Number of Times Binary String Is Prefix-Aligned

Number of Times Binary String Is Prefix-Aligned

What is this problem about?

The Number of Times Binary String Is Prefix-Aligned problem gives you a sequence of flip operations on a binary string (initially all 0s). Each operation flips bit at a given position. After each flip, check if the string is "prefix-aligned" — meaning the first k bits are all 1s and the rest are 0s for some k ≥ 0. Count the number of times this condition holds. This coding problem requires tracking the maximum flipped position vs. the count of flipped bits.

Why is this asked in interviews?

Microsoft asks this to test the elegant observation: the string is prefix-aligned after n operations if and only if max(flipped positions so far) == count of operations so far. This one-liner insight separates candidates who simulate from those who reason mathematically. The array interview pattern is demonstrated with a mathematical shortcut.

Algorithmic pattern used

Track max position and step count. After each flip operation at position p: update max_pos = max(max_pos, p). The string is prefix-aligned if max_pos == current_step (meaning all positions 1..max_pos have been flipped, since max_pos must equal count of unique positions flipped so far). Increment count when this holds.

Example explanation

flips = [3,2,4,1,5]. (1-indexed positions)

• After flip 3: max=3, step=1. 3≠1. Not aligned.
• After flip 2: max=3, step=2. 3≠2. Not aligned.
• After flip 4: max=4, step=3. 4≠3. Not aligned.
• After flip 1: max=4, step=4. 4==4. Aligned! Count=1.
• After flip 5: max=5, step=5. 5==5. Aligned! Count=2. Answer = 2.

Common mistakes candidates make

• Simulating the actual binary string and checking prefix alignment each time.
• Using 0-indexed positions when problem uses 1-indexed.
• Not recognizing the max_pos == step_count equivalence.
• Checking all flipped positions manually instead of just tracking max.

Interview preparation tip

Prefix alignment problems often have elegant mathematical characterizations. The insight here: the string is prefix-aligned iff every position from 1 to max has been flipped. Since each position is flipped exactly once, this holds iff max_pos == number of flips so far. Practice finding these "one-liner condition" problems — they reward mathematical observation over simulation and are often the type of problem that gets candidates hired quickly.