Merge Intervals in Python

Suppose we have a collection of intervals, we have to merge all overlapping intervals. So if the intervals are like [[1,3], [2,6], [8,10], [15,18]], then the intervals after merging will be [[1,6],[8,10],[15,18]]. This is because there were two intervals those are overlapping, the intervals are [1,3] and [2,6], these are merged to [1,6]

Let us see the steps −

• if interval list length is 0, then return a blank list
• sort the interval list using quicksort mechanism
• stack := an empty stack, and insert intervals[0] into the stack
• for i in range 1 to length of intervals – 1
  • last_element := top element of stack
  • if end of last_element >= first element of intervals[i], then
    • end of last_element = max of end of intervals[i], and end of last_element
    • pop element from stack
    • push last_element into stack
  • else push intervals[i] into stack
• return stack

Let us see the following implementation to get better understanding −

Example

 Live Demo

class Solution(object):
   def merge(self, intervals):
      """
      :type intervals: List[Interval]
      :rtype: List[Interval]
      """
      if len(intervals) == 0:
         return []
      self.quicksort(intervals,0,len(intervals)-1)
      #for i in intervals:
         #print(i.start, i.end)
      stack = []
      stack.append(intervals[0])
      for i in range(1,len(intervals)):
         last_element= stack[len(stack)-1]
         if last_element[1] >= intervals[i][0]:
            last_element[1] = max(intervals[i][1],last_element[1])
            stack.pop(len(stack)-1)
            stack.append(last_element)
         else:
            stack.append(intervals[i])
      return stack
   def partition(self,array,start,end):
      pivot_index = start
      for i in range(start,end):
         if array[i][0]<=array[end][0]:
            array[i],array[pivot_index] =array[pivot_index],array[i]
            pivot_index+=1
      array[end],array[pivot_index] =array[pivot_index],array[end]
      return pivot_index
   def quicksort(self,array,start,end):
      if start<end:
         partition_index = self.partition(array,start,end)
         self.quicksort(array,start,partition_index-1)
         self.quicksort(array, partition_index + 1, end)
ob1 = Solution()
print(ob1.merge([[1,3],[2,6],[8,10],[15,18]]))

Input

[[1,3],[2,6],[8,10],[15,18]]

Output

[[1, 6], [8, 10], [15, 18]]