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Adding one to number represented as array of digits

Last Updated : 13 Feb, 2025
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Given a non-negative number represented as an array of digits. The is to add 1 to the number (increment the number represented by the digits by 1). The digits are stored such that the most significant digit is the first element of the array.

Examples :

Input : [1, 2, 4]
Output : 125
Explanation: 124 + 1 = 125

Input : [9, 9, 9]
Output: 1000
Explanation: 999 + 1 = 1000

Table of Content

[Approach – 1] – Using Carry – O(n) Time and O(1) Space

To add one to the number represented by digits, follow the below steps : 

  • Parse the given array from the end as we do in school addition.
  • If the last elements are 9, make it 0 and carry = 1.
  • For the next iteration check carry and if it adds to 10, do the same as step 2.
  • After adding carry, make carry = 0 for the next iteration.
  • If the carry still remains after traversing the entire array, append 1 in the beginning.
C++ 
// C++ program to add 1 to a
// number represented as an array
#include <bits/stdc++.h>
using namespace std;

vector<int> addOne(vector<int> &arr) {

  
    int carry = 1;

    for(int i = arr.size() - 1; i >= 0; i--) {
        int sum = arr[i] + carry;
        arr[i] = sum % 10;
        carry = sum / 10;
    }

    if(carry) {
        arr.insert(arr.begin(), carry);
    }

    return arr;
}

int main() {
    vector<int> arr = {9, 9, 9};
    vector<int> res = addOne(arr);
    for(auto i:res) {
        cout << i;
    }
    return 0;
}
Java 
// Java program to add 1 to a
// number represented as an array
import java.util.*;

class GFG {

    static int[] addOne(int[] arr) {

       
        int carry = 1;

        for(int i = arr.length - 1; i >= 0; i--) {
            int sum = arr[i] + carry;
            arr[i] = sum % 10;
            carry = sum / 10;
        }

        if(carry > 0) {
            int[] newArr = new int[arr.length + 1];
            newArr[0] = carry;
            System.arraycopy(arr, 0, newArr, 1, arr.length);
            return newArr;
        }

        return arr;
    }

    public static void main(String[] args) {
        int[] arr = {9, 9, 9};
        int[] res = addOne(arr);
        for(int i : res) {
            System.out.print(i);
        }
    }
}
Python 
# Python program to add 1 to a
# number represented as an array

def addOne(arr):

  
    carry = 1

    for i in range(len(arr) - 1, -1, -1):
        sum = arr[i] + carry
        arr[i] = sum % 10
        carry = sum // 10

    if carry:
        arr.insert(0, carry)

    return arr

# Driver code
if __name__ == "__main__":
    arr = [9, 9, 9]
    res = addOne(arr)
    for i in res:
        print(i, end="")
C# 
// C# program to add 1 to a
// number represented as an array
using System;
using System.Collections.Generic;

class GFG {

  
    static int[] addOne(int[] arr) {

       
        int carry = 1;

        for(int i = arr.Length - 1; i >= 0; i--) {
            int sum = arr[i] + carry;
            arr[i] = sum % 10;
            carry = sum / 10;
        }

        if(carry > 0) {
            int[] newArr = new int[arr.Length + 1];
            newArr[0] = carry;
            Array.Copy(arr, 0, newArr, 1, arr.Length);
            return newArr;
        }

        return arr;
    }

    public static void Main() {
        int[] arr = {9, 9, 9};
        int[] res = addOne(arr);
        foreach(int i in res) {
            Console.Write(i);
        }
    }
}
JavaScript 
// JavaScript program to add 1 to a
// number represented as an array


function addOne(arr) {

    
    let carry = 1;

    for(let i = arr.length - 1; i >= 0; i--) {
        let sum = arr[i] + carry;
        arr[i] = sum % 10;
        carry = Math.floor(sum / 10);
    }

    if(carry > 0) {
        arr.unshift(carry);
    }

    return arr;
}

// Driver code
let arr = [9, 9, 9];
let res = addOne(arr);
for(let i of res) {
    process.stdout.write(i.toString());
}

Output
1000

Time Complexity: O(n), where n is the size of array.
Space Complexity: O(1)

[Approach – 2] – O(n) Time and O(1) Space

The idea is to start from the end of the vector and if the element is 9 set it to 0, else increment the digit by 1 and exit the loop.

  • If the loop set all digits to 0 (if all digits were 9) insert 1 at the beginning.
  • Else increment the element at the position where the loop stopped.
C++ 
// C++ program to add 1 to a
// number represented as an array
#include <bits/stdc++.h>
using namespace std;

// function to add one 
vector<int> addOne(vector<int> &arr) {

    // initialize an index to end of array
    int index = arr.size() - 1;

    // while the index is valid and the value
    // at index is 9
    while (index >= 0 && arr[index] == 9)
        arr[index--] = 0;

    // if index < 0 (if all arr were 9)
    if (index < 0)

        // insert an one at the beginning of the vector
        arr.insert(arr.begin(), 1, 1);

    // else increment the value at [index]
    else
        arr[index]++;

    return arr;
}

int main() {
    vector<int> arr = {9, 9, 9};
    vector<int> res = addOne(arr);
    for(auto i:res) {
        cout << i;
    }
    return 0;
}
Java 
// Java program to add 1 to a
// number represented as an array
import java.util.*;

class GFG {

    // function to add one 
    static int[] addOne(int[] arr) {

        // initialize an index to end of array
        int index = arr.length - 1;

        // while the index is valid and the value
        // at index is 9
        while (index >= 0 && arr[index] == 9)
            arr[index--] = 0;

        // if index < 0 (if all arr were 9)
        if (index < 0) {

            // insert an one at the beginning of the array
            int[] newArr = new int[arr.length + 1];
            newArr[0] = 1;
            System.arraycopy(arr, 0, newArr, 1, arr.length);
            return newArr;
        }

        // else increment the value at [index]
        else
            arr[index]++;

        return arr;
    }

    public static void main(String[] args) {
        int[] arr = {9, 9, 9};
        int[] res = addOne(arr);
        for (int i : res) {
            System.out.print(i);
        }
    }
}
Python 
# Python program to add 1 to a
# number represented as an array

# function to add one 
def addOne(arr):

    # initialize an index to end of array
    index = len(arr) - 1

    # while the index is valid and the value
    # at index is 9
    while index >= 0 and arr[index] == 9:
        arr[index] = 0
        index -= 1

    # if index < 0 (if all arr were 9)
    if index < 0:

        # insert an one at the beginning of the list
        arr.insert(0, 1)

    # else increment the value at [index]
    else:
        arr[index] += 1

    return arr

if __name__ == "__main__":

    # Driver code
    arr = [9, 9, 9]
    res = addOne(arr)
    for i in res:
        print(i, end="")
C# 
// C# program to add 1 to a
// number represented as an array
using System;
using System.Collections.Generic;

class GFG {

    // function to add one 
    static int[] addOne(int[] arr) {

        // initialize an index to end of array
        int index = arr.Length - 1;

        // while the index is valid and the value
        // at index is 9
        while (index >= 0 && arr[index] == 9)
            arr[index--] = 0;

        // if index < 0 (if all arr were 9)
        if (index < 0) {

            // insert an one at the beginning of the array
            int[] newArr = new int[arr.Length + 1];
            newArr[0] = 1;
            Array.Copy(arr, 0, newArr, 1, arr.Length);
            return newArr;
        }

        // else increment the value at [index]
        else
            arr[index]++;

        return arr;
    }

    public static void Main() {
        int[] arr = {9, 9, 9};
        int[] res = addOne(arr);
        foreach (int i in res) {
            Console.Write(i);
        }
    }
}
JavaScript 
// JavaScript program to add 1 to a
// number represented as an array

// function to add one 
function addOne(arr) {

    // initialize an index to end of array
    let index = arr.length - 1;

    // while the index is valid and the value
    // at index is 9
    while (index >= 0 && arr[index] === 9)
        arr[index--] = 0;

    // if index < 0 (if all arr were 9)
    if (index < 0) {

        // insert an one at the beginning of the array
        arr.unshift(1);
    }

    // else increment the value at [index]
    else
        arr[index]++;

    return arr;
}

// Driver code
let arr = [9, 9, 9];
let res = addOne(arr);
for (let i of res) {
    process.stdout.write(i.toString());
}

Output
1000

Time Complexity: O(n), where n is the number of digits / size of the array.
Auxiliary Space: O(1)

[Alternate Approach] – O(n) Time and O(1) Space

To avoid inserting at front of array, we can firstly reverse the array, and then append the value at the last. Thereafter, we can reverse the array again to get the result.

C++ 
// C++ program to add 1 to a
// number represented as an array
#include <bits/stdc++.h>
using namespace std;

// function to add one 
vector<int> addOne(vector<int> &arr) {

    // reverse the digits
    reverse(arr.begin(), arr.end());

    // initialize an index to start of array
    int index = 0;

    // while the index is valid and the value
    // at index is 9
    while (index < arr.size() && arr[index] == 9)
        arr[index++] = 0;

    // if index == arr.size() (if all arr were 9)
    if (index == arr.size())

        // insert an one at the end
        arr.push_back(1);

    // else increment the value at [index]
    else
        arr[index]++;
    
    // reverse the array
    reverse(arr.begin(), arr.end());

    return arr;
}

int main() {
    vector<int> arr = {9, 9, 9};
    vector<int> res = addOne(arr);
    for(auto i:res) {
        cout << i;
    }
    return 0;
}
Java 
// Java program to add 1 to a
// number represented as an array
import java.util.*;

class GFG {

    // function to add one 
    static int[] addOne(int[] arr) {

        // reverse the digits
        for (int i = 0, j = arr.length - 1; i < j; i++, j--) {
            int temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
        }

        // initialize an index to start of array
        int index = 0;

        // while the index is valid and the value
        // at index is 9
        while (index < arr.length && arr[index] == 9)
            arr[index++] = 0;

        // if index == arr.length (if all arr were 9)
        if (index == arr.length) {

            // insert an one at the end
            int[] newArr = new int[arr.length + 1];
            System.arraycopy(arr, 0, newArr, 0, arr.length);
            newArr[arr.length] = 1;
            arr = newArr;
        }

        // else increment the value at [index]
        else
            arr[index]++;

        // reverse the array
        for (int i = 0, j = arr.length - 1; i < j; i++, j--) {
            int temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
        }

        return arr;
    }

    public static void main(String[] args) {
        int[] arr = {9, 9, 9};
        int[] res = addOne(arr);
        for (int i : res) {
            System.out.print(i);
        }
    }
}
Python 
# Python program to add 1 to a
# number represented as an array

# function to add one 
def addOne(arr):

    # reverse the digits
    arr.reverse()

    # initialize an index to start of array
    index = 0

    # while the index is valid and the value
    # at index is 9
    while index < len(arr) and arr[index] == 9:
        arr[index] = 0
        index += 1

    # if index == len(arr) (if all arr were 9)
    if index == len(arr):

        # insert an one at the end
        arr.append(1)

    # else increment the value at [index]
    else:
        arr[index] += 1
    
    # reverse the array
    arr.reverse()

    return arr

# Driver code
if __name__ == "__main__":
    arr = [9, 9, 9]
    res = addOne(arr)
    for i in res:
        print(i, end="")
C# 
// C# program to add 1 to a
// number represented as an array
using System;
using System.Collections.Generic;

class GFG {

    // function to add one 
    static int[] addOne(int[] arr) {

        // reverse the digits
        Array.Reverse(arr);

        // initialize an index to start of array
        int index = 0;

        // while the index is valid and the value
        // at index is 9
        while (index < arr.Length && arr[index] == 9)
            arr[index++] = 0;

        // if index == arr.Length (if all arr were 9)
        if (index == arr.Length) {

            // insert an one at the end
            int[] newArr = new int[arr.Length + 1];
            Array.Copy(arr, newArr, arr.Length);
            newArr[arr.Length] = 1;
            arr = newArr;
        }

        // else increment the value at [index]
        else
            arr[index]++;

        // reverse the array
        Array.Reverse(arr);

        return arr;
    }

    public static void Main() {
        int[] arr = {9, 9, 9};
        int[] res = addOne(arr);
        foreach (int i in res) {
            Console.Write(i);
        }
    }
}
JavaScript 
// JavaScript program to add 1 to a
// number represented as an array

// function to add one 
function addOne(arr) {

    // reverse the digits
    arr.reverse();

    // initialize an index to start of array
    let index = 0;

    // while the index is valid and the value
    // at index is 9
    while (index < arr.length && arr[index] === 9)
        arr[index++] = 0;

    // if index == arr.length (if all arr were 9)
    if (index === arr.length) {

        // insert an one at the end
        arr.push(1);
    }

    // else increment the value at [index]
    else
        arr[index]++;

    // reverse the array
    arr.reverse();

    return arr;
}

// Driver code
let arr = [9, 9, 9];
let res = addOne(arr);
for (let i of res) {
    process.stdout.write(i.toString());
}

Output
1000

Time Complexity: O(n), where n is the number of digits / size of the array.
Auxiliary Space: O(1)




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