{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8561e0a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>.container{width:100%}</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%HTML\n",
    "<style>.container{width:100%}</style>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "12f36b2f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "21"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def eucld_gcd(a,b):\n",
    "    if(a < b):\n",
    "        a , b = b , a\n",
    "    if(b==0):\n",
    "        return a\n",
    "    r = a%b\n",
    "    if(r==0):\n",
    "        return b\n",
    "    return eucld_gcd(b,r)\n",
    "eucld_gcd(252,105)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c060ee17",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, -48]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "def ext_eucld(a,b):\n",
    "    swap = False\n",
    "    if(a < b):\n",
    "            a , b = b , a\n",
    "            swap = True\n",
    "    def eucld(a,b):\n",
    "        if(b==0 or b==1):\n",
    "            return []\n",
    "        ls = []\n",
    "        while b!=1:\n",
    "            r = a%b\n",
    "            if(r==0):\n",
    "                return ls\n",
    "            idx = (a-r)//b\n",
    "            ls.append(idx)\n",
    "            a = b\n",
    "            b = r\n",
    "        return ls\n",
    "    \n",
    "    row = np.array([[1,0],[0,1]])\n",
    "    ls = eucld(a,b)\n",
    "    for i in ls:\n",
    "        row = np.append(row, [row[-2] - i*row[-1]] ,axis=0)\n",
    "    if(swap):\n",
    "        return list(row[-1])[::-1]\n",
    "    return list(row[-1])\n",
    "ext_eucld(97,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d3edd1f6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a=5, b=7, gcd=1, m=3, n=-2, ma+nb=1\n"
     ]
    }
   ],
   "source": [
    "a = 5\n",
    "b = 7\n",
    "gcd = eucld_gcd(a,b)\n",
    "m,n = ext_eucld(a,b)\n",
    "print(f\"a={a}, b={b}, gcd={gcd}, m={m}, n={n}, ma+nb={m*a+n*b}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "782bb8d3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e224063e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "63f1d5a4",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.3"
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