LeetCode #3211 — MEDIUM

Generate Binary Strings Without Adjacent Zeros

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

Solve on LeetCode

The Problem

Problem Statement

You are given a positive integer n.

A binary string x is valid if all substrings of x of length 2 contain at least one "1".

Return all valid strings with length n, in any order.

Example 1:

Input: n = 3

Output: ["010","011","101","110","111"]

Explanation:

The valid strings of length 3 are: "010", "011", "101", "110", and "111".

Example 2:

Input: n = 1

Output: ["0","1"]

Explanation:

The valid strings of length 1 are: "0" and "1".

Constraints:

1 <= n <= 18

Step 01

Brute Force Baseline

Problem summary: You are given a positive integer n. A binary string x is valid if all substrings of x of length 2 contain at least one "1". Return all valid strings with length n, in any order.

Baseline thinking

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

Pattern signal: Backtracking · Bit Manipulation

Example 1

Example 2

Core Insight

What unlocks the optimal approach

If we have a string <code>s</code> of length <code>x</code>, we can generate all strings of length <code>x + 1</code>.
If <code>s</code> has 0 as the last character, we can only append 1, whereas if the last character is 1, we can append both 0 and 1.
We can use recursion and backtracking to generate all such strings.

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 #3211: Generate Binary Strings Without Adjacent Zeros
class Solution {
    private List<String> ans = new ArrayList<>();
    private StringBuilder t = new StringBuilder();
    private int n;

    public List<String> validStrings(int n) {
        this.n = n;
        dfs(0);
        return ans;
    }

    private void dfs(int i) {
        if (i >= n) {
            ans.add(t.toString());
            return;
        }
        for (int j = 0; j < 2; ++j) {
            if ((j == 0 && (i == 0 || t.charAt(i - 1) == '1')) || j == 1) {
                t.append(j);
                dfs(i + 1);
                t.deleteCharAt(t.length() - 1);
            }
        }
    }
}

// Accepted solution for LeetCode #3211: Generate Binary Strings Without Adjacent Zeros
func validStrings(n int) (ans []string) {
	t := []byte{}
	var dfs func(int)
	dfs = func(i int) {
		if i >= n {
			ans = append(ans, string(t))
			return
		}
		for j := 0; j < 2; j++ {
			if (j == 0 && (i == 0 || t[i-1] == '1')) || j == 1 {
				t = append(t, byte('0'+j))
				dfs(i + 1)
				t = t[:len(t)-1]
			}
		}
	}
	dfs(0)
	return
}

# Accepted solution for LeetCode #3211: Generate Binary Strings Without Adjacent Zeros
class Solution:
    def validStrings(self, n: int) -> List[str]:
        def dfs(i: int):
            if i >= n:
                ans.append("".join(t))
                return
            for j in range(2):
                if (j == 0 and (i == 0 or t[i - 1] == "1")) or j == 1:
                    t.append(str(j))
                    dfs(i + 1)
                    t.pop()

        ans = []
        t = []
        dfs(0)
        return ans

// Accepted solution for LeetCode #3211: Generate Binary Strings Without Adjacent Zeros
/**
 * [3211] Generate Binary Strings Without Adjacent Zeros
 */
pub struct Solution {}

// submission codes start here

impl Solution {
    pub fn valid_strings(n: i32) -> Vec<String> {
        let n = n as usize;
        let mut result = Vec::new();
        let mut str = vec!['0'; n];

        Self::dfs(0, false, &mut str, &mut result);

        result
    }

    fn dfs(i: usize, last_zero: bool, str: &mut Vec<char>, result: &mut Vec<String>) {
        if i >= str.len() {
            result.push(str.iter().collect());
            return;
        }

        if !last_zero {
            str[i] = '0';
            Self::dfs(i + 1, true, str, result);
        }

        str[i] = '1';
        Self::dfs(i + 1, false, str, result);
    }
}

// submission codes end

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_3211() {
        assert_eq!(
            vec_string!("010", "011", "101", "110", "111"),
            Solution::valid_strings(3)
        );
        assert_eq!(vec_string!("0", "1"), Solution::valid_strings(1));
    }
}

// Accepted solution for LeetCode #3211: Generate Binary Strings Without Adjacent Zeros
function validStrings(n: number): string[] {
    const ans: string[] = [];
    const t: string[] = [];
    const dfs = (i: number) => {
        if (i >= n) {
            ans.push(t.join(''));
            return;
        }
        for (let j = 0; j < 2; ++j) {
            if ((j == 0 && (i == 0 || t[i - 1] == '1')) || j == 1) {
                t.push(j.toString());
                dfs(i + 1);
                t.pop();
            }
        }
    };
    dfs(0);
    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(n)

Approach Breakdown

EXHAUSTIVE

O(nⁿ) time

O(n) space

Generate every possible combination without any filtering. At each of n positions we choose from up to n options, giving nⁿ total candidates. Each candidate takes O(n) to validate. No pruning means we waste time on clearly invalid partial solutions.

BACKTRACKING + PRUNING

O(n!) time

O(n) space

Backtracking explores a decision tree, but prunes branches that violate constraints early. Worst case is still factorial or exponential, but pruning dramatically reduces the constant factor in practice. Space is the recursion depth (usually O(n) for n-level decisions).

Shortcut: Backtracking time = size of the pruned search tree. Focus on proving your pruning eliminates most branches.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Missing undo step on backtrack

Wrong move: Mutable state leaks between branches.

Usually fails on: Later branches inherit selections from earlier branches.

Fix: Always revert state changes immediately after recursive call.