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    "# Binary Heap Implementation\n",
    "\n",
    "Here is the reference code for the Binary Heap Implementation. Make sure to refer to the video lecture for the full explanation!"
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    "### Binary Heap Operations\n",
    "**The basic operations we will implement for our binary heap are as follows:**\n",
    "\n",
    "* BinaryHeap() creates a new, empty, binary heap.\n",
    "* insert(k) adds a new item to the heap.\n",
    "* findMin() returns the item with the minimum key value, leaving item in the heap.\n",
    "* delMin() returns the item with the minimum key value, removing the item from the heap.\n",
    "* isEmpty() returns true if the heap is empty, false otherwise.\n",
    "* size() returns the number of items in the heap.\n",
    "* buildHeap(list) builds a new heap from a list of keys."
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    "class BinHeap:\n",
    "    def __init__(self):\n",
    "        self.heapList = [0]\n",
    "        self.currentSize = 0\n",
    "\n",
    "\n",
    "    def percUp(self,i):\n",
    "        \n",
    "        while i // 2 > 0:\n",
    "            \n",
    "            if self.heapList[i] < self.heapList[i // 2]:\n",
    "                \n",
    "            \n",
    "                tmp = self.heapList[i // 2]\n",
    "                self.heapList[i // 2] = self.heapList[i]\n",
    "                self.heapList[i] = tmp\n",
    "            i = i // 2\n",
    "\n",
    "    def insert(self,k):\n",
    "        \n",
    "        self.heapList.append(k)\n",
    "        self.currentSize = self.currentSize + 1\n",
    "        self.percUp(self.currentSize)\n",
    "\n",
    "    def percDown(self,i):\n",
    "        \n",
    "        while (i * 2) <= self.currentSize:\n",
    "            \n",
    "            mc = self.minChild(i)\n",
    "            if self.heapList[i] > self.heapList[mc]:\n",
    "                \n",
    "                tmp = self.heapList[i]\n",
    "                self.heapList[i] = self.heapList[mc]\n",
    "                self.heapList[mc] = tmp\n",
    "            i = mc\n",
    "\n",
    "    def minChild(self,i):\n",
    "        \n",
    "        if i * 2 + 1 > self.currentSize:\n",
    "            \n",
    "            return i * 2\n",
    "        else:\n",
    "            \n",
    "            if self.heapList[i*2] < self.heapList[i*2+1]:\n",
    "                return i * 2\n",
    "            else:\n",
    "                return i * 2 + 1\n",
    "\n",
    "    def delMin(self):\n",
    "        retval = self.heapList[1]\n",
    "        self.heapList[1] = self.heapList[self.currentSize]\n",
    "        self.currentSize = self.currentSize - 1\n",
    "        self.heapList.pop()\n",
    "        self.percDown(1)\n",
    "        return retval\n",
    "\n",
    "    def buildHeap(self,alist):\n",
    "        i = len(alist) // 2\n",
    "        self.currentSize = len(alist)\n",
    "        self.heapList = [0] + alist[:]\n",
    "        while (i > 0):\n",
    "            self.percDown(i)\n",
    "            i = i - 1"
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