LeetCode #2166 — MEDIUM

Design Bitset

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

Solve on LeetCode
The Problem

Problem Statement

A Bitset is a data structure that compactly stores bits.

Implement the Bitset class:

  • Bitset(int size) Initializes the Bitset with size bits, all of which are 0.
  • void fix(int idx) Updates the value of the bit at the index idx to 1. If the value was already 1, no change occurs.
  • void unfix(int idx) Updates the value of the bit at the index idx to 0. If the value was already 0, no change occurs.
  • void flip() Flips the values of each bit in the Bitset. In other words, all bits with value 0 will now have value 1 and vice versa.
  • boolean all() Checks if the value of each bit in the Bitset is 1. Returns true if it satisfies the condition, false otherwise.
  • boolean one() Checks if there is at least one bit in the Bitset with value 1. Returns true if it satisfies the condition, false otherwise.
  • int count() Returns the total number of bits in the Bitset which have value 1.
  • String toString() Returns the current composition of the Bitset. Note that in the resultant string, the character at the ith index should coincide with the value at the ith bit of the Bitset.

Example 1:

Input
["Bitset", "fix", "fix", "flip", "all", "unfix", "flip", "one", "unfix", "count", "toString"]
[[5], [3], [1], [], [], [0], [], [], [0], [], []]
Output
[null, null, null, null, false, null, null, true, null, 2, "01010"]

Explanation
Bitset bs = new Bitset(5); // bitset = "00000".
bs.fix(3);     // the value at idx = 3 is updated to 1, so bitset = "00010".
bs.fix(1);     // the value at idx = 1 is updated to 1, so bitset = "01010". 
bs.flip();     // the value of each bit is flipped, so bitset = "10101". 
bs.all();      // return False, as not all values of the bitset are 1.
bs.unfix(0);   // the value at idx = 0 is updated to 0, so bitset = "00101".
bs.flip();     // the value of each bit is flipped, so bitset = "11010". 
bs.one();      // return True, as there is at least 1 index with value 1.
bs.unfix(0);   // the value at idx = 0 is updated to 0, so bitset = "01010".
bs.count();    // return 2, as there are 2 bits with value 1.
bs.toString(); // return "01010", which is the composition of bitset.

Constraints:

  • 1 <= size <= 105
  • 0 <= idx <= size - 1
  • At most 105 calls will be made in total to fix, unfix, flip, all, one, count, and toString.
  • At least one call will be made to all, one, count, or toString.
  • At most 5 calls will be made to toString.
Patterns Used

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: A Bitset is a data structure that compactly stores bits. Implement the Bitset class: Bitset(int size) Initializes the Bitset with size bits, all of which are 0. void fix(int idx) Updates the value of the bit at the index idx to 1. If the value was already 1, no change occurs. void unfix(int idx) Updates the value of the bit at the index idx to 0. If the value was already 0, no change occurs. void flip() Flips the values of each bit in the Bitset. In other words, all bits with value 0 will now have value 1 and vice versa. boolean all() Checks if the value of each bit in the Bitset is 1. Returns true if it satisfies the condition, false otherwise. boolean one() Checks if there is at least one bit in the Bitset with value 1. Returns true if it satisfies the condition, false otherwise. int count() Returns the total number of bits in the Bitset which have value 1. String toString() Returns

Baseline thinking

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

Pattern signal: Array · Hash Map · Design

Example 1

["Bitset","fix","fix","flip","all","unfix","flip","one","unfix","count","toString"]
[[5],[3],[1],[],[],[0],[],[],[0],[],[]]

Related Problems

  • Design Underground System (design-underground-system)
Step 02

Core Insight

What unlocks the optimal approach

  • Note that flipping a bit twice does nothing.
  • In order to determine the value of a bit, consider how you can efficiently count the number of flips made on the bit since its latest update.
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. 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 #2166: Design Bitset
class Bitset {
    private char[] a;
    private char[] b;
    private int cnt;

    public Bitset(int size) {
        a = new char[size];
        b = new char[size];
        Arrays.fill(a, '0');
        Arrays.fill(b, '1');
    }

    public void fix(int idx) {
        if (a[idx] == '0') {
            a[idx] = '1';
            ++cnt;
        }
        b[idx] = '0';
    }

    public void unfix(int idx) {
        if (a[idx] == '1') {
            a[idx] = '0';
            --cnt;
        }
        b[idx] = '1';
    }

    public void flip() {
        char[] t = a;
        a = b;
        b = t;
        cnt = a.length - cnt;
    }

    public boolean all() {
        return cnt == a.length;
    }

    public boolean one() {
        return cnt > 0;
    }

    public int count() {
        return cnt;
    }

    public String toString() {
        return String.valueOf(a);
    }
}

/**
 * Your Bitset object will be instantiated and called as such:
 * Bitset obj = new Bitset(size);
 * obj.fix(idx);
 * obj.unfix(idx);
 * obj.flip();
 * boolean param_4 = obj.all();
 * boolean param_5 = obj.one();
 * int param_6 = obj.count();
 * String param_7 = obj.toString();
 */
Step 06

Interactive Study Demo

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

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(1) per op
Space
O(n)

Approach Breakdown

NAIVE
O(n) per op time
O(n) space

Use a simple list or array for storage. Each operation (get, put, remove) requires a linear scan to find the target element — O(n) per operation. Space is O(n) to store the data. The linear search makes this impractical for frequent operations.

OPTIMIZED DESIGN
O(1) per op time
O(n) space

Design problems target O(1) amortized per operation by combining data structures (hash map + doubly-linked list for LRU, stack + min-tracking for MinStack). Space is always at least O(n) to store the data. The challenge is achieving constant-time operations through clever structure composition.

Shortcut: Combine two data structures to get O(1) for each operation type. Space is always O(n).
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.

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.