Binary Search on Answer Technique in DSA Javascript - Execution Trace

Concept Flow - Binary Search on Answer Technique

Set low and high bounds for answer

↓

Calculate mid = (low + high) / 2

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Check if mid is a valid answer

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Update high = mid

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Repeat until low >= high

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Return low as answer

Start with a range of possible answers, check the middle value, adjust range based on validity, repeat until the answer is found.

Execution Sample

DSA Javascript

function binarySearchAnswer(low, high, isValid) {
  while (low < high) {
    let mid = Math.floor((low + high) / 2);
    if (isValid(mid)) high = mid;
    else low = mid + 1;
  }
  return low;
}

This code finds the smallest valid answer between low and high using binary search on the answer space.

Execution Table

Step	Operation	low	high	mid	isValid(mid)	Action	Range After Action
1	Initialize	1	10	-	-	-	[1, 10]
2	Calculate mid	1	10	5	false	low = mid + 1	[6, 10]
3	Calculate mid	6	10	8	true	high = mid	[6, 8]
4	Calculate mid	6	8	7	true	high = mid	[6, 7]
5	Calculate mid	6	7	6	false	low = mid + 1	[7, 7]
6	Check low < high	7	7	-	-	Stop	[7, 7]
7	Return answer	7	7	-	-	Answer = 7	[7, 7]

💡 Loop ends when low equals high, which is the smallest valid answer.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	Final
low	1	6	6	6	7	7	7
high	10	10	8	7	7	7	7
mid	-	5	8	7	6	-	-
isValid(mid)	-	false	true	true	false	-	-

Key Moments - 3 Insights

Why do we update 'low' to mid + 1 when isValid(mid) is false?

Because mid is not a valid answer, so the answer must be greater than mid. This is shown in step 2 and 5 where low moves past mid.

Why do we update 'high' to mid when isValid(mid) is true?

Because mid might be the smallest valid answer, so we keep it by setting high = mid. This happens in steps 3 and 4.

Why does the loop stop when low equals high?

Because the search space is narrowed down to one value, which is the smallest valid answer, as seen in step 6.

Visual Quiz - 3 Questions

Look at the execution table, what is the value of 'mid' at step 4?

A 8

B 7

C 6

D 5

💡 Hint

Check the 'mid' column in row with Step 4 in the execution_table.

At which step does 'low' first become 7?

A Step 5

B Step 3

C Step 2

D Step 6

💡 Hint

Look at the 'low' values in variable_tracker after each step.

If isValid(mid) was true at step 2, what would be the new value of 'high' after that step?

A 10

B 6

C 5

D 1

💡 Hint

When isValid(mid) is true, high is set to mid, see steps 3 and 4 for reference.

Concept Snapshot

Binary Search on Answer Technique:
- Define low and high as answer bounds
- Calculate mid = (low + high) // 2
- Check if mid is valid
- If valid, set high = mid (keep mid)
- Else, set low = mid + 1 (discard mid)
- Repeat until low == high
- Return low as smallest valid answer

Full Transcript

Binary Search on Answer Technique starts by setting a range of possible answers with low and high. We find the middle value mid and check if it is a valid answer using a condition function. If mid is valid, we move the high bound down to mid to keep searching for a smaller valid answer. If mid is not valid, we move the low bound up to mid plus one to discard invalid answers. This process repeats until low equals high, which is the smallest valid answer. The code example shows this logic in a loop, updating low and high based on validity checks. The execution table traces each step, showing how low, high, and mid change, and when the loop stops. Key moments clarify why we update low or high in certain ways and why the loop ends when low equals high. The visual quiz tests understanding of mid values, variable updates, and the effect of validity checks. This technique is useful for problems where the answer lies within a range and can be checked for validity efficiently.