Reachable-prefix DP
Split a Joined Field Note
01. The question
A lowercase field note lost its spaces. Decide whether the whole note can be split into dictionary words, reusing words as needed. Original scenario; the empty note is explicitly segmentable. Supply distinct dictionary words as comma-separated plain parameter text.
Before revealing the idea, predict the result and describe what information you would need to track.
02. Worked example
Input"sunroomlit"; dictionary = "sun,room,lit"
Outputtrue
- The empty prefix is reachable.
- "sun" reaches prefix length 3, then "room" reaches 7.
- "lit" reaches 10, so the complete note is segmentable.
Try your code
Define solve(data, parameter="") and return your result. Your code runs locally, not on a server.
Edit your test cases
Use 1-10 objects with data and an optional string parameter. Expected outputs are computed from the lesson. An optional expected field must be correct.
Input contract & reference code
Example data: "sunflower". Parameter: "sun,flower,flow". Numeric parameters arrive as strings; convert them with int(parameter) when needed.
The example and generated cases use the question’s exact variant. This checks behavior on a small test batch—not performance on every possible input.
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Printed output
Five-second execution limit per batch. Standard-library Python only; additional packages and network access are unavailable. Stop ends execution without blocking the lesson.
03. The idea
Try sketching your own approach first. What would you track, and why would it work?
Reveal the idea
- Mark the empty prefix true.
- For each endpoint try a split after any reachable prefix.
- Mark true and stop testing that endpoint when the suffix is a dictionary word.
04. Watch it happen
Use Step to move slowly, or Play to follow the whole trace. Change a preset or load your own input.
Input & settings
Red = current item / blue = active window or cells / green = completed work. A value docks at its actual destination; the original input stays unchanged. Positions start at 0.
Working state / what changes
Ready to begin
Enable JavaScript to step through the animation. The worked example and solution below remain readable without it.
Python / why it changes
The line behind the step
def solve(data, parameter=''):
words = set(parameter.split(',')) if parameter else set()
reachable = [False] * (len(data) + 1)
reachable[0] = True
for end in range(1, len(data) + 1):
for start in range(end):
if reachable[start] and data[start:end] in words:
reachable[end] = True
break
return reachable[-1]How to use this walkthrough
Hover or focus a control for its label. Play forms the input and follows values into the working state. Step shows one change; Back and the slider restore exact snapshots. Reduced motion uses instant updates. Saved snapshots and sorted heap displays are teaching overhead, not algorithm complexity.
05. Python solution
def solve(data, parameter=''):
words = set(parameter.split(',')) if parameter else set()
reachable = [False] * (len(data) + 1)
reachable[0] = True
for end in range(1, len(data) + 1):
for start in range(end):
if reachable[start] and data[start:end] in words:
reachable[end] = True
break
return reachable[-1]06. Cost & edge cases
- Time
- O(n³ + d) with Python substring slicing; d is dictionary text length
- Space
- O(n + d)
- An empty note returns true even with an empty dictionary.
- A nonempty note with no dictionary returns false.
- Note: 0-16 lowercase letters. Dictionary: 0-8 distinct words of 1-5 lowercase letters, comma-separated with no spaces.