Why does indexing a string inside of a recursive call yield a different result?

Question

In my naive implementation of edit-distance finder, I have to check whether the last characters of two strings match:

ulong editDistance(const string a, const string b) {
    if (a.length == 0)
        return b.length;
    if (b.length == 0)
        return a.length;

    const auto delt = a[$ - 1] == b[$ - 1] ? 0 : 1;

    import std.algorithm : min;

    return min(
        editDistance(a[0 .. $ - 1], b[0 .. $ - 1]) + delt, 
        editDistance(a, b[0 .. $ - 1]) + 1, 
        editDistance(a[0 .. $ - 1], b) + 1
    );
}

This yields the expected results but if I replace delt with its definition it always returns 1 on non-empty strings:

ulong editDistance(const string a, const string b) {
    if (a.length == 0)
        return b.length;
    if (b.length == 0)
        return a.length;

    //const auto delt = a[$ - 1] == b[$ - 1] ? 0 : 1;

    import std.algorithm : min;

    return min(
        editDistance(a[0 .. $ - 1], b[0 .. $ - 1]) + a[$ - 1] == b[$ - 1] ? 0 : 1, //delt, 
        editDistance(a, b[0 .. $ - 1]) + 1, 
        editDistance(a[0 .. $ - 1], b) + 1
    );
}

Why does this result change?

Answer 1

The operators have different precedence from what you expect. In const auto delt = a[$ - 1] == b[$ - 1] ? 0 : 1; there is no ambiguity, but in editDistance(a[0 .. $ - 1], b[0 .. $ - 1]) + a[$ - 1] == b[$ - 1] ? 0 : 1, there is (seemingly).

Simplifying:

auto tmp = editDistance2(a[0..$-1], b[0..$-1]);
return min(tmp + a[$-1] == b[$-1] ? 0 : 1),
    //...
);

The interesting part here is parsed as (tmp + a[$-1]) == b[$-1] ? 0 : 1, and tmp + a[$-1] is not equal to b[$-1]. The solution is to wrap things in parentheses:

editDistance(a[0 .. $ - 1], b[0 .. $ - 1]) + (a[$ - 1] == b[$ - 1] ? 0 : 1)