Plus One

Plus One - Problem

Array Math Easy

You are given a large integer represented as an integer array digits, where each digits[i] is the ith digit of the integer. The digits are ordered from most significant to least significant in left-to-right order. The large integer does not contain any leading zeros.

Increment the large integer by one and return the resulting array of digits.

Input & Output

Example 1 — Basic Case

$ Input: digits = [1,2,3]

› Output: [1,2,4]

💡 Note: The array represents 123, and 123 + 1 = 124. So we return [1,2,4].

Example 2 — Carry Required

$ Input: digits = [4,3,2,1,9]

› Output: [4,3,2,2,0]

💡 Note: The array represents 43219, and 43219 + 1 = 43220. The last digit 9 becomes 0 and we carry 1.

Example 3 — All Nines

$ Input: digits = [9,9,9]

› Output: [1,0,0,0]

💡 Note: The array represents 999, and 999 + 1 = 1000. We need an extra digit at the beginning.

Constraints

1 ≤ digits.length ≤ 100
0 ≤ digits[i] ≤ 9
digits does not contain any leading zeros

Visualization

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Asked in

G Google 45 a Amazon 38 M Microsoft 32 Apple 25

The key insight is to process digits from right to left, handling carries naturally. When we encounter a digit less than 9, we can simply add 1 and return. The special case is when all digits are 9 - we need to create a new array with 1 followed by zeros. Best approach is the right-to-left carry method with Time: O(n), Space: O(1).

Common Approaches

Approach	Time	Space	Notes
✓ All 9s Special Case	O(n)	O(1)	Optimize for the special case when all digits are 9
Convert to Number	O(n)	O(1)	Convert array to number, add 1, convert back to array
Right-to-Left with Carry	O(n)	O(1)	Process digits from right to left, handling carries properly

All 9s Special Case — Algorithm Steps

Step 1: Check if all digits are 9
Step 2: If yes, return [1,0,0,...,0]
Step 3: Otherwise, process right-to-left
Step 4: Return modified array

Visualization

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Step-by-Step Walkthrough

Check All 9s

Input [9,9,9] - all digits are 9

Special Case

Cannot just add 1, need extra digit

Create Result

Return [1,0,0,0] - 999 + 1 = 1000

Code -

solution.c — C

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

int* solution(int* digits, int digitsSize, int* returnSize) {
    // Check if all digits are 9
    bool allNines = true;
    for (int i = 0; i < digitsSize; i++) {
        if (digits[i] != 9) {
            allNines = false;
            break;
        }
    }
    
    if (allNines) {
        *returnSize = digitsSize + 1;
        int* result = (int*)calloc(digitsSize + 1, sizeof(int));
        result[0] = 1;
        return result;
    }
    
    // Standard case: process from right to left
    int carry = 1;
    for (int i = digitsSize - 1; i >= 0; i--) {
        int total = digits[i] + carry;
        digits[i] = total % 10;
        carry = total / 10;
        if (carry == 0) {
            break;
        }
    }
    
    *returnSize = digitsSize;
    int* result = (int*)malloc(digitsSize * sizeof(int));
    memcpy(result, digits, digitsSize * sizeof(int));
    return result;
}

int main() {
    char line[1000];
    fgets(line, sizeof(line), stdin);
    
    // Simple parsing - assumes format [1,2,3]
    int digits[100];
    int size = 0;
    char* ptr = strchr(line, '[') + 1;
    while (*ptr != ']') {
        if (*ptr >= '0' && *ptr <= '9') {
            digits[size++] = *ptr - '0';
        }
        ptr++;
    }
    
    int returnSize;
    int* result = solution(digits, size, &returnSize);
    
    printf("[");
    for (int i = 0; i < returnSize; i++) {
        printf("%d", result[i]);
        if (i < returnSize - 1) printf(",");
    }
    printf("]\n");
    
    free(result);
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

One pass to check all 9s, then one pass for normal processing

✓ Linear Growth

Space Complexity

O(1)

Only using constant extra space except for the result array

✓ Linear Space

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Input & Output

Constraints

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Related Problems

Common Approaches

All 9s Special Case — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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