C++ program for Solving Cryptarithmetic Puzzles

Newspapers and magazines often have crypt-arithmetic puzzles of the form:
Examples:

Input : s1 = SEND, s2 = "MORE", s3 = "MONEY"
Output : One of the possible solution is:
         D=1 E=5 M=0 N=3 O=8 R=2 S=7 Y=6  
Explanation:
The above values satisfy below equation : 
  SEND
+ MORE
--------
 MONEY
-------- 

It is strongly recommended to refer Backtracking | Set 8 (Solving Cryptarithmetic Puzzles) for approach of this problem.



The idea is to assign each letter a digit from 0 to 9 so that the arithmetic works out correctly. A permutation is a recursive function which calls a check function for every possible permutation of integers.
Check function checks whether the sum of first two numbers corresponding to first two string is equal to the third number corresponding to third string. If the solution is found then print the solution.

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// CPP program for solving cryptographic puzzles
#include <bits/stdc++.h>
using namespace std;
  
// vector stores 1 corresponding to index
// number which is already assigned
// to any char, otherwise stores 0
vector<int> use(10);
  
// structure to store char and its corresponding integer
struct node
{
    char c;
    int v;
};
  
// function check for correct solution
int check(node* nodeArr, const int count, string s1,
                               string s2, string s3)
{
    int val1 = 0, val2 = 0, val3 = 0, m = 1, j, i;
  
    // calculate number corresponding to first string
    for (i = s1.length() - 1; i >= 0; i--)
    {
        char ch = s1[i];
        for (j = 0; j < count; j++)
            if (nodeArr[j].c == ch)
                break;
  
        val1 += m * nodeArr[j].v;
        m *= 10;
    }
    m = 1;
  
    // calculate number corresponding to second string
    for (i = s2.length() - 1; i >= 0; i--)
    {
        char ch = s2[i];
        for (j = 0; j < count; j++)
            if (nodeArr[j].c == ch)
                break;
  
        val2 += m * nodeArr[j].v;
        m *= 10;
    }
    m = 1;
  
    // calculate number corresponding to third string
    for (i = s3.length() - 1; i >= 0; i--)
    {
        char ch = s3[i];
        for (j = 0; j < count; j++)
            if (nodeArr[j].c == ch)
                break;
  
        val3 += m * nodeArr[j].v;
        m *= 10;
    }
  
    // sum of first two number equal to third return true
    if (val3 == (val1 + val2))
        return 1;
  
    // else return false
    return 0;
}
  
// Recursive function to check solution for all permutations
bool permutation(const int count, node* nodeArr, int n,
                 string s1, string s2, string s3)
{
    // Base case
    if (n == count - 1)
    {
  
        // check for all numbers not used yet
        for (int i = 0; i < 10; i++)
        {
  
            // if not used
            if (use[i] == 0)
            {
  
                // assign char at index n integer i
                nodeArr[n].v = i;
  
                // if solution found
                if (check(nodeArr, count, s1, s2, s3) == 1)
                {
                    cout << "\nSolution found: ";
                    for (int j = 0; j < count; j++)
                        cout << " " << nodeArr[j].c << " = "
                             << nodeArr[j].v;
                    return true;
                }
            }
        }
        return false;
    }
  
    for (int i = 0; i < 10; i++)
    {
  
        // if ith integer not used yet
        if (use[i] == 0)
        {
  
            // assign char at index n integer i
            nodeArr[n].v = i;
  
            // mark it as not available for other char
            use[i] = 1;
  
            // call recursive function
            if (permutation(count, nodeArr, n + 1, s1, s2, s3))
                return true;
  
            // backtrack for all other possible solutions
            use[i] = 0;
        }
    }
    return false;
}
  
bool solveCryptographic(string s1, string s2,
                                   string s3)
{
    // count to store number of unique char
    int count = 0;
  
    // Length of all three strings
    int l1 = s1.length();
    int l2 = s2.length();
    int l3 = s3.length();
  
    // vector to store frequency of each char
    vector<int> freq(26);
  
    for (int i = 0; i < l1; i++)
        ++freq[s1[i] - 'A'];
  
    for (int i = 0; i < l2; i++)
        ++freq[s2[i] - 'A'];
  
    for (int i = 0; i < l3; i++)
        ++freq[s3[i] - 'A'];
  
    // count number of unique char
    for (int i = 0; i < 26; i++)
        if (freq[i] > 0)
            count++;
  
    // solution not possible for count greater than 10
    if (count > 10)
    {
        cout << "Invalid strings";
        return 0;
    }
  
    // array of nodes
    node nodeArr[count];
  
    // store all unique char in nodeArr
    for (int i = 0, j = 0; i < 26; i++)
    {
        if (freq[i] > 0)
        {
            nodeArr[j].c = char(i + 'A');
            j++;
        }
    }
    return permutation(count, nodeArr, 0, s1, s2, s3);
}
  
// Driver function
int main()
{
    string s1 = "SEND";
    string s2 = "MORE";
    string s3 = "MONEY";
  
    if (solveCryptographic(s1, s2, s3) == false)
        cout << "No solution";
    return 0;
}

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Output:

Solution found:  D=1 E=5 M=0 N=3 O=8 R=2 S=7 Y=6



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