Largest Number

Largest Number - Problem

Given a list of non-negative integers nums, arrange them such that they form the largest number and return it.

Since the result may be very large, you need to return a string instead of an integer.

Example: Given [10,2], return "210" (not "102")

Input & Output

Example 1 — Basic Case

$ Input: nums = [10,2]

› Output: "210"

💡 Note: Compare arrangements: [10,2] gives "102" vs [2,10] gives "210". Since "210" > "102", return "210".

Example 2 — Multiple Numbers

$ Input: nums = [3,30,34,5,9]

› Output: "9534330"

💡 Note: Custom sort compares concatenations: "9"+"5" > "5"+"9", "34"+"3" > "3"+"34", "3"+"30" > "30"+"3", resulting in [9,5,34,3,30] → "9534330".

Example 3 — Edge Case with Zeros

$ Input: nums = [0,0]

› Output: "0"

💡 Note: All numbers are zero, so result is "0" (not "00").

Constraints

1 ≤ nums.length ≤ 100
0 ≤ nums[i] ≤ 10⁹

Visualization

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Asked in

G Google 25 a Amazon 20 M Microsoft 15

The key insight is to use a custom comparator that compares concatenated strings xy vs yx to determine optimal ordering. Best approach is custom sorting with Time: O(n log n), Space: O(n).

Common Approaches

✓ Brute Force - All Permutations

⏱️ Time: O(n! × n) Space: O(n! × n)

Generate all permutations of the numbers, convert each to string, and return the lexicographically largest one. This explores every possible ordering.

Custom Sorting Approach

⏱️ Time: O(n log n) Space: O(n)

Convert numbers to strings and sort them using a custom comparator that determines which order produces a larger concatenated result. For two numbers x and y, compare xy vs yx.

Brute Force - All Permutations — Algorithm Steps

Step 1: Generate all permutations of input array
Step 2: Convert each permutation to concatenated string
Step 3: Return the lexicographically maximum string

Visualization

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Step-by-Step Walkthrough

Generate Permutations

Create all possible orderings of numbers

Compare Results

Find lexicographically largest concatenated string

Return Maximum

Select the arrangement forming largest number

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

void swap(int* a, int* b) {
    int temp = *a;
    *a = *b;
    *b = temp;
}

void permute(int* nums, int start, int end, char* maxResult) {
    if (start == end) {
        char current[1000] = "";
        for (int i = 0; i <= end; i++) {
            char temp[20];
            sprintf(temp, "%d", nums[i]);
            strcat(current, temp);
        }
        if (strcmp(current, maxResult) > 0) {
            strcpy(maxResult, current);
        }
        return;
    }
    
    for (int i = start; i <= end; i++) {
        swap(&nums[start], &nums[i]);
        permute(nums, start + 1, end, maxResult);
        swap(&nums[start], &nums[i]);
    }
}

char* solution(int* nums, int size) {
    if (size == 0) {
        char* result = (char*)malloc(2);
        strcpy(result, "0");
        return result;
    }
    
    // Handle edge case where all numbers are 0
    int allZero = 1;
    for (int i = 0; i < size; i++) {
        if (nums[i] != 0) {
            allZero = 0;
            break;
        }
    }
    if (allZero) {
        char* result = (char*)malloc(2);
        strcpy(result, "0");
        return result;
    }
    
    char* maxResult = (char*)malloc(1000);
    strcpy(maxResult, "");
    
    permute(nums, 0, size - 1, maxResult);
    
    return maxResult;
}

int main() {
    char line[1000];
    fgets(line, sizeof(line), stdin);
    line[strcspn(line, "\n")] = 0;
    
    // Parse JSON array manually
    int nums[100];
    int size = 0;
    char* token = strtok(line + 1, ",]");
    while (token != NULL) {
        nums[size++] = atoi(token);
        token = strtok(NULL, ",]");
    }
    
    char* result = solution(nums, size);
    printf("%s\n", result);
    free(result);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n! × n)

n! permutations, each taking O(n) time to concatenate

⚠ Quadratic Growth

Space Complexity

O(n! × n)

Storing all n! permutations, each of length n

⚠ Quadratic Space

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Input & Output

Constraints

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Related Problems

Common Approaches

Brute Force - All Permutations — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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