python | 算法大神左神（左程云）算法课程 第二节

#归并排序-递归

class solution():
    def mergeSort(self, array):
        """
        归并排序
        :param array: List[int]
        :return: None
        """
        self.process(array, 0, len(array)-1)

    def process(self, array, left, right):
        """
        递归过程
        :param array: List[int]
        :param left: int
        :param right: int
        :return: None
        """
        if left == right: return

        mid = left + (right-left)>>1
        self.process(array, left, mid)
        self.process(array, mid+1, right)
        self.merge(array, left, mid, right)

    def merge(self, array, left, mid, right):
        #整一个辅助空间，存放已经排好序的部分
        help = []
        #比较
        i = left
        j = mid+1
        while i <= mid and j <= right:
            #判断
            if array[i] <= array[j]:
                help.append(array[i])
                i += 1
            else:
                help.append(array[j])
                j += 1
        #谁还剩，就都copy到help中
        while i <= mid:
            help.append(array[i])
            i += 1
        while j <= right:
            help.append(array[j])
            j += 1

        #将help中的排好序的数再copy回array中
        for i in range(len(help)):
            array[left+i] = help[i]

# 归并排序扩展
# 小和问题

class solution():
    def lowerSum(self, array):
        """
        求数组的array的小和
        :param array: List[int]
        :return: int
        """
        if len(array) < 2:
            return 0
        return self.process(array, 0, len(array)-1)

    def process(self, array, left, right):
        """
        递归过程
        :param array: List[int]
        :param left: int
        :param right: int
        :return: int
        """
        if left == right:
            return 0
        mid = left + (right-left)>>1
        return self.process(array, left, mid)+self.process(array, mid+1, right)+self.merge(array, left, mid, right)

    def merge(self, array, left, mid, right):
        """
        将排好序且求出小和的左右两个部分整合
        :param array: List[int]
        :param left: int
        :param mid: int
        :param right: int
        :return: int
        """
        help = []
        sum = 0
        i = left
        j = mid + 1
        while i <= mid and j <= right:
            if array[i] < array[j]:
                sum += array[i]*(right-j+1)
                help.append(array[i])
                i += 1
            else:
                help.append(array[j])
                j += 1

        while i <= mid:
            help.append(array[i])
            i += 1

        while j <= right:
            help.append(array[j])
            j += 1

        for i in range(len(help)):
            array[left+i] = help[i]

        return sum