Here is some code that I am trying to use. Why wouldn't this work the way I am assuming it should?

here is a sample of vector<string> mine:
***
*2*
*1*
so mine[1][1] = 2.

// In a function that has passed in vector<string> &mine
int dist[2000][100];
cout << mine[1][1] << endl;   // This correctly displays 2
cout << dist[1][1] << endl; // This correctly displays 0 (not initiallized yet)
dist[1][1] = mine[1][1];
cout << mine[1][1] << endl;   // This correctly displays 2
cout << dist[1][1] << endl; // This incorrectly displays 50

Well 50 is the decimal value of the ASCII character '2'
If you still want a '2', then try a char array and not an int array.

Chars are just small ints, but the magic of seeing '2' rather than 50 only works if you store them in char variables.

>cout << dist[1][1] << endl; // This correctly displays 0 (not initiallized yet)
Which means either you got extremely lucky, your snippet is misleading and dist has static storage duration, or you're relying on a compiler extension that automagically fills arrays with 0. The following would be more correct:

int dist[2000][100] = {0};

>cout << dist[1][1] << endl; // This incorrectly displays 50
It looks correct to me. You just weren't expecting this behavior. For your homework, I want you to figure out the integer value of the character '2'. You can do this by looking at an ASCII table (which matches your result), or by writing a simple test program that casts the character to an integer.

Using a char array did let me do that assignment correctly for the character 2,
But I also have to do integer addition, like this

dist[2][1] = dist[1][1] + maze[2][1];

2 + 1 = 3 is what I need,
this is giving me character 2(50) + character 1(49) = character c (99)

This is resulting in the character c (decimal 99) when I need it to be decimal 3.
I feel like I need to use the atoi() function or something...

Subtract '0' from '2' and see what happens. Then do it for '0' through '9' to verify that it works across the board.

Thanks a lot, seems I was so caught up on using dijkstra's that I forgot my basic char manipulation. Solved.

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