Binary Search on Answer Technique in DSA Typescript - Execution Trace

Concept Flow - Binary Search on Answer Technique

Set low and high bounds for answer

↓

Calculate mid = (low + high) / 2

↓

Check if mid is a valid answer

↓

Update high = mid

↓

Repeat until low >= high

↓

Return low as answer

This flow shows how we guess an answer between low and high, check if it works, then narrow the range until we find the best answer.

Execution Sample

DSA Typescript

function canPlace(mid: number): boolean {
  // Check if mid satisfies problem condition
  return true; // placeholder implementation
}

let low = 1, high = 10;
while (low < high) {
  let mid = Math.floor((low + high) / 2);
  if (canPlace(mid)) high = mid;
  else low = mid + 1;
}
return low;

This code tries to find the smallest number between 1 and 10 that satisfies canPlace.

Execution Table

Step	Operation	low	high	mid	canPlace(mid)	Action	Range After Action
1	Initialize low and high	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 loop	[7, 7]
7	Return answer	7	7	-	-	Answer = 7	[7]

💡 Loop stops when low equals high, meaning the smallest valid answer is found.

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	-	-
canPlace(mid)	-	false	true	true	false	-	-

Key Moments - 3 Insights

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

Because mid does not satisfy the condition, 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 canPlace(mid) is true?

Because mid satisfies the condition, so the answer could be mid or smaller. We narrow the search by setting high to mid, as seen in steps 3 and 4.

Why does the loop stop when low equals high?

Because the search space is reduced to one number, which must be the smallest valid answer. This is shown in step 6.

Visual Quiz - 3 Questions

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

A 7

B 6

C 8

D 5

💡 Hint

Check the 'mid' column in the execution table at step 4.

At which step does 'low' first become greater than 5?

A Step 3

B Step 5

C Step 2

D Step 4

💡 Hint

Look at the 'low' values in the variable tracker after each step.

If canPlace(mid) was always true, what would happen to 'high'?

A It would stay the same

B It would decrease

C It would increase

D It would become equal to low immediately

💡 Hint

Refer to the action column in the execution table when canPlace(mid) is true.

Concept Snapshot

Binary Search on Answer Technique:
- Set low and high bounds for possible answers.
- Calculate mid = (low + high) / 2.
- Check if mid satisfies the condition (canPlace).
- If yes, move high to mid to find smaller answer.
- If no, move low to mid + 1 to find larger answer.
- Repeat until low == high, which is the answer.

Full Transcript

Binary Search on Answer Technique is a way to find the smallest or largest value that meets a condition. We start with a low and high range. We pick the middle value and check if it works. If it does, we try smaller values by moving the high down. If it doesn't, we try bigger values by moving the low up. We repeat this until low and high meet. The final low is the answer. This method helps solve problems where direct search is slow but checking a guess is fast.