Add Two Numbers Represented by Two Arrays

Summary

Given two arrays representing numbers in base 10, write a program to add these two numbers. For example, given two arrays [1,2,3] and [4,5], the sum should be [5,7,8].

Detailed Explanation

The problem involves adding two numbers represented as arrays of digits. We can solve this problem by treating each array as a number in base 10, then performing addition.

Here's a step-by-step breakdown:

1. Initialize an empty result array.
2. Iterate through the two input arrays from right to left (i.e., from least significant digit to most).
3. For each pair of digits, add them together and store the result modulo 10 in the corresponding position of the result array.
4. If the sum is greater than or equal to 10, append the carry (the quotient when dividing the sum by 10) to the front of the result array.
5. Repeat steps 2-4 until all pairs of digits have been processed.

Time complexity: O(n), where n is the length of the longer input array. Space complexity: O(n), as we need to store the result in an array of size n.

Optimized Solutions

Java

java
public int[] addArrays(int[] arr1, int[] arr2) {
    int maxLen = Math.max(arr1.length, arr2.length);
    int[] res = new int[maxLen];
    for (int i = 0; i < maxLen; i++) {
        int sum = (i < arr1.length ? arr1[i] : 0) + (i < arr2.length ? arr2[i] : 0);
        res[i] = sum % 10;
        if (sum >= 10) {
            res[0] = (res[0] == 0) ? 1 : res[0];
        }
    }
    return res;
}

Python

python
def add_arrays(arr1, arr2):
    max_len = max(len(arr1), len(arr2))
    res = [0] * max_len
    for i in range(max_len):
        sum = (i < len(arr1) and arr1[i] or 0) + (i < len(arr2) and arr2[i] or 0)
        res[i] = sum % 10
        if sum >= 10:
            res[0] += 1
    return res

C++