Stack versus Integer

Question

I've created a program to solve Cryptarithmetics for a class on Data Structures. The professor recommended that we utilize a stack consisting of linked nodes to keep track of which letters we replaced with which numbers, but I realized an integer could do the same trick. Instead of a stack {A, 1, B, 2, C, 3, D, 4} I could hold the same info in 1234.

My program, though, seems to run much more slowly than the estimation he gave us. Could someone explain why a stack would behave much more efficiently? I had assumed that, since I wouldn't be calling methods over and over again (push, pop, top, etc) and instead just add one to the 'solution' that mine would be faster.

This is not an open ended question, so do not close it. Although you can implement things different ways, I want to know why, at the heart of C++, accessing data via a Stack has performance benefits over storing in ints and extracting by moding.

Although this is homework, I don't actually need help, just very intrigued and curious.

Thanks and can't wait to learn something new!

EDIT (Adding some code)

letterAssignments is an int array of size 26. for a problem like SEND + MORE = MONEY, A isn't used so letterAssignments[0] is set to 11. All chars that are used are initialized to 10. answerNum is a number with as many digits as there are unique characters (in this case, 8 digits).

int Cryptarithmetic::solve(){
while(!solved()){       
    for(size_t z = 0; z < 26; z++){
        if(letterAssignments[z] != 11) letterAssignments[z] = 10;
    }
    if(answerNum < 1) return NULL;
    size_t curAns = answerNum;

    for(int i = 0; i < numDigits; i++){ 
        if(nextUnassigned() != '$') {
            size_t nextAssign = curAns % 10;
            if(isAssigned(nextAssign)){
                    answerNum--;
                    continue;
                }
            assign(nextUnassigned(), nextAssign);
            curAns /= 10;
        }
    }
    answerNum--;
}
return answerNum;
}

Two helper methods in case you'd like to see them:

char Cryptarithmetic::nextUnassigned(){ 
char nextUnassigned = '$';
for(int i = 0; i < 26; i++) {
    if(letterAssignments[i] == 10) return ('A' + i);
}
}

void Cryptarithmetic::assign(char letter, size_t val){
assert('A' <= letter && letter <= 'Z');  // valid letter
assert(letterAssignments[letter-'A'] != 11); // has this letter
assert(!isAssigned(val)); // not already assigned.
letterAssignments[letter-'A'] = val;
}

Answer 1

From the looks of things the way you are doing things here is quite inefficiant.

As a general rule try to have the least amount of for loops possible since each one will slow down your implementation greatly.

for instance if we strip all other code away, your program looks like

while(thing) {
  for(z < 26) {

  }
  for(i < numDigits) {
    for(i < 26) {

    }
    for(i < 26) {

    }
  }
}

this means that for each while loop you are doing ((26+26)*numDigits)+26 loop operations. Thats assuming isAssigned() does not use a loop.

Idealy you want:

while(thing) {
  for(i < numDigits) {
  }
}

which i'm sure is possible with changes to your code. This is why your implementation with the integer array is much slower than an implementation using the stack which does not use the for(i < 26) loops (I assume).

In Answer to your original question however, storing an array of integers will always be faster than any struct you can come up with simply because there are more overheads involved in assigning the memory, calling functions, etc.

But as with everything, implementation is the key difference between a slow program and a fast program.