Filtering and Transforming

Running Total

Produce a cumulative-sum list where each element is the sum of all values up to that point. The trace shows running advancing with every element and cumulative growing by one entry per step.

By hand

Keep a running accumulator and append its current value to cumulative after each addition. After the loop, cumulative[i] equals the sum of the first i + 1 values.

naive.py
Replay: real traced execution (multi-file project)
values = [2, 5, 3, 8, 1, 6, 4]
running = 0
cumulative = []
for v in values:
    running = running + v
    cumulative.append(running)
print('RESULT:', cumulative)

  1. values ← [2, 5, 3, 8, 1, 6, 4]

    1values = [2, 5, 3, 8, 1, 6, 4]2running = 0
    values this step[2, 5, 3, 8, 1, 6, 4]values

  2. running ← 0

    1values = [2, 5, 3, 8, 1, 6, 4]2running = 03cumulative = []
    values this step0running

  3. cumulative ← []

    2running = 03cumulative = []4for v in values:
    values this step[]cumulative

  4. v ← 2

    3cumulative = []4for v in values:5    running = running + v
    values this step2v

  5. running ← 2

    4for v in values:5    running = running + v6    cumulative.append(running)
    values this step0 → 2running

  6. cumulative ← [2]

    5    running = running + v6    cumulative.append(running)7print('RESULT:', cumulative)
    values this step[] → [2]cumulative

  7. v ← 5

    3cumulative = []4for v in values:5    running = running + v
    values this step2 → 5v

  8. running ← 7

    4for v in values:5    running = running + v6    cumulative.append(running)
    values this step2 → 7running

  9. cumulative ← [2, 7]

    5    running = running + v6    cumulative.append(running)7print('RESULT:', cumulative)
    values this step[2] → [2, 7]cumulative

  10. v ← 3

    3cumulative = []4for v in values:5    running = running + v
    values this step5 → 3v

  11. running ← 10

    4for v in values:5    running = running + v6    cumulative.append(running)
    values this step7 → 10running

  12. cumulative ← [2, 7, 10]

    5    running = running + v6    cumulative.append(running)7print('RESULT:', cumulative)
    values this step[2, 7] → [2, 7, 10]cumulative

  13. v ← 8

    3cumulative = []4for v in values:5    running = running + v
    values this step3 → 8v

  14. running ← 18

    4for v in values:5    running = running + v6    cumulative.append(running)
    values this step10 → 18running

  15. cumulative ← [2, 7, 10, 18]

    5    running = running + v6    cumulative.append(running)7print('RESULT:', cumulative)
    values this step[2, 7, 10] → [2, 7, 10, 18]cumulative

  16. v ← 1

    3cumulative = []4for v in values:5    running = running + v
    values this step8 → 1v

  17. running ← 19

    4for v in values:5    running = running + v6    cumulative.append(running)
    values this step18 → 19running

  18. cumulative ← [2, 7, 10, 18, 19]

    5    running = running + v6    cumulative.append(running)7print('RESULT:', cumulative)
    values this step[2, 7, 10, 18] → [2, 7, 10, 18, 19]cumulative

  19. v ← 6

    3cumulative = []4for v in values:5    running = running + v
    values this step1 → 6v

  20. running ← 25

    4for v in values:5    running = running + v6    cumulative.append(running)
    values this step19 → 25running

  21. cumulative ← [2, 7, 10, 18, 19, 25]

    5    running = running + v6    cumulative.append(running)7print('RESULT:', cumulative)
    values this step[2, 7, 10, 18, 19] → [2, 7, 10, 18, 19, 25]cumulative

  22. v ← 4

    3cumulative = []4for v in values:5    running = running + v
    values this step6 → 4v

  23. running ← 29

    4for v in values:5    running = running + v6    cumulative.append(running)
    values this step25 → 29running

  24. cumulative ← [2, 7, 10, 18, 19, 25, 29]

    5    running = running + v6    cumulative.append(running)7print('RESULT:', cumulative)
    values this step[2, 7, 10, 18, 19, 25] → [2, 7, 10, 18, 19, 25, 29]cumulative

  25. for v in values:

    3cumulative = []4for v in values:5    running = running + v

  26. stdout ← RESULT: [2, 7, 10, 18, 19, 25, 29]

    6    cumulative.append(running)7print('RESULT:', cumulative)
    values this stepRESULT: [2, 7, 10, 18, 19, 25, 29]stdout

The Pythonic way

itertools.accumulate(values) is a lazy iterator that yields exactly these prefix sums; wrapping with list() materialises them all at once.

library.py 
import itertools
values = [2, 5, 3, 8, 1, 6, 4]
cumulative = list(itertools.accumulate(values))
print('RESULT:', cumulative)

RESULT: [2, 7, 10, 18, 19, 25, 29]

Implementation notes

  • running and cumulative both update every iteration, so no events are zero-delta except the loop-exhaustion step.
  • itertools.accumulate accepts an optional func argument (default: operator.add); passing operator.mul gives a running product instead.
  • The final value of cumulative[-1] equals sum(values) — a useful sanity check.