yummy

int min, max
bool failEVEN, failODD = false // init both sequence checks with false so we can check them each cycle
vector = array of ints

foreach (var i in vector)
{
    // did both sequences fail already?
    if (failEVEN && failODD)
    {
        // stop the loop as there is no point checking further...
        break;
    }

    // check if i is an EVEN number (using MODULO it will return 0 when it is an EVEN number (no failsafe used here as no mega numbers are expected!))
    if (i % 2 == 0 && !failEVEN)
    {
        // is our current number bigger or the same as our last one?
        if (i >= max)
        {
            // yeah we got a valid number.. now store it to check against the next one...
            max = i;
        }
        else
        {
            // don't tell mom that we failed on our EVEN sequence... but tell our boss!
            failEVEN = true;
        }
    }
    else if (!failODD)
    {
        // is our current number smaller or the same as our last one?
        if (i <= min)
        {
            // yeah we got a valid number.. now store it to check against the next one...
            min = i;
        }
        else
        {
            // tell our superiors that we failed on the ODD sequence...
            failODD = true;
        }
    }
}

if (!failEVEN)
{
    print "EVEN sequence is valid!";
}
else
{
    print "EVEN sequence is NOT valid!";
}
if (!failODD)
{
    print "ODD sequence is valid!";
}
else
{
    print "ODD sequence is NOT valid!";
}