06-13-2023, 06:28 PM
You keep doing this back and forth because each pick keeps the new row in order without any extra sorting later. I found it helps when you imagine the pointers as little fingers tapping the current spot in each row you hold. But sometimes one row empties first and then you just sweep the leftover numbers from the other row straight into the end of your new row. You never have to compare anything else after that point since the remaining stuff already sits sorted. Perhaps you notice how this whisking action avoids any backtracking which keeps things quick even on bigger sets.
Now the whole trick sits in those repeated comparisons you make while both rows still hold items. I watched myself mess up the pointers once and the new row turned jumbled so you really watch where each finger lands after every move. Then you copy the winner each round and you build the merged pile one spot at a time until nothing remains to compare. Or you might hit equal numbers and you can choose either since the order stays stable anyway. Also this method lets the bigger picture of merge sort work because every merge level stays clean and predictable.
You end up with a single sorted row that holds every original item exactly once and you never needed extra space beyond what the two input rows already used. I usually count the steps by hand on a small example to see how the pointers dance around each other. But the beauty shows when the rows start different sizes because the sweep of leftovers handles any imbalance without special rules. Perhaps you try it on numbers that repeat and you see the original order of equals never flips which matters for some later steps. Then the total work stays linear in the size of the combined row since each item moves exactly once per merge level.
You realize the pointers only move forward so no item gets looked at more than a couple times during the whole merge. I tried sketching the flow on paper and it clicked faster once I marked every advance with an arrow. But you still have to watch the end conditions or one row might leave stray items behind. Also the fresh row grows steadily as you fill it so you allocate just enough room upfront to hold everything. Perhaps the process feels mechanical after a few tries yet it stays efficient because comparisons happen only when both rows have candidates left.
You notice that every merge builds on the sorted halves the recursion already gave you so the overall sort never restarts from scratch. I keep coming back to how simple the rule stays even though the surrounding recursion tree can grow tall. Then you finish one merge and you hand the result up to the next level where another pair waits to combine. Or the last merge at the top level finally produces the fully ordered set you wanted from the start. Also this bottom up building means you never juggle unsorted chunks after they leave their first split.
You see the merging step itself costs time only in proportion to the total items being combined right then. I always remind myself that repeated merges across all levels add up to the full log factor without any hidden waste. But the real fun comes when you trace a single number through every merge it joins because it gets copied exactly once per level. Perhaps you experiment with uneven splits and you still see the leftovers get copied cleanly at the end of each merge. Then the pointers reset for the next independent merge so nothing carries over between separate pairs.
You handle the final leftovers by simply appending whatever sits after the exhausted pointer which avoids any extra loops or checks. I learned to code the copy in one clean pass after the main comparison loop stops. But you keep the two original halves untouched until the merge finishes so you can reuse memory safely in place. Also the method works the same whether your halves come from recursion or from a bottom up pass you wrote yourself. Perhaps the flow stays the same across languages because the logic never changes.
You end up trusting the merge because every item travels through exactly the same comparison path until it lands in its final spot. I like how the process turns two ordered piles into one without ever looking back or swapping already placed numbers. Then the whole sort gains its speed from this reliable building block you repeat at every scale.
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