Merging Overlapping Intervals

Question

Currently, I have intervals of:

temp_tuple = [[-25, -14], [-21, -16], [-20, -15], [-10, -7], [-8, -5], [-6, -3], [2, 4], [2, 3], [3, 6], [12, 15], [13, 18], [14, 17], [22, 27], [25, 30], [26, 29]]

in an ascending order by the lower bound. My task is to merge overlapping intervals so that the outcome comes out to be:

[-25, -14]
[-10, -3]
[2, 6]
[12, 18]
[22, 30]

My first attempt involved deleting intervals that are completely within previous intervals, like [-21, -16] which falls within [-25, -14]. But deleting objects within a list kept interfering with the loop condition. My second attempt at deleting unnecessary intervals was:

i = 0
j = 1
while i < len(temp_tuples):
    while j < len(temp_tuples):
        if temp_tuples[i][1] > temp_tuples[j][1]:
            del temp_tuples[j]
        j += 1
    i += 1

but this doesn't delete all the unnecessary intervals for some reason. What should I do?

Answer 1

It makes it a bit easier to process (as in think about) if you instead setup a new list. You additionally also get to keep your original data.

temp_tuple.sort(key=lambda interval: interval[0])
merged = [temp_tuple[0]]
for current in temp_tuple:
    previous = merged[-1]
    if current[0] <= previous[1]:
        previous[1] = max(previous[1], current[1])
    else:
        merged.append(current)

If you now print(merged) it would output:

[[-25, -14], [-10, -3], [2, 6], [12, 18], [22, 30]]

Answer 2

This is a numpy solution I came up with:

import numpy as np

def merge_intervals(intervals):
    starts = intervals[:,0]
    ends = np.maximum.accumulate(intervals[:,1])
    valid = np.zeros(len(intervals) + 1, dtype=np.bool)
    valid[0] = True
    valid[-1] = True
    valid[1:-1] = starts[1:] >= ends[:-1]
    return np.vstack((starts[:][valid[:-1]], ends[:][valid[1:]])).T

#example
a=[]
a.append([1,3])
a.append([4,10])
a.append([5,12])
a.append([6,8])
a.append([20,33])
a.append([30,35])

b = np.array(a)

print("intervals")
print(b)
print()
print("merged intervals")
print(merge_intervals(b))

Output:

intervals
[[ 1  3]
 [ 4 10]
 [ 5 12]
 [ 6  8]
 [20 33]
 [30 35]]

merged intervals
[[ 1  3]
 [ 4 12]
 [20 35]]

Please note that the input array must be sorted by start positions.