Largest Number
A medium Greedy problem included in Love Babbar 450, Striver A2Z. Below: the roles whose interviews prioritise this topic, and how to practise it.
- Topic
- Greedy
- Sheets
- 2
- Core for
- 3 roles
- Platform
- LeetCode
The problem
Given a list of non-negative integers, arrange them such that they form the largest possible number and return it as a string.
Example 1
- Input
- nums = [10,2]
- Output
- "210"
- Why
- The arrangement [2,10] gives "210" which is larger than "102".
Example 2
- Input
- nums = [3,30,34,5,9]
- Output
- "9534330"
- Why
- The largest arrangement of these numbers is "9534330".
Constraints
- 1 <= nums.length <= 100
- 0 <= nums[i] <= 10^9
How to think about it
Updated 2026-09-09Standard numerical or alphabetical sorting fails when comparing numbers of different lengths like 3 and 30. Comparing pairwise concatenations `a + b` against `b + a` directly answers which number belongs ahead of the other in the final sequence.
Approaches, worst first
Permute all arrangements
time O(n! * n) · space O(n! * n)
Generate every permutation of the numbers, convert each to string, and identify the lexicographically largest. Factorial explosion makes this unusable beyond ten numbers.
Custom comparator sortWrite this one
time O(n log n * k) · space O(n * k)
Convert each number to a string and sort using a comparator that checks if `b + a` is larger than `a + b`. Concatenate sorted strings. This pairwise relation is transitive and guarantees the global optimum.
Where people lose marks · 3
- Arrays containing only zeroes like `[0, 0]` output `"00"` if not handled; the result must be collapsed to `"0"`.
- Comparing strings using standard lexicographical sort puts `"30"` before `"3"`, yielding `"303"` instead of the larger `"330"`.
- Assuming transitiveness fails for non-length-equal comparisons: concatenation ordering `(b + a).compareTo(a + b)` is strictly required.
The theory behind it
Greedy — the ground this problem stands on. All Greedy problems
What Greedy is
A greedy algorithm makes the best-looking choice available right now, at every step, without ever looking back or second-guessing its decision. Think of a cashier making change by handing over the largest possible coin first, repeatedly, until the total is reached. Unlike dynamic programming, which saves and compares answers to multiple overlapping paths, a greedy strategy commits to one immediate option and keeps moving forward.
When to reach for it
Reach for greedy when problems ask for minimum jumps, interval scheduling, assigning resources to maximize satisfaction, or finding fractional values. Key signals include sorted orders where greedily taking the next item never hurts future options, or gas station round trips where running balances prove reachability. If you can prove that taking the immediate best choice never leaves you worse off than any alternative, greedy gives the fastest answer.
How the pattern works
Start by sorting the input to bring the most promising candidates to the front. At each position, evaluate your local rule, take the best available piece, and update your running state. The crucial mental step is proving the greedy choice property: demonstrate that picking this immediate winner cannot block a better global solution down the road. If choosing an item now forces you to reconsider past decisions when conditions change later, greedy fails and you must switch to dynamic programming instead.
What each operation costs
| Operation | Time |
|---|---|
| sort elements to enable greedy selection | O(n log n) |
| greedy single-pass scan through sorted input | O(n) |
| greedy choice using a priority queue | O(n log n) |
What usually goes wrong with Greedy
- Applying a greedy choice without proving it yields the global optimum, such as picking the largest coin first for arbitrary denominations where dynamic programming was required.
- Forgetting to sort the input before running the greedy loop, making local decisions on unordered elements that produce invalid answers.
- Picking items based on only one attribute when the optimal decision depends on a ratio or combination of multiple attributes.
Which roles need this problem
Greedy is a core topic for these 3 roles — if you're targeting one of them, this problem is early in your path, not optional.
Secondary for 4 more roles, including Site Reliability Engineer, Search Engineer, Quant Developer.
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