Add two numbers represented by two arrays in C Program

A number represented by an array is stored in such a form that each digit of the number is represented by an element of the array. For example −

Number 234 in array is {2,3,4}

To add two such numbers we will first add digits from the least significant position and if the sum is greater than 9, we propagate the carry. We continue this process for consecutive digits until all digits are processed.

Syntax

void addArrays(int arr1[], int arr2[], int size1, int size2, int result[]);

Algorithm

To find the sum of numbers stored as arrays −

• Start from the rightmost digits (least significant)
• Add corresponding digits along with any carry from previous addition
• Store the result digit (sum % 10) and calculate new carry (sum / 10)
• Continue until all digits are processed
• Handle remaining digits of the longer array

Example

Let's add two numbers represented as arrays −

#include <stdio.h>

void addArrays(int arr1[], int arr2[], int size1, int size2) {
    int maxSize = (size1 > size2) ? size1 : size2;
    int result[maxSize + 1];
    int carry = 0;
    int i = size1 - 1;
    int j = size2 - 1;
    int k = maxSize;
    
    /* Initialize result array */
    for(int x = 0; x <= maxSize; x++) {
        result[x] = 0;
    }
    
    /* Add digits from right to left */
    while(i >= 0 || j >= 0 || carry > 0) {
        int sum = carry;
        
        if(i >= 0) {
            sum += arr1[i];
            i--;
        }
        
        if(j >= 0) {
            sum += arr2[j];
            j--;
        }
        
        result[k] = sum % 10;
        carry = sum / 10;
        k--;
    }
    
    /* Print result */
    printf("Sum: ");
    int started = 0;
    for(int x = 0; x <= maxSize; x++) {
        if(result[x] != 0 || started) {
            printf("%d", result[x]);
            started = 1;
        }
    }
    if(!started) {
        printf("0");
    }
    printf("<br>");
}

int main() {
    int arr1[] = {2, 9, 6};
    int arr2[] = {6, 3, 8};
    int size1 = sizeof(arr1) / sizeof(arr1[0]);
    int size2 = sizeof(arr2) / sizeof(arr2[0]);
    
    printf("Array 1: ");
    for(int i = 0; i < size1; i++) {
        printf("%d", arr1[i]);
    }
    printf("<br>");
    
    printf("Array 2: ");
    for(int i = 0; i < size2; i++) {
        printf("%d", arr2[i]);
    }
    printf("<br>");
    
    addArrays(arr1, arr2, size1, size2);
    
    return 0;
}

Array 1: 296
Array 2: 638
Sum: 934

How It Works

For arrays {2,9,6} and {6,3,8} −

• Step 1: Add rightmost digits: 6 + 8 = 14 ? digit = 4, carry = 1
• Step 2: Add next digits with carry: 9 + 3 + 1 = 13 ? digit = 3, carry = 1
• Step 3: Add leftmost digits with carry: 2 + 6 + 1 = 9 ? digit = 9, carry = 0
• Result: {9,3,4} which represents 934

Conclusion

Adding numbers represented as arrays involves digit-by-digit addition from right to left with proper carry handling. This approach works for numbers of any length and handles cases where arrays have different sizes.