class Heap(object):

    @classmethod
    def parent(cls, i):
        """父結點下標"""
        return int((i - 1) >> 1);

    @classmethod
    def left(cls, i):
        """左兒子下標"""
        return (i << 1) + 1;

    @classmethod
    def right(cls, i):
        """右兒子下標"""
        return (i << 1) + 2;

class MaxPriorityQueue(list, Heap):

    @classmethod
    def max_heapify(cls, A, i, heap_size):
        """最大堆化A[i]為根的子樹"""
        l, r = cls.left(i), cls.right(i)
        if l < heap_size and A[l] > A[i]:
            largest = l
        else:
            largest = i
        if r < heap_size and A[r] > A[largest]:
            largest = r
        if largest != i:
            A[i], A[largest] = A[largest], A[i]
            cls.max_heapify(A, largest, heap_size)

    def maximum(self):
        """返回最大元素，偽碼如下：
        HEAP-MAXIMUM(S)
        1  return A[1]

        T(n) = O(1)
        """
        return self[0]

    def extract_max(self):
        """去除并返回最大元素，偽碼如下：
        HEAP-EXTRACT-MAX(A)
        1  if heap-size[A] < 1
        2    then error "heap underflow"
        3  max ← A[1]
        4  A[1] ← A[heap-size[A]] // 尾元素放到第一位
        5  heap-size[A] ← heap-size[A] - 1 // 減小heap-size[A]
        6  MAX-HEAPIFY(A, 1) // 保持最大堆性質
        7  return max

        T(n) = θ(lgn)
        """
        heap_size = len(self)
        assert heap_size > 0, "heap underflow"
        val = self[0]
        tail = heap_size - 1
        self[0] = self[tail]
        self.max_heapify(self, 0, tail)
        self.pop(tail)
        return val

    def increase_key(self, i, key):
        """將i處的值增加到key，偽碼如下：
        HEAP-INCREASE-KEY(A, i, key)
        1  if key < A[i]
        2    the error "new key is smaller than current key"
        3  A[i] ← key
        4  while i > 1 and A[PARENT(i)] < A[i] // 不是根結點且父結點更小時
        5    do exchange A[i] ↔ A[PARENT(i)] // 交換兩元素
        6       i ← PARENT(i) // 指向父結點位置

        T(n) = θ(lgn)
        """
        val = self[i]
        assert key >= val, "new key is smaller than current key"
        self[i] = key
        parent = self.parent
        while i > 0 and self[parent(i)] < self[i]:
            self[i], self[parent(i)] = self[parent(i)], self[i]
            i = parent(i)

    def insert(self, key):
        """將key插入A，偽碼如下：
        MAX-HEAP-INSERT(A, key)
        1  heap-size[A] ← heap-size[A] + 1 // 對元素個數增加
        2  A[heap-size[A]] ← -∞ // 初始新增加元素為-∞
        3  HEAP-INCREASE-KEY(A, heap-size[A], key) // 將新增元素增加到key

        T(n) = θ(lgn)
        """
        self.append(float('-inf'))
        self.increase_key(len(self) - 1, key)

if __name__ == '__main__':
    import random

    keys = range(10)
    random.shuffle(keys)
    print(keys)

    queue = MaxPriorityQueue() # 插入方式建最大堆
    for i in keys:
        queue.insert(i)
    print(queue)

    print('*' * 30)

    for i in range(len(keys)):
        val = i % 3
        if val == 0:
            val = queue.extract_max() # 去除并返回最大元素
        elif val == 1:
            val = queue.maximum() # 返回最大元素
        else:
            val = queue[1] + 10
            queue.increase_key(1, val) # queue[1]增加10
        print(queue, val)

    print([queue.extract_max() for i in range(len(queue))])