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[darwinrlo]

Problem

Given a collection of intervals, merge all overlapping intervals.

Source: LeetCode

The idea is, in sorted array of intervals, if interval[i] doesn’t overlap with interval[i-1], then interval[i+1] cannot overlap with interval[i-1] because starting time of interval[i+1] must be greater than or equal to interval[i].

Source: Geeks for Geeks

Why does sorting the intervals by first field put overlapping intervals next to each other?

If overlapping intervals were not placed next to other overlapping intervals after sorting by first, then there should be intervals in between two specific overlapping intervals that do not overlap with either overlapping interval or each other. Let's call these overlapping intervals A and C, A being the one that occurs earlier in the sort order, that is, A.start < C.start. And let the intervals between A and C be B[0], ..., B[n].

• As we stipulated, B[0] does not overlap with B[n], so B[0].start < B[n].end.
• As we stipulated, A does not overlap with B[0], so A.end < B[0].start.
• As we stipulated, B[n] does not overlap with C, so B[n].end < C.start.

Since A.end < C.start ー which would mean that A and C do not overlap. So the specific instance of overlapping intervals with intervening non-overlapping intervals we're looking for does not exist. Hence, after sorting by start, overlapping intervals are placed next to each other.

[darwinrlo]

Keep your ideas in a list. For each idea, keep a collection of positive and negative signals. Categorize each reason as strong or moderate -- don't bother to keep track of weak reasons, whether for or against.

As you run across new information or think of new considerations, add them to the list (which is really a tree) and re-rank your ideas. The ranking of your ideas will be very dynamic -- they will go up and down. And hopefully, the ideas themselves will evolve. Workflowy could be a viable UI: It provides the ability to re-order, restructure, and collapse/expand bullet points.

Ultimately, go with your gut. But the gut feeling you should go with is the gut feeling you get when this list is fairly well-developed and the entirety of it is loaded into your working memory.

[darwinrlo]

Considerations

• How passionate are you about this idea? That is, what is the degree of founder-market fit? It may be a great idea but not a great idea for you.
• How well-developed is your intuition? To what extent are you scratching your own itch? If you wouldn't be a superuser of the product, can you see if you can get into it?
• Do you have a way to access users who would love your product? Is it a small segment that would be overlooked by big incumbents that could be used as a "wedge" or "beachhead" into the bigger market?
• Is there a big market? Are there existing players who are succeeding in the space? How formidable are they?
• How right is the timing for you idea?
• Can you make the experience 10x better by building 10x better tech?
• Is there a network effect?

[darwinrlo]

Possibilities

• Defer your big mission for when you're more established: With greater personal resources, social capital, and skills/judgment, you'll be better poised to attack your life's calling. For now, decide on the smallest satisfying exit size, reverse-engineer the lowest risk project that would get you there, and execute perfectly (or rather, work on executing well).
• Work at a company in the space you wish to get into and identify what the technical bottlenecks are for achieving a 10x better experience. Enter a research program at a university with favorable policies around intellectual property, build the tech, and start your company.
• If you're not scratching your own itch, see if you can get into it. Perhaps you'll "get it," become a "superuser" of the product, and feel the pain points (or limiting factors) yourself.
• Give yourself constraints that you believe in, e.g.: Over the next three years, I will plan on starting 1-3 companies, allowing each one two years to reach product-market fit.