day 13 - extended euclidean algorithm.ipynb

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   "source": [
    "## algorithm"
   ]
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   "execution_count": 1,
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   "source": [
    "def gcd(x, y):\n",
    "    u0, v0 = 1, 0\n",
    "    u1, v1 = 0, 1\n",
    "    while y:\n",
    "        q = x // y\n",
    "        u0, u1 = u1, u0 - q * u1\n",
    "        v0, v1 = v1, v0 - q * v1\n",
    "        x, y = y, x % y\n",
    "    return x, u0, v0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## run"
   ]
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   "cell_type": "code",
   "execution_count": 2,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 3, -2)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gcd(5, 7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(18, -9, 40)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gcd(2*3*7*9*11, 6*12*13)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6, -1351389, 189739)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gcd(32423940, 230934894)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 1, -1)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gcd(150, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, -49, 74)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gcd(151, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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