1. 2^n masks
Shifting 1 left by n gives 2^n, the number of subsets.
const total = 1 << nums.lengthTyporithm · medium
Subsets via Bitmask
▷ Interactive algorithm labsubsets-bitmaskbit-manipulationbitmaskenumeratemembership
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Step 1 of 8 · intro card
Learn Subsets via Bitmask
Bit Manipulation
Each integer mask from 0 to 2^n-1 encodes a subset; bit i decides if nums[i] is included.
There are exactly 2^n subsets, one for every n-bit binary number.
Looping masks from 0 to 2^n-1 enumerates all of them with no recursion.
For each mask, a set bit at position i means the ith element is in that subset.
Preparing algorithm lab…
01
2^n masks = 2^n subsets.
02
Bit i selects nums[i].
03
Iterative, no recursion.
function subsets(nums) {
const result = [];
const total = 1 << nums.length;
for (let mask = 0; mask < total; mask += 1) {
const subset = [];
for (let i = 0; i < nums.length; i += 1) {
if (mask & (1 << i)) {
subset.push(nums[i]);
}
}
result.push(subset);
}
return result;
}Read the implementation
Connect each part of the code to the concept before you type.
2. Each mask
Every integer from 0 to 2^n-1 encodes one subset.
for (let mask = 0; mask < total; mask += 1)3. Bit i set?
Bit i of the mask decides whether nums[i] is in the subset.
if (mask & (1 << i))4. Include element
A set bit means include the corresponding element.
subset.push(nums[i])A complete learning loop
01
Understand
Read the concept map and follow the code breakdown.
02
Reconstruct
Type the implementation, repair mistakes and work through every recall exercise.
03
Verify
Use the final check without hints; revisit weak concepts in short practice sessions.