Grokking with ChatGPT - The "Triple Sum Close to Target" algorithm, explained.

This morning I was going crazy trying to complete "Triplet Sum Close to Target", a medium-level two-pointer algorithm. Basically,

I could not "grok" how a number's difference could be used to evaluate its size relative to another number. I was also trying to keep track of too many numbers in my head. Here's a convo with ChatGPT that helped a lot.

Real-World example of differences - Shot Put

me: Can you help me understand why using the diff is key to determining if two numbers are closer than two other numbers?

gpt: Yep — this is the heart of why “the diff” is the comparison tool in these problems.

Let’s slow down and strip away the “triplet” part — we’ll just compare two sums and see which is closer to the target.

1. What is diff?

We define:

diff = target - sum

• If diff is positive, the sum is too small (we’re under target by diff units).
• If diff is negative, the sum is too big (we’re over target by |diff| units).
• If diff is zero, the sum exactly matches the target.

1. Why not compare sums directly?

• If you compare sums directly, you have to handle two cases:
• Sum is less than target (how much less?)
• Sum is greater than target (how much more?)
• The diff unifies these into one number that encodes both direction (sign) and distance (magnitude).

So the key insight is:

diff = target - sum shifts the problem so that “closeness to target” becomes “closeness to zero,” which is way easier to reason about and compare.

me: ok, I see. I'm picturing a shot put competition and how far someone is throwing something. That helps.

gpt:
Got it — let’s put your triple sum closest loop into shot put competition mode so every diff update feels like a throw getting measured.

1. Vocabulary swap

target → the mark on the field where you want to land.
sum → the throw’s landing spot.
diff = target - sum → how far you missed the mark and in which direction:
Positive diff → short throw (didn’t reach the mark).
Negative diff → long throw (overshot the mark).
Zero diff → bullseye.

1. Algorithm in “coach-speak”

int mark = targetSum;  // the distance you want to throw
Integer bestMiss = null; // best miss distance so far (diff)

for (int p = 0; p < arr.length - 2; p++) {
    int l = p + 1;
    int r = arr.length - 1;

    while (l < r) {
        int throwSpot = arr[p] + arr[l] + arr[r];
        int miss = mark - throwSpot; // how far you missed the mark

        if (miss == 0) {
            // Landed exactly on the mark, competition over
            return throwSpot;
        }

        if (bestMiss == null || isCloserToMark(miss, bestMiss)) {
            // New best throw
            bestMiss = miss;
        }

        // Adjust next throw attempt:
        if (throwSpot < mark) {
            // Short throw — try to throw further
            l++;
        } else {
            // Long throw — pull back a little
            r--;
        }
    }
}

private boolean isCloserToMark(int newMiss, int bestMiss) {
    // Case 1: both throws land short
    if (newMiss >= 0 && bestMiss >= 0) {
        return newMiss < bestMiss; // smaller miss is closer
    }
    // Case 2: both throws land long
    if (newMiss < 0 && bestMiss < 0) {
        return newMiss > bestMiss; // less negative miss is closer
    }
    // Case 3: one short, one long — choose the one closer to zero
    return Math.abs(newMiss) < Math.abs(bestMiss); // <-- here you could replace abs with sign logic if you want to go full no-abs
}

me: I get it. The one with the bigger sign in the end "wins". It was far enough away from zero to preserve its sign! Thus the other one was closer to zero.

gpt: Exactly — you nailed it.

When the signs differ, the one with the bigger magnitude will “pull” the total (diff + bestDiff) over to its side of zero.
So if adding them doesn’t pull the sum away from bestDiff’s sign, it means the new one (diff) must have had the smaller magnitude — it was closer to zero.

That’s the little mental judo move that lets you compare distances without ever taking an absolute value.

It’s like two kids in a tug-of-war:

If the rope ends up on the same side it started, the other kid wasn’t strong enough to pull it across — meaning they were “weaker” (smaller magnitude).

If the rope flips sides, the new kid overpowered the old one.

Want me to diagram that tug-of-war analogy with number lines so you can see it visually?

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How to Simplify when Thinking about Algorithms

me: I was trying to relate the diffs to the sums instead of just thinking about how the diffs relate and that was too many variables to keep in my head.

gpt:

Yep — that’s a super common trap.

When you keep flipping back and forth between sum space (“how far is this sum from target?”) and diff space (“how far is this number from zero?”), your brain ends up juggling two number lines at the same time.
That’s cognitive overload — especially when the signs flip.

The beauty of using diff consistently is:

• You stay in one number line (zero is the goalpost).
• Every comparison is about one thing: “Which is closer to zero?”
• You don’t have to re-map to the original sums until the very end, once you know the winning diff.

It’s like translating everything into one currency before comparing prices — instead of trying to mentally compare yen to dollars to euros all at once.

Then, because we all know chatGPT likes to offer things :-) it made me this checklist to avoid overthinking in algorithm problems. I thought I'd share

gpt: here’s a pattern list you can keep in mind for avoiding overload in algorithm problems.
Think of it as your “mental clutter cleanup” checklist.

1. Distance / Target Problems → Switch to Diff Space

• Example: Closest sum, nearest point, minimal adjustment
• Work with diff = target - value instead of raw values.
• Stay in “distance from zero” land until done.
• Translate back at the very end. (You just did this with Triple Sum Closest.)

2. Geometry / Coordinates → Shift or Rotate Origin

• Example: Distance between points, closest pair
• Translate the system so one point is (0,0).
• For angles/slopes, rotate so a key line is horizontal.
• You avoid carrying extra terms in all your calculations.

3. Intervals / Ranges → Normalize to Start=0

• Example: Meeting rooms, merging intervals, timeline problems
• Shift all intervals so the earliest start is 0.
• Makes overlap and gap checks easier.
• Often turns into simple array index math.

4. Percent / Ratio Problems → Use a Single Ratio Space

• Example: Speed/distance/time, growth rate comparisons
• Convert to one ratio type (miles/hour, profit/unit cost).
• Keep all comparisons in that space until final answer.

5. Modular Arithmetic → Work Modulo Early

• Example: Rotations, circular arrays, cyclic patterns
• Reduce numbers modulo n immediately.
• Avoid juggling big numbers and wrap-around logic later.

6. Graph Problems → Fix a Single Perspective

• Example: BFS shortest path, Dijkstra’s
• Store only the current cost-to-reach node instead of storing both “steps” and “path length” in separate forms.
• Add metadata back if needed at the end.

7. Counting / Frequency → Use One Aggregation Metric

• Example: Anagrams, inventory matching
• Convert items to one comparable form (sorted string, hash, vector of counts).
• Compare those forms instead of juggling raw items.

💡 Meta-rule: Always look for a transformation that removes at least one dimension of thinking.
That’s the lever that turns a problem from “too many moving parts” to “just compare this one thing.”