Definition
n = k³
Includes positive, negative, and zero values.
Check Cube Number in Java
Overview
What You’ll Learn
A perfect cube is an integer n = k3 for some integer k. This tutorial covers float estimate + verify, pure integer search, binary search, a live preview, worked Java examples, edge cases, and complexity.
Estimate + Verify
Math.cbrt
Round the cube root, then check k * k * k == n.
Integer Scan
No float
Grow k until k³ ≥ |n|, then test equality.
Binary Search
O(log |n|)
Faster integer route for large magnitudes.
Live Preview
Try any n
Classify positive, negative, and zero instantly.
Float Pitfall
Always verify
Never trust a floating estimate alone.
Introduction
Perfect cubes (cube numbers) are integers of the form n = k3. Classic examples: 0, 1, 8, 27, 64 and negatives like -8, -27.
A practical check estimates an integer cube root, then verifies with exact integer multiplication. You can also avoid floating point entirely with a linear or binary search on k.
Why it matters?
It drills integer roots, sign handling, floating-point caution, and search-based number checks.
Key Highlights
Integer k Exists
n equals some integer cubed.
Verify Always
Final check: k * k * k == n.
Signs Matter
Odd powers keep negatives as cubes.
0 and 1 Count
Both are perfect cubes.
In short: find a candidate integer root k, then accept n only if k³ == n exactly.
Foundation
📝 Problem & Approach
Given an integer n, decide whether n = k3 for some integer k.
java
// 27 = 3^3 → yes
// 28 sits between 3^3 and 4^3 → no
// -8 = (-2)^3 → yesInputs & Outputs
| Item | Type | Description |
|---|---|---|
n | int | Any integer (positive, negative, or zero). |
| Return / print | bool / text | true if n is a perfect cube. |
Minimal workflow
Pseudocode (integer route)
function isPerfectCube(n):
x = Math.abs(n)
k = 0
while k * k * k < x:
k = k + 1
return k * k * k == xMethod comparison
| Method | Idea | Notes |
|---|---|---|
| Root + verify | Math.cbrt(|n|), then k³ == n | Fast; watch float precision |
| Linear scan | Increment k until k³ ≥ |n| | No float; O(|n|^(1/3)) |
| Binary search | Search k on [0, |n|] | O(log |n|) integer route |
Cheat Sheet
⚡ Quick Reference
| Goal | Pattern |
|---|---|
| Estimate root | k = Math.round(Math.cbrt(Math.abs(n))) |
| Apply sign | if (n < 0) k = -k; |
| Exact verify | k * k * k == n |
| Integer scan | while (k * k * k < x) k++; |
| Classic yes | 27 = 3³, -8 = (-2)³ |
| Classic no | 28 (between 27 and 64) |
Compare
📋 Float Estimate vs Linear Scan vs Binary Search
Same yes/no answer — different precision and speed trade-offs.
Float estimate
round + verifyShort; must verify in integer arithmetic
Linear scan
grow kNo float; simple for interviews
Binary search
O(log |n|)Best pure-integer route for large n
Interview tip
verify alwaysSay why floating estimate alone is unsafe
Context
When This Problem Shows Up
Reach for perfect-cube checks when integer roots and precision matter.
Interview warm-ups
Tests roots, signs, and float-vs-integer reasoning.
Sibling of square checks
Same pattern as perfect-square problems, with odd powers.
Range / filter tasks
List cubes in 1…N for small classroom ranges.
Precision discussions
Great prompt for “why verify after float math?”
Not for float cubes alone
Perfect-cube interviews usually mean integer n and integer k.
Key benefit: one short boolean check that covers roots, signs, float caution, and search complexity.
Interactive
🔮 Live Preview
JavaScript safe integers. Uses integer scan on absolute value, then applies sign logic.
Hands-On
Examples Gallery
Three complete Java programs — float estimate + verify, integer range scan, and binary search. Click View Output to reveal sample console results.
📚 Getting Started
Estimate an integer root, then verify exactly.
Example 1 — Cube-Root Estimate + Integer Verification
Fast for one value. Round the floating cube root, then confirm with integer multiplication.
java
public class Main {
static boolean isCube(int number) {
long k = Math.round(Math.cbrt(Math.abs((long) number)));
if (number < 0) {
k = -k;
}
return k * k * k == number;
}
public static void main(String[] args) {
int inputNumber = 27;
if (isCube(inputNumber)) {
System.out.println(inputNumber + " is a cube number.");
} else {
System.out.println(inputNumber + " is not a cube number.");
}
}
}How It Works
The rounded root is only a candidate. The final check k * k * k == number is what guarantees correctness, including for negatives.
⚡ Pure Integer Range
No floating point — scan and filter a small interval.
Example 2 — Integer Scan: Cubes from 1 to 50
Grow k until k³ ≥ num; equality means a perfect cube.
java
public class Main {
static boolean isCubeNumber(int num) {
int k = 0;
while ((long) k * k * k < num) {
k++;
}
return (long) k * k * k == num;
}
public static void main(String[] args) {
System.out.println("Cube numbers in the range 1 to 50:");
for (int i = 1; i <= 50; i++) {
if (isCubeNumber(i)) {
System.out.print(i + " ");
}
}
}
}How It Works
The loop finds the smallest k with k³ ≥ num. From 1 to 50 the cubes are exactly 1, 8, and 27.
⚙️ Faster Integer Route
Binary search on k for large magnitudes.
Example 3 — Binary Search on Cube Root
Search k on [0, |n|] and verify equality; apply sign for negatives.
java
public class Main {
static boolean isCubeBinary(int n) {
long x = Math.abs((long) n);
long lo = 0;
long hi = x;
while (lo <= hi) {
long mid = (lo + hi) / 2;
long cube = mid * mid * mid;
if (cube == x) {
return true;
}
if (cube < x) {
lo = mid + 1;
} else {
hi = mid - 1;
}
}
return false;
}
public static void main(String[] args) {
int[] values = {27, 28, -8, 0, 64};
for (int value : values) {
System.out.println(value + ": " + (isCubeBinary(value) ? "cube" : "not a cube"));
}
}
}How It Works
Because x ≥ 0, searching nonnegative k is enough; odd powers mean negatives are cubes whenever |n| is. Each step halves the search range — O(log |n|) comparisons.
🧠 How the Algorithm Decides
1
Take magnitude
Work with x = |n| (0 is immediately a cube).
Normalize
2
Find candidate k
Estimate with float, scan linearly, or binary-search.
Search
3
Cube and compare
Accept only if k * k * k equals |n| (then restore sign conceptually).
Verify
=
Yes or no
Equality → perfect cube; otherwise not.
Trace
🔎 Worked Walkthrough — n = 28
Trace the integer scan. Cubes nearby: 27 = 3³, 64 = 4³.
| k | k³ | Compare to 28 | Action |
|---|---|---|---|
0 | 0 | < 28 | Increment |
1 | 1 | < 28 | Increment |
2 | 8 | < 28 | Increment |
3 | 27 | < 28 | Increment |
4 | 64 | > 28 | Stop; 64 ≠ 28 |
Final: 28 is not a perfect cube.
Use Cases
Where perfect-cube checks show up beyond the interview prompt.
1. Interview Warm-Ups
Roots, signs, and verify-after-estimate in one problem.
Example: write isCube(n).
2. Teaching Integer Powers
Makes 1, 8, 27, 64… memorable with counterexamples.
Example: chalkboard 27 vs 28.
3. Float Safety Lessons
Shows why estimates need an exact check.
Example: “is round enough?”
4. Range Filters
Print cubes in a classroom interval.
Example: 1 to 50 → 1 8 27.
5. Binary-Search Practice
Monotone k³ is a clean search predicate.
Example: find integer cube root.
6. Factorization Follow-Ups
Exponents divisible by 3 ↔ perfect cube.
Example: prime-factor argument.
Pro Tip: always say “estimate, then verify with integer cube” — that sentence scores well in interviews.
Advantages
Why this pattern works well in interviews and classwork.
1. Clear Definition
n = k³ is easy to state and test.
2. Multiple Valid Methods
Float estimate, linear scan, or binary search all work.
3. Tiny Extra Memory
A few integers suffice — O(1) extra space.
4. Rich Edge Cases
Negatives, zero, and float precision give structured follow-ups.
Pro Tip: prefer k * k * k over Math.pow(k, 3) in interviews when discussing overflow in fixed-width languages.
Usage Tips
Small habits that keep cube checks interview-ready.
1. Always Verify
Never accept a floating estimate without
k³ == n.2. Handle Signs
Negate k when n is negative for the estimate method.
3. Mention Zero
0 = 0³ — include it in tests.
4. Spot-Check Classics
Assert 27 and -8 are cubes; 28 is not.
5. Offer Binary Search
Upgrade from linear scan when |n| can be huge.
Pro Tip: for the scan method, searching |n| is enough — odd powers make negatives automatic.
Common Pitfalls
Mistakes that commonly break perfect-cube solutions.
1. Trusting Float Alone
Near-boundary roots can round wrong for large n.
→ Always verify with integer cubing.
2. Rejecting Negatives
-8 and -27 are perfect cubes.
→ Preserve sign or search on absolute value.
3. Forgetting Zero
0 = 0³ is a valid cube.
→ Include n = 0 in your tests.
4. Comparing to Float Cubes
Checking
Math.pow(root, 3) == nin float can fail.→ Cubing must happen with integers.
5. Linear Scan on Huge n
O(|n|^(1/3)) can be slow for large magnitudes.
→ Offer binary search as an upgrade.
Edge Cases
Check these inputs before calling the solution done.
Sign
Negative cubes
Negative perfect cubes exist (-8, -27). Preserve sign correctly.
Zero
n = 0
Always a cube because 0 = 0³.
Float
Precision limits
For very large magnitudes, floating-point root may be slightly off.
Near miss
28, 26
Neighbors of 27 are not cubes — good counterexamples.
One
n = 1
1 = 1³ — smallest positive cube.
Performance
Linear scan cost
Grows with |n|^(1/3). Use binary search if needed.
Math
⚖️ Facts Worth Knowing
Handy follow-ups interviewers sometimes ask.
- Prime factors. Nonzero n is a cube iff every exponent in its factorization is a multiple of 3.
- Spacing. Cubes spread quickly: gaps grow like ~3k² between consecutive cubes.
- Odd powers. Cubes (unlike squares) can be negative.
- Monotone search. k ↦ k³ is strictly increasing for k ≥ 0 — binary search is valid.
Drill
🎯 Practice Problems
Try these variations to lock in the pattern.
1. Verify classics
- 27, -8, 0, 1 → yes
- 28, 9, -7 → no
2. Match methods
- Estimate vs scan vs binary
- Assert identical results
3. Range 1 to 200
- List all perfect cubes
- Expect 1, 8, 27, 64, 125
4. Return the root
- If cube, return k
- Else return None
Important
Notes
- Definition: n is a perfect cube if n = k³ for some integer k.
- Methods: root estimate + integer verify, linear scan, or binary search.
- Watch-outs: negatives, zero, and floating-point precision.
- State O(1)-style estimate, O(|n|^(1/3)) scan, or O(log |n|) binary search.
Quick Takeaway: find a candidate integer k, then accept n only if k * k * k == n.
Analysis
⏱️ Time and Space Complexity
| Method | Time | Extra space |
|---|---|---|
| Root estimate + verify | O(1) style | O(1) |
| Linear integer scan | O(|n|^(1/3)) | O(1) |
| Binary search on k | O(log |n|) | O(1) |
For scan-based methods, n denotes input magnitude and root growth is about |n|^(1/3).
🎉 Conclusion
A perfect cube is an integer n = k³. Estimate a root if you like, but always verify with exact integer cubing — or skip floats with a scan / binary search.
Practice the three examples above, then continue to decimal-to-binary for another classic conversion warm-up.
Handle negatives and zero, never trust float alone, and mention binary search for large |n|.
Pro Tips
💡 Best Practices
✅ Do
- Verify with integer cubing
- Handle negatives and zero
- Test 27, -8, and 28
- Mention float precision risk
- Offer binary search for large n
❌ Don’t
- Trust Math.round(Math.cbrt(...)) alone
- Reject negative cubes
- Forget n = 0
- Compare using float cubes
- Ignore O(|n|^(1/3)) cost
Summary
Key Takeaways
Knowledge Unlocked
Five things to remember about cube numbers
Check perfect cubes the interview-friendly way.
5
Core concepts 01
Rule
n = k³
Definition 02
Verify
k*k*k == n
Guard 03
Signs
Negatives OK
Math 04
Zero
0 is a cube
Edge 05
Speed
Binary O(log)
Analysis❓ Frequently Asked Questions
An integer n is a perfect cube if n = k^3 for some integer k. Examples: 0 = 0^3, 1 = 1^3, 8 = 2^3, 27 = 3^3, -8 = (-2)^3.
Floating-point values can be close to an integer but not exact. The safe approach is: estimate k, then verify k*k*k == n in integer arithmetic.
Yes for very large values. For typical interview-sized integers, Math.round(Math.cbrt(Math.abs(n))) plus final integer verification is usually fine.
Yes. Use an integer loop (or binary search) to find k such that k^3 reaches |n|, then compare.
Yes. 0 = 0^3, so it is a perfect cube.
It runs in O(|n|^(1/3)) iterations because k grows until k^3 is at least |n|.
Yes. Odd powers preserve sign, so -8 = (-2)^3 is a perfect cube.
When |n| is huge and a linear scan of k would be too slow — binary search finds k in O(log |n|) steps.
Did you Know? 🔊
A nonzero integer n is a perfect cube iff in its prime factorization every exponent is a multiple of three. Also, 0 and 1 are perfect cubes.
Continue to Decimal to Binary
Learn how to convert decimal integers to binary with loops and built-ins.
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