Python/Complexity_analysis.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 复杂度分析"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O(1)时间复杂度代码例子"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n"
     ]
    }
   ],
   "source": [
    "a = 3\n",
    "b = 4\n",
    "print(a + b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O(logn)代码例子"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "while 循环运行了 5 次\n"
     ]
    }
   ],
   "source": [
    "i = 1\n",
    "count = 0\n",
    "n = 20\n",
    "while i <= n:\n",
    "    count += 1\n",
    "    i *= 2\n",
    "print('while 循环运行了 {} 次'.format(count))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O(m+n)代码例子"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cal(n, m):\n",
    "    result = 0\n",
    "    for i in range(n):\n",
    "        result += i\n",
    "\n",
    "    for j in range(m):\n",
    "        result += j * 2\n",
    "\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result:  65\n"
     ]
    }
   ],
   "source": [
    "print('result: ', cal(10, 5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 最好、最坏、平均、均摊时间复杂度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 在数组 arr 中查找目标数值 x\n",
    "def find(arr, x):\n",
    "    for val in arr:\n",
    "        if val == x:\n",
    "            return True\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = [3, 2, 1]\n",
    "x = 1\n",
    "find(arr, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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