LeetCode #1016 — MEDIUM

Binary String With Substrings Representing 1 To N

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

The Problem

Problem Statement

Given a binary string s and a positive integer n, return true if the binary representation of all the integers in the range [1, n] are substrings of s, or false otherwise.

A substring is a contiguous sequence of characters within a string.

Example 1:

Input: s = "0110", n = 3
Output: true

Example 2:

Input: s = "0110", n = 4
Output: false

Constraints:

1 <= s.length <= 1000
s[i] is either '0' or '1'.
1 <= n <= 10⁹

Step 01

Brute Force Baseline

Problem summary: Given a binary string s and a positive integer n, return true if the binary representation of all the integers in the range [1, n] are substrings of s, or false otherwise. A substring is a contiguous sequence of characters within a string.

Baseline thinking

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

Pattern signal: Hash Map · Bit Manipulation · Sliding Window

Example 1

"0110"
3

Example 2

"0110"
4

Step 02

Core Insight

What unlocks the optimal approach

We only need to check substrings of length at most 30, because 10^9 has 30 bits.

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 #1016: Binary String With Substrings Representing 1 To N
class Solution {
    public boolean queryString(String s, int n) {
        if (n > 1000) {
            return false;
        }
        for (int i = n; i > n / 2; i--) {
            if (!s.contains(Integer.toBinaryString(i))) {
                return false;
            }
        }
        return true;
    }
}

// Accepted solution for LeetCode #1016: Binary String With Substrings Representing 1 To N
func queryString(s string, n int) bool {
	if n > 1000 {
		return false
	}
	for i := n; i > n/2; i-- {
		if !strings.Contains(s, strconv.FormatInt(int64(i), 2)) {
			return false
		}
	}
	return true
}

# Accepted solution for LeetCode #1016: Binary String With Substrings Representing 1 To N
class Solution:
    def queryString(self, s: str, n: int) -> bool:
        if n > 1000:
            return False
        return all(bin(i)[2:] in s for i in range(n, n // 2, -1))

// Accepted solution for LeetCode #1016: Binary String With Substrings Representing 1 To N
impl Solution {
    pub fn query_string(s: String, n: i32) -> bool {
        if n > 1000 {
            return false;
        }
        for i in (n / 2 + 1..=n).rev() {
            if !s.contains(&format!("{:b}", i)) {
                return false;
            }
        }
        true
    }
}

// Accepted solution for LeetCode #1016: Binary String With Substrings Representing 1 To N
function queryString(s: string, n: number): boolean {
    if (n > 1000) {
        return false;
    }
    for (let i = n; i > n / 2; --i) {
        if (s.indexOf(i.toString(2)) === -1) {
            return false;
        }
    }
    return true;
}

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(m^2 × log m)

Space

O(log n)

Approach Breakdown

SORT + SCAN

O(n log n) time

O(n) space

Sort the array in O(n log n), then scan for the missing or unique element by comparing adjacent pairs. Sorting requires O(n) auxiliary space (or O(1) with in-place sort but O(n log n) time remains). The sort step dominates.

BIT MANIPULATION

O(n) time

O(1) space

Bitwise operations (AND, OR, XOR, shifts) are O(1) per operation on fixed-width integers. A single pass through the input with bit operations gives O(n) time. The key insight: XOR of a number with itself is 0, which eliminates duplicates without extra space.

Shortcut: Bit operations are O(1). XOR cancels duplicates. Single pass → O(n) time, O(1) space.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Mutating counts without cleanup

Wrong move: Zero-count keys stay in map and break distinct/count constraints.

Usually fails on: Window/map size checks are consistently off by one.

Fix: Delete keys when count reaches zero.

Shrinking the window only once

Wrong move: Using `if` instead of `while` leaves the window invalid for multiple iterations.

Usually fails on: Over-limit windows stay invalid and produce wrong lengths/counts.

Fix: Shrink in a `while` loop until the invariant is valid again.