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Check if Word Equals Summation of Two Words

EasyUpdated: Aug 2, 2025
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Problem

The letter value of a letter is its position in the alphabet starting from 0 (i.e. 'a' -> 0, 'b' -> 1, 'c' -> 2, etc.).

The numerical value of some string of lowercase English letters s is the concatenation of the letter values of each letter in s, which is then converted into an integer.

  • For example, if s = "acb", we concatenate each letter's letter value, resulting in "021". After converting it, we get 21.

You are given three strings firstWord, secondWord, and targetWord, each consisting of lowercase English letters 'a' through 'j' inclusive.

Return true if the summation of the numerical values of firstWord and secondWord equals the numerical value of targetWord, or false otherwise.

Examples

Example 1:

Input: firstWord = "acb", secondWord = "cba", targetWord = "cdb"
Output: true
Explanation:
The numerical value of firstWord is "acb" -> "021" -> 21.
The numerical value of secondWord is "cba" -> "210" -> 210.
The numerical value of targetWord is "cdb" -> "231" -> 231.
We return true because 21 + 210 == 231.

Example 2:

Input: firstWord = "aaa", secondWord = "a", targetWord = "aab"
Output: false
Explanation: 
The numerical value of firstWord is "aaa" -> "000" -> 0.
The numerical value of secondWord is "a" -> "0" -> 0.
The numerical value of targetWord is "aab" -> "001" -> 1.
We return false because 0 + 0 != 1.

Example 3:

Input: firstWord = "aaa", secondWord = "a", targetWord = "aaaa"
Output: true
Explanation: 
The numerical value of firstWord is "aaa" -> "000" -> 0.
The numerical value of secondWord is "a" -> "0" -> 0.
The numerical value of targetWord is "aaaa" -> "0000" -> 0.
We return true because 0 + 0 == 0.

Solution

Method 1 - Get numerical value

Here is the approach:

  • Create a helper function to convert a word to its numerical value by:
    • Calculating the letter value of each character.
    • Concatenating these values into a string.
    • Converting the string to an integer.
  • Compute the numerical values of firstWord, secondWord, and targetWord.
  • Check if the sum of the numerical values of firstWord and secondWord is equal to the numerical value of targetWord.

Code

Java
public class Solution {
    private int getNumericalValue(String word) {
        StringBuilder sb = new StringBuilder();
        for (char c : word.toCharArray()) {
            sb.append(c - 'a');
        }
        return Integer.parseInt(sb.toString());
    }
    
    public boolean isSumEqual(String firstWord, String secondWord, String targetWord) {
        int num1 = getNumericalValue(firstWord);
        int num2 = getNumericalValue(secondWord);
        int target = getNumericalValue(targetWord);
        
        return num1 + num2 == target;
    }
}
Python
class Solution:
    def get_numerical_value(self, word: str) -> int:
        num_str = ''.join(str(ord(c) - ord('a')) for c in word)
        return int(num_str)
    
    def is_sum_equal(self, firstWord: str, secondWord: str, targetWord: str) -> bool:
        num1 = self.get_numerical_value(firstWord)
        num2 = self.get_numerical_value(secondWord)
        target = self.get_numerical_value(targetWord)
        
        return num1 + num2 == target

Complexity

  • ⏰ Time complexity: O(n) where n is the length of the longest word among firstWord, secondWord, and targetWord.
  • 🧺 Space complexity: O(1) since we are only using a fixed amount of space for variables and not additional data structures.

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