU5H4C2GJmmwmS+l7gY6U33X0SWFt6bWZ/Cfza/MTeNBo9YEszYEQkBhXLMu5+BdgPHANeAZ52\n99Nm9rCZ9SYdYF2pFVFEMkLjB0p0OzoRaQK6zV611IooIhmi5F6iVkQRyRAl9xK1IopIhmgqZDm1\nIopIRii5z6dWRBHJgNYoyyQ0RndiapZTF99iYmo21v2KiCxX9s/cDx0KpivefHPwgemTTwbll2U6\ncnKMgaER8rkchWKRwT3b6N2+ofJ/KCJSB9k+c09ojO7E1CwDQyPMFIq8PXuFmUKRA0MjOoMXkdTI\ndnJPqHd99PI0+dzcQ5fP5Ri9PL3IfyEiUl/ZTu4J9a53remgUCzO3W2xSNeajmXtV0QkLtlO7gn1\nrneubGdwzzZW5HOsar+JFfkcg3u26cbWIpIarTFbJqFJjxNTs4xenqZrTYcSu4jURdTZMtnvloHE\netc7V7YrqYtIKjVvWUa96yIii2rOM3f1rouILKn5ztzVuy4iUlHzJXf1rouIVNR8yV296yIiFTVf\nclfvuohIRc3b567edRFpQbHeQ9XMdpvZq2Z2zsweXOD9/2hm3zKzk2b212Z2Zy1BV2OiYzWn3ruF\niY7Vse63c2U7H9h4ixK7iDS1iq2QZtYGPArsAkaBE2Z21N3PlC37irt/IVzfC3wO2J1AvIBaFkVE\nKoly5n4PcM7d33D3d4DDwP3lC9z9B2Uv3wUkVutRy6KISGVRLmLaAFwsez0KfHD+IjP7JPArwM3A\nvbFEt4BSy+IM1ztbSi2LKqWIiARi65Zx90fd/XZgAPiNhdaY2T4zGzaz4fEaLzpSy6KISGVRkvsY\nsLHsdVe4bTGHgZ9e6A13f9zdd7j7jnU1drioZVFEpLIoZZkTwBYz20yQ1PcCHytfYGZb3P074cuf\nAr5Dgnq3b6DnjrVqWRQRWUTF5O7uV8xsP3AMaAOecvfTZvYwMOzuR4H9ZrYTKACXgY8nGTRo3K6I\nyFIiTYV092eBZ+dt+0zZ80/HHJeIiCxD840fEBGRipTcRUQySMldRCSDWiK569Z5ItJqmvM2e1XQ\nHBoRaUWZPnPXHBoRaVWZTu66dZ6ItKpMJ3fNoRGRVpXp5K45NCLSqjL/garm0IhIK8p8cgfNoRGR\n1pPpsoyISKtSchcRySAldxGRDFJyFxHJICV3EZEMUnIXEckgJXcRkQwyd2/MNzYbBy4k+C3WAv+Q\n4P7j0AwxQnPEqRjj0wxxtnKMm9x9XaVFDUvuSTOzYXff0eg4ltIMMUJzxKkY49MMcSrGylSWERHJ\nICV3EZEMynJyf7zRAUTQDDFCc8SpGOPTDHEqxgoyW3MXEWllWT5zFxFpWU2b3M3sKTN708y+Xbbt\ns2Y2ZmYnw6/7yt57yMzOmdmrZvav6xTjRjN73szOmNlpM/t0uP09ZvYNM/tO+Lgm3G5m9kgY54iZ\n3dXAGFNzLM1shZn9nZmdCmP8r+H2zWb2UhjLV83s5nB7e/j6XPh+d9IxVojzS2b23bJjuT3cXvef\nd1msbWb2TTP70/B1qo7lIjGm8TieN7NvhfEMh9vS8fvt7k35BfwEcBfw7bJtnwV+bYG1dwKngHZg\nM/A60FaHGG8D7gqfrwJeC2MZBB4Mtz8IHAyf3wf8GWDAh4CXGhhjao5leDxWhs/zwEvh8Xka2Btu\n/wLwn8Lnvwh8IXy+F/hqnf4/uVicXwI+usD6uv+8y773rwBfAf40fJ2qY7lIjGk8jueBtfO2peL3\nu2nP3N39r4B/jLj8fuCwu8+6+3eBc8A9iQUXcvfvufv/C5+/DbwCbAjj+XK47MvAT5fF+QceeBG4\nxcxua1CMi6n7sQyPx1T4Mh9+OXAv8LVw+/zjWDq+XwN+0swsyRgrxLmYuv+8AcysC/gp4InwtZGy\nYzk/xgoachwrxNPw3++mTe5L2B/+yfNU6c8hgmR1sWzNKEsnsNiFf87+GMHZ3K3u/r3wrb8Hbg2f\nNzTOeTFCio5l+Cf6SeBN4BsEfzG85e5XFojjWozh+5NAZ9IxLhSnu5eO5W+Gx/J3zKx0W7BG/bx/\nFzgAlO4e30n6juX8GEvSdBwh+Mf762b2spntC7el4vc7a8n994Dbge3A94D/0dhwAma2EhgC/rO7\n/6D8PQ/+Xmt4y9ICMabqWLr7VXffDnQR/KWwtZHxLGZ+nGb2fuAhgnjvBt4DDDQqPjP7N8Cb7v5y\no2KoZIkYU3Mcy/y4u98FfAT4pJn9RPmbjfz9zlRyd/fvh79cReCLXC8XjAEby5Z2hdsSZ2Z5gqT5\nv9z9j8PN3y/9ORY+vtnIOBeKMY3HMozrLeB54F8Q/Flbug9weRzXYgzffzcwUa8Y58W5Oyx9ubvP\nAr9PY49lD9BrZueBwwTlmM+TrmN5Q4xm9kcpO44AuPtY+Pgm8CdhTKn4/c5Ucp9Xv/oZoNRJcxTY\nG37yvxnYAvxdHeIx4EngFXf/XNlbR4GPh88/Dhwp2/7z4afqHwImy/68q2uMaTqWZrbOzG4Jn3cA\nuwg+G3ge+Gi4bP5xLB3fjwLHwzOoRC0S59myX3QjqL+WH8u6/rzd/SF373L3boIPSI+7+8+SomO5\nSIwPpOk4hnG8y8xWlZ4D/yqMKR2/30l+WpvkF3CIoFxQIKhd9QN/CHwLGAkP5G1l63+doE77KvCR\nOsX44wR/ko0AJ8Ov+whqln8BfAd4DnhPuN6AR8M4vwXsaGCMqTmWwDbgm2Es3wY+E27/EYJ/WM4B\nzwDt4fYV4etz4fs/Uqef92JxHg+P5beBP+J6R03df97z4v0w1ztRUnUsF4kxVccxPGanwq/TwK+H\n21Px+60rVEVEMihTZRkREQkouYuIZJCSu4hIBim5i4hkkJK7iEgGKbmLiGSQkruISAYpuYuIZND/\nBw64xNshlVSTAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "outputId": "21cace21-51a4-4ca5-f570-3801dd8ee47c",
        "id": "jdn_RdWZ6ElF",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 126
        }
      },
      "source": [
        "n = 50000\n",
        "theta = 0.2\n",
        "r = 30\n",
        "\n",
        "k = int(n**theta)\n",
        "print(n,k)\n",
        "\n",
        "c = np.log(k)\n",
        "m_base = int(k*(1-theta)/theta)\n",
        "r_20per = int(r/5)\n",
        "\n",
        "ans_01 = list()\n",
        "ans_01_2 = list()\n",
        "ans_c = list()\n",
        "print()\n",
        "for alpha in range(1,r):\n",
        "  if alpha % r_20per == 0:\n",
        "    print(alpha/r)\n",
        "    \n",
        "  m = int((1+3 * (alpha/r)) * c * m_base)\n",
        "  \n",
        "  tmp = list()\n",
        "  for i in range(4):\n",
        "    tmp.append(solve_with_zero_one(n, k, m, t_values=[m, k]))\n",
        "  ans_01.append(np.average(tmp, axis=0))\n",
        "\n",
        "  tmp = list()\n",
        "  for i in range(4):\n",
        "    tmp.append(solve_with_zero_one_2(n, k, m, t_values=[m, k]))\n",
        "  ans_01_2.append(np.average(tmp, axis=0))\n",
        "\n",
        "\n",
        "  tmp = list()\n",
        "  for i in range(4):\n",
        "    tmp.append(solve_with_choose(n, k, m, t_values=[m, k]))\n",
        "  ans_c.append(np.average(tmp, axis=0))"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "50000 8\n",
            "\n",
            "0.2\n",
            "0.4\n",
            "0.6\n",
            "0.8\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "riOCjBXH6ElZ",
        "colab": {}
      },
      "source": [
        "h_01=np.array(ans_01)\n",
        "h_01_2=np.array(ans_01_2)\n",
        "h_c=np.array(ans_c)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "outputId": "14c3905a-a2c5-44c4-d00c-b8b8931d12ab",
        "id": "M04GgjAEQbUb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 521
        }
      },
      "source": [
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01[:,0], c='r', s=20)\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_c[:,0], s=20)\n",
        "plt.show()\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01[:,0], c='r', s=20)\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01_2[:,0], c='g', s=20)\n",
        "plt.show()"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nyOFuZpZBDnczswxyuJuZZdD/BxKCUpr+6OnwAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "outputId": "5bef7a1c-d732-4d21-f5e4-1ba5b0259ca0",
        "id": "YMYkCfFXQbUe",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 521
        }
      },
      "source": [
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01[:,1], c='r', s=20)\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_c[:,1], s=20)\n",
        "plt.show()\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01[:,1], c='r', s=20)\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01_2[:,1], c='g', s=20)\n",
        "plt.show()"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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5vSipVkuWgJPOSztXvwhECkvbMjmqdAtflU2KFJq2ZXISLUTUj9VpL10qLRzZPsLcbXPl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\nchcRqSAldxGRClJyFxGpICV3EZEK+n+xHE9zSmcNEQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "outputId": "2bd6ef99-5afb-4bf5-d980-0cb189cec0f1",
        "id": "NTQPvSTesjnU",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        }
      },
      "source": [
        "n = 50000\n",
        "theta = 0.5\n",
        "r = 30\n",
        "\n",
        "k = int(n**theta)\n",
        "print(n,k)\n",
        "\n",
        "c = np.log(k)\n",
        "m_base = int(k*(1-theta)/theta)\n",
        "r_20per = int(r/5)\n",
        "\n",
        "ans_01 = list()\n",
        "ans_01_2 = list()\n",
        "ans_c = list()\n",
        "print()\n",
        "for alpha in range(1,r):\n",
        "  if alpha % r_20per == 0:\n",
        "    print(alpha/r)\n",
        "    \n",
        "  m = int((1+3 * (alpha/r)) * c * m_base)\n",
        "  \n",
        "  tmp = list()\n",
        "  for i in range(4):\n",
        "    tmp.append(solve_with_zero_one(n, k, m, t_values=[m, k]))\n",
        "  ans_01.append(np.average(tmp, axis=0))\n",
        "\n",
        "  tmp = list()\n",
        "  for i in range(4):\n",
        "    tmp.append(solve_with_zero_one_2(n, k, m, t_values=[m, k]))\n",
        "  ans_01_2.append(np.average(tmp, axis=0))\n",
        "\n",
        "\n",
        "  tmp = list()\n",
        "  for i in range(4):\n",
        "    tmp.append(solve_with_choose(n, k, m, t_values=[m, k]))\n",
        "  ans_c.append(np.average(tmp, axis=0))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "50000 223\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "vEI5VLSWsjn4",
        "colab": {}
      },
      "source": [
        "h_01=np.array(ans_01)\n",
        "h_01_2=np.array(ans_01_2)\n",
        "h_c=np.array(ans_c)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "z25D2dx-Qdw7",
        "colab": {}
      },
      "source": [
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01[:,0], c='r', s=20)\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_c[:,0], s=20)\n",
        "plt.show()\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01[:,0], c='r', s=20)\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01_2[:,0], c='g', s=20)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "vMfZQ4U4Qdw9",
        "colab": {}
      },
      "source": [
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01[:,1], c='r', s=20)\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_c[:,1], s=20)\n",
        "plt.show()\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01[:,1], c='r', s=20)\n",
        "plt.scatter([int((1+3 * (alpha/r)) * c * m_base) for alpha in range(1,r)], h_01_2[:,1], c='g', s=20)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8WZA6HoCQp8p",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}