C++ program for Solving Cryptarithmetic Puzzles

In the crypt-arithmetic problem, some letters are used to assign digits to it. Like ten different letters are holding digit values from 0 to 9 to perform arithmetic operations correctly. There are two words are given and another word is given as answer of addition for those two words. As an example we can say that two words ‘BASE’ and ‘BALL’, and the result is ‘GAMES’. Now if we try to add BASE and BALL by their symbolic digits, we will get the answer GAMES.

NOTE − There must be ten letters maximum, otherwise it cannot be solved.

Input

This algorithm will take three words.

Output

It will show which letter holds which number from 0 – 9.

For this case it is like this.

Algorithm

For this problem, we will define a node, which contains a letter and its corresponding values.

isValid(nodeList, count, word1, word2, word3)

Input - A list of nodes, the number of elements in the node list and three words.
Output  - True if the sum of the value for word1 and word2 is same as word3 value.

Begin
   m := 1
   for each letter i from right to left of word1, do
      ch := word1[i]
      for all elements j in the nodeList, do
         if nodeList[j].letter = ch, then
            break
      done
      val1 := val1 + (m * nodeList[j].value)
      m := m * 10
   done
   m := 1
   for each letter i from right to left of word2, do
      ch := word2[i]
      for all elements j in the nodeList, do
         if nodeList[j].letter = ch, then
            break
      done
      val2 := val2 + (m * nodeList[j].value)
      m := m * 10
   done
   m := 1
   for each letter i from right to left of word3, do
      ch := word3[i]
      for all elements j in the nodeList, do
         if nodeList[j].letter = ch, then
            break
      done
      val3 := val3 + (m * nodeList[j].value)
      m := m * 10
   done
   if val3 = (val1 + val2), then
      return true
   return false
End

permutation(nodeList, count, n, word1, word2, word3)

Input - List of nodes, number of items in the list, number of assigned letters and three words.
Output - True when all letters are assigned with values correctly to solve the sum.

Begin
   if n letters are assigned, then
      for all digits i from 0 to 9, do
         if digit i is not used, then
            nodeList[n].value := i
            if isValid(nodeList, count, word1, word2, word3) = true
               for all items j in the nodeList, do
                  show the letter and corresponding values.
               done
               return true
      done
      return fasle
   for all digits i from 0 to 9, do
      if digit i is not used, then
         nodeList[n].value := i
         mark as i is used
         if permutation(nodeList, count, n+1, word1, word2, word3),
            return true
         otherwise mark i as not used
   done
   return false
End

Example

 Live Demo

#include <iostream>
#include<vector<
using namespace std;
vector<int< use(10); //set 1, when one character is assigned previously
struct node {
   char letter;
   int value;
};
int isValid(node* nodeList, const int count, string s1, string s2, string s3) {
   int val1 = 0, val2 = 0, val3 = 0, m = 1, j, i;
   for (i = s1.length() - 1; i >= 0; i--){ //find number for first string
      char ch = s1[i];
      for (j = 0; j < count; j++)
         if (nodeList[j].letter == ch) //when ch is present, break the loop
            break;
            val1 += m * nodeList[j].value;
            m *= 10;
   }
   m = 1;
   for (i = s2.length() - 1; i >= 0; i--){ //find number for second string
      char ch = s2[i];
      for (j = 0; j < count; j++)
         if (nodeList[j].letter == ch)
            break;
            val2 += m * nodeList[j].value;
            m *= 10;
   }
   m = 1;
   for (i = s3.length() - 1; i >= 0; i--){ //find number for third string
      char ch = s3[i];
      for (j = 0; j < count; j++)
         if (nodeList[j].letter == ch)
            break;
            val3 += m * nodeList[j].value;
            m *= 10;
   }
   if (val3 == (val1 + val2)) //check whether the sum is same as 3rd string or not
      return 1;
   return 0;
}
bool permutation(int count, node* nodeList, int n, string s1, string s2, string s3) {
   if (n == count - 1){ //when values are assigned for all characters
      for (int i = 0; i < 10; i++){
         if (use[i] == 0){ // for those numbers, which are not used
            nodeList[n].value = i; //assign value i
            if (isValid(nodeList, count, s1, s2, s3) == 1){ //check validation
               cout << "Solution found: ";
               for (int j = 0; j < count; j++) //print code, which are assigned
                  cout << " " << nodeList[j].letter << " = "
                  << nodeList[j].value;
               return true;
            }
         }
      }
      return false;
   }
   for (int i = 0; i < 10; i++){
      if (use[i] == 0){ // for those numbers, which are not used
         nodeList[n].value = i; //assign value i and mark as not available for future use
         use[i] = 1;
         if (permutation(count, nodeList, n + 1, s1, s2, s3)) //go for next characters
            return true;
            use[i] = 0; //when backtracks, make available again
      }
   }
   return false;
}
bool solvePuzzle(string s1, string s2,string s3) {
   int uniqueChar = 0; //Number of unique characters
   int len1 = s1.length();
   int len2 = s2.length();
   int len3 = s3.length();
   vector<int> freq(26); //There are 26 different characters
   for (int i = 0; i < len1; i++)
      ++freq[s1[i] - 'A'];
   for (int i = 0; i < len2; i++)
      ++freq[s2[i] - 'A'];
   for (int i = 0; i < len3; i++)
      ++freq[s3[i] - 'A'];
   for (int i = 0; i < 26; i++)
      if (freq[i] > 0) //whose frequency is > 0, they are present
         uniqueChar++;
   if (uniqueChar > 10) { //as there are 10 digits in decimal system
      cout << "Invalid strings";
      return 0;
   }
   node nodeList[uniqueChar];
   for (int i = 0, j = 0; i < 26; i++) { //assign all characters found in three strings
      if (freq[i] > 0) {
         nodeList[j].letter = char(i + 'A');
         j++;
      }
   }
   return permutation(uniqueChar, nodeList, 0, s1, s2, s3);
}
int main() {
   string s1 = "BASE";
   string s2 = "BALL";
   string s3 = "GAMES";
   if (solvePuzzle(s1, s2, s3) == false)
      cout << "No solution";
}

Output

Solution found: A = 4 B = 2 E = 1 G = 0 L = 5 M = 9 S = 6