Running Sum of 1d Array

This is a Leetcode question that is asking users to create a running sum. Given an array of numbers, create a running sum of the array. For instance, if you have an array of nums = [1,2,3,4], then you would have a running_sum = [1,3,6,10] where you have [1, (1+2), (1+2+3), (1+2+3+4)].

I solved this problem by using a loop that takes each value in the array and adds it to the latest sum. It’s on the order of O(n) for time complexity and space complexity, in which I loop through each element of the array (n is the number of elements).

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To hear this, I start with 4 MIDI notes, nums = [21,22,23,24] and I convert it to a running sum of MIDI notes, running_sum_final = [21, 43, 66, 90]. Note that MIDI goes from 21 to 108 in terms of the 88 keys of a piano, so 21, 22, 23, and 24 are the lowest notes, and then once we do the running sum, they jump up to higher notes in MIDI.

Here is the code:

# initialize the array of MIDI notes
# Create the running sum array

nums = [21,22,23,24]
running_sum_final = [] # initialize the final list
running_sum = 0 # initialize with 0

for i in nums: 
    running_sum = i + running_sum
    running_sum_final.append(running_sum)  

print(running_sum_final)  

melody = music21.converter.parseFile('major-scale.mid')
melody.show('midi')

# pip install midiutil 
# pip install music21
# import the library  
from midiutil import MIDIFile

# Create the MIDI file with the nums array 

degrees  = nums  # MIDI note number
track    = 0
channel  = 0
time     = 0    # In beats

duration = 1    # In beats
tempo    = 60   # In BPM
volume   = 100  # 0-127, as per the MIDI standard

MyMIDI = MIDIFile(1)  # One track, defaults to format 1 (tempo track is created
                      # automatically)
MyMIDI.addTempo(track, time, tempo)

for i, pitch in enumerate(degrees):
    MyMIDI.addNote(track, channel, pitch, time + i, duration, volume)

with open("major-scale.mid", "wb") as output_file:
    MyMIDI.writeFile(output_file)

Play the nums MIDI array

melody = music21.converter.parseFile('major-scale.mid')
melody.show('midi')

# Create the MIDI file with the running sums array

degrees  = running_sum_final  # MIDI note number
track    = 0
channel  = 0
time     = 0    # In beats
duration = 1    # In beats
tempo    = 60   # In BPM
volume   = 100  # 0-127, as per the MIDI standard

MyMIDI = MIDIFile(1)  # One track, defaults to format 1 (tempo track is created
                      # automatically)
MyMIDI.addTempo(track, time, tempo)

for i, pitch in enumerate(degrees):
    MyMIDI.addNote(track, channel, pitch, time + i, duration, volume)

with open("major-scale_running_sum_final.mid", "wb") as output_file:
    MyMIDI.writeFile(output_file) 

Play the running_nums MIDI array

melody = music21.converter.parseFile('major-scale_running_sum_final.mid')
melody.show('midi')

Here is the link to the Jupyter Notebook to play it in your browser. Sounds pretty cool!

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