#1375

Medium

auto_awesomeArray-driven solution strategy

LeetCode Problem Workspace

Number of Times Binary String Is Prefix-Aligned

Count how many times a 1-indexed binary string becomes prefix-aligned as bits are flipped sequentially using an array-driven strategy.

array

Problem Statement

You are given a 1-indexed binary string of length n initialized with all zeros. An integer array flips of length n is provided where flips[i] indicates the bit to flip from 0 to 1 at step i.

A binary string is prefix-aligned at step i if all bits in positions 1 through i are 1 and all remaining bits are 0. Return the total number of steps where the string is prefix-aligned during the flipping process.

Examples

Example 1

Input: flips = [3,2,4,1,5]

Output: 2

The binary string is initially "00000". After applying step 1: The string becomes "00100", which is not prefix-aligned. After applying step 2: The string becomes "01100", which is not prefix-aligned. After applying step 3: The string becomes "01110", which is not prefix-aligned. After applying step 4: The string becomes "11110", which is prefix-aligned. After applying step 5: The string becomes "11111", which is prefix-aligned. We can see that the string was prefix-aligned 2 times, so we return 2.

Example 2

Input: flips = [4,1,2,3]

Output: 1

The binary string is initially "0000". After applying step 1: The string becomes "0001", which is not prefix-aligned. After applying step 2: The string becomes "1001", which is not prefix-aligned. After applying step 3: The string becomes "1101", which is not prefix-aligned. After applying step 4: The string becomes "1111", which is prefix-aligned. We can see that the string was prefix-aligned 1 time, so we return 1.

Constraints

n == flips.length
1 <= n <= 5 * 104
flips is a permutation of the integers in the range [1, n].

Solution Approach

Track Maximum Index Flipped

Iterate through flips while keeping track of the highest index flipped so far. If this maximum equals the current step number, the prefix is aligned. This method directly applies the array-driven solution strategy by using the sequence of flips to monitor alignment efficiently.

Increment Counter on Alignment

Each time the maximum flipped index equals the current step, increment a counter. This ensures that only steps where all preceding bits are set are counted, avoiding unnecessary array scans.

Return Total Alignment Count

After processing all flips, return the counter. This produces the number of prefix-aligned moments, capturing the key pattern where the string transitions to a full prefix of ones.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

Time complexity is O(n) because each flip is processed once and only simple max comparisons are performed. Space complexity is O(1) since no additional structures beyond counters are needed.

What Interviewers Usually Probe

Tracking maximum flipped index indicates you understand the prefix alignment property.
Recognizing that step count equals maximum flipped index signals optimal use of array-driven checks.
Using a single pass with minimal storage demonstrates efficiency in handling the array pattern.

Common Pitfalls or Variants

Common pitfalls

Checking all bits at each step instead of tracking max index can lead to O(n^2) time.
Misinterpreting 1-indexed positions can cause off-by-one errors in alignment detection.
Counting alignment at incorrect steps, ignoring that only max index equal to step matters.

Follow-up variants

Count prefix-aligned moments in a binary string where flips can include repeated indices.
Determine moments of suffix alignment where the trailing bits are all ones after each flip.
Compute prefix-aligned moments with a dynamic stream of flips arriving in real time.

FAQ

What does prefix-aligned mean in this problem?

A binary string is prefix-aligned if all bits from position 1 to the current step are 1, and all remaining bits are 0.

How do I efficiently detect prefix alignment using the flips array?

Track the maximum index flipped at each step; if it equals the step number, the string is prefix-aligned.

Does the array-driven solution require extra space?

No, it only needs counters for maximum flipped index and total aligned moments, keeping space O(1).

Why is it important that flips is 1-indexed?

Because the prefix alignment check relies on comparing the step number with indices directly, matching 1-based positions.

Can GhostInterview help me understand the Number of Times Binary String Is Prefix-Aligned problem pattern?

Yes, it highlights the key array-driven pattern, guiding step-by-step through maximum index tracking and alignment counting.

terminal

Solution

Solution 1: Direct Traversal

We can traverse the array $flips$, keeping track of the maximum value $mx$ of the elements we have traversed so far. If $mx$ equals the current index $i$ we are traversing, it means that the first $i$ elements have all been flipped, i.e., the prefix is consistent, and we increment the answer.

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class Solution:
    def numTimesAllBlue(self, flips: List[int]) -> int:
        ans = mx = 0
        for i, x in enumerate(flips, 1):
            mx = max(mx, x)
            ans += mx == i
        return ans

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