LeetCode #1375 — MEDIUM

Number of Times Binary String Is Prefix-Aligned

Move from brute-force thinking to an efficient approach using array strategy.

The Problem

Problem Statement

You have a 1-indexed binary string of length n where all the bits are 0 initially. We will flip all the bits of this binary string (i.e., change them from 0 to 1) one by one. You are given a 1-indexed integer array flips where flips[i] indicates that the bit at index flips[i] will be flipped in the i^th step.

A binary string is prefix-aligned if, after the i^th step, all the bits in the inclusive range [1, i] are ones and all the other bits are zeros.

Return the number of times the binary string is prefix-aligned during the flipping process.

Example 1:

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

Step 01

Brute Force Baseline

Problem summary: You have a 1-indexed binary string of length n where all the bits are 0 initially. We will flip all the bits of this binary string (i.e., change them from 0 to 1) one by one. You are given a 1-indexed integer array flips where flips[i] indicates that the bit at index flips[i] will be flipped in the ith step. A binary string is prefix-aligned if, after the ith step, all the bits in the inclusive range [1, i] are ones and all the other bits are zeros. Return the number of times the binary string is prefix-aligned during the flipping process.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array

Example 1

[3,2,4,1,5]

Example 2

[4,1,2,3]

Core Insight

What unlocks the optimal approach

If in the step x all bulb shines then bulbs 1,2,3,..,x should shines too.

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Upper-end input sizes

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #1375: Number of Times Binary String Is Prefix-Aligned
class Solution {
    public int numTimesAllBlue(int[] flips) {
        int ans = 0, mx = 0;
        for (int i = 1; i <= flips.length; ++i) {
            mx = Math.max(mx, flips[i - 1]);
            if (mx == i) {
                ++ans;
            }
        }
        return ans;
    }
}

// Accepted solution for LeetCode #1375: Number of Times Binary String Is Prefix-Aligned
func numTimesAllBlue(flips []int) (ans int) {
	mx := 0
	for i, x := range flips {
		mx = max(mx, x)
		if mx == i+1 {
			ans++
		}
	}
	return
}

# Accepted solution for LeetCode #1375: Number of Times Binary String Is Prefix-Aligned
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

// Accepted solution for LeetCode #1375: Number of Times Binary String Is Prefix-Aligned
struct Solution;

impl Solution {
    fn num_times_all_blue(light: Vec<i32>) -> i32 {
        let n = light.len();
        let mut res = 0;
        let mut max = std::usize::MIN;
        for i in 0..n {
            max = max.max((light[i] - 1) as usize);
            if max == i {
                res += 1;
            }
        }
        res
    }
}

#[test]
fn test() {
    let light = vec![2, 1, 3, 5, 4];
    let res = 3;
    assert_eq!(Solution::num_times_all_blue(light), res);
    let light = vec![3, 2, 4, 1, 5];
    let res = 2;
    assert_eq!(Solution::num_times_all_blue(light), res);
    let light = vec![4, 1, 2, 3];
    let res = 1;
    assert_eq!(Solution::num_times_all_blue(light), res);
    let light = vec![2, 1, 4, 3, 6, 5];
    let res = 3;
    assert_eq!(Solution::num_times_all_blue(light), res);
    let light = vec![1, 2, 3, 4, 5, 6];
    let res = 6;
    assert_eq!(Solution::num_times_all_blue(light), res);
}

// Accepted solution for LeetCode #1375: Number of Times Binary String Is Prefix-Aligned
function numTimesAllBlue(flips: number[]): number {
    let ans = 0;
    let mx = 0;
    for (let i = 1; i <= flips.length; ++i) {
        mx = Math.max(mx, flips[i - 1]);
        if (mx === i) {
            ++ans;
        }
    }
    return ans;
}

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(n)

Space

O(1)

Approach Breakdown

BRUTE FORCE

O(n²) time

O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED

O(n) time

O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.