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    "<h1>118. Pascal's Triangle</h1>\n",
    "<hr>\n",
    "\n",
    "<!--Copy Paste Leetcode statement between-->\n",
    "<p>Given a non-negative integer&nbsp;<em>numRows</em>, generate the first <em>numRows</em> of Pascal's triangle.</p>\n",
    "\n",
    "<p><img alt=\"\" src=\"./img1.gif\" style=\"height:240px; width:260px\"><br>\n",
    "<small>In Pascal's triangle, each number is the sum of the two numbers directly above it.</small></p>\n",
    "\n",
    "<p><strong>Example:</strong></p>\n",
    "\n",
    "<pre><strong>Input:</strong> 5\n",
    "<strong>Output:</strong>\n",
    "[\n",
    "     [1],\n",
    "    [1,1],\n",
    "   [1,2,1],\n",
    "  [1,3,3,1],\n",
    " [1,4,6,4,1]\n",
    "]\n",
    "</pre>\n",
    "<!--Copy Paste Leetcode statement between-->\n",
    "\n",
    "<p>&nbsp;</p>\n",
    "<a href=\"https://leetcode.com/problems/pascals-triangle/\">Source</a> \n",
    "<hr>\n",
    "\n",
    "<h4>Code</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pascal_triangle(numRows):\n",
    "    \"\"\"Dynamic Programming approach.\"\"\"\n",
    "    # Base cases\n",
    "    if numRows == 0:\n",
    "        return []\n",
    "    if numRows == 1:\n",
    "        return [[1]]\n",
    "    \n",
    "    result = [[1], [1, 1]]\n",
    "    for i in range(2, numRows):\n",
    "        result.append([1, i])   # start new row with 1, i\n",
    "        for j in range(2, i):\n",
    "            result[i].append(result[i-1][j-1] + result[i-1][j])\n",
    "        result[i].append(1)     # end row with 1\n",
    "    return result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Check</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1]]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pascal_triangle(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1],\n",
       " [1, 1],\n",
       " [1, 2, 1],\n",
       " [1, 3, 3, 1],\n",
       " [1, 4, 6, 4, 1],\n",
       " [1, 5, 10, 10, 5, 1],\n",
       " [1, 6, 15, 20, 15, 6, 1],\n",
       " [1, 7, 21, 35, 35, 21, 7, 1],\n",
       " [1, 8, 28, 56, 70, 56, 28, 8, 1],\n",
       " [1, 9, 36, 84, 126, 126, 84, 36, 9, 1],\n",
       " [1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1],\n",
       " [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1],\n",
       " [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1],\n",
       " [1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1],\n",
       " [1, 14, 91, 364, 1001, 2002, 3003, 3432, 3003, 2002, 1001, 364, 91, 14, 1]]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pascal_triangle(15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "<h4>Follow up:</h4>\n",
    "<p>Solve it both recursively and iteratively.</p>\n",
    "\n",
    "<h4>Code</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pascal_triangle(numRows):\n",
    "    \"\"\"Recursive approach.\"\"\"\n",
    "    # Base cases\n",
    "    if numRows == 0:\n",
    "        return []\n",
    "    if numRows == 1:\n",
    "        return [[1]]\n",
    "\n",
    "    prev = pascal_triangle(numRows-1)\n",
    "    row = [1]*numRows\n",
    "    for i in range(1, numRows-1):\n",
    "        row[i] = prev[-1][i-1]+prev[-1][i]\n",
    "    return prev + [row]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Check</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1]]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pascal_triangle(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1],\n",
       " [1, 1],\n",
       " [1, 2, 1],\n",
       " [1, 3, 3, 1],\n",
       " [1, 4, 6, 4, 1],\n",
       " [1, 5, 10, 10, 5, 1],\n",
       " [1, 6, 15, 20, 15, 6, 1],\n",
       " [1, 7, 21, 35, 35, 21, 7, 1],\n",
       " [1, 8, 28, 56, 70, 56, 28, 8, 1],\n",
       " [1, 9, 36, 84, 126, 126, 84, 36, 9, 1],\n",
       " [1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1],\n",
       " [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1],\n",
       " [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1],\n",
       " [1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1],\n",
       " [1, 14, 91, 364, 1001, 2002, 3003, 3432, 3003, 2002, 1001, 364, 91, 14, 1]]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pascal_triangle(15)"
   ]
  }
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