Can someone help me solve this programming problem?

[deanhystad]

This might do what you want. It splits the data into a bunch of localized peak valleys using your 10% change threshold. The localized peak valleys for [100, 99, 90, 79, 62, 94, 88, 75, 80, 72, 74, 87, 84, 90] are [100, 99, 90], [90, 79], [79, 62], [62, 94], [94, 88, 75], [75, 80, 72, 74, 87], [87, 84, 90]. This is done by the Trend class, a list with a special append() method.

The Trends class creates a list of trends. When a Trend is appended to the list, Trends combines the new trend with the previous trend. If both trends trend in the same direction, the new trend is absorbed into the previous trend. If the new trend changes direction, Trends searches for the peak or valley (depending on direction) in the new trend. This is the start of the new trend, and points prior to this are moved to the previous trend.

class Trend(list):
    """A list of numbers that trend in the same direction."""

    def __init__(self, value=None):
        super().__init__()
        self.direction = 0
        super().append(value)

    def append(self, value):
        """Add number to Trend.  Return direction of trend (-1, 0, 1)."""
        super().append(value)
        if value <= self[0] * 0.9 or value >= self[0] * 1.1:
            self.direction = 1 if self[-1] > self[0] else -1
        return self.direction


class Trends(list):
    """Convert list of numbers to a list of trends."""

    def __init__(self, values):
        super().__init__()
        trend = Trend(values[0])
        for value in values[1:]:
            if trend.append(value) != 0:
                self._add_trend(trend)
                trend = Trend(value)
        self._add_trend(trend)

    def _add_trend(self, trend):
        """Combine last trend into list"""
        prev = self[-1] if self else None
        if prev:
            i = trend.index(max(trend) if prev.direction == 1 else min(trend))
            prev.extend(trend[1:i+1])
            del trend[:i]
        if len(trend) > 1:
            super().append(trend)


print(Trends([100, 99, 90, 79, 62, 94, 88, 75, 80, 72, 74, 87, 84, 90]))

And as a generator without using classes:

def trends(numbers):
    prev = None
    trend = []
    prev_dir = trend_dir = 0
    for number in numbers:
        trend.append(number)
        if number > trend[0] * 1.1 or number < trend[0] * 0.9:
            trend_dir = 1 if number > trend[0] else -1
            if prev:
                if trend_dir in (0, prev_dir):
                    prev.extend(trend)
                else:
                    elbow = min(trend) if trend_dir > 0 else max(trend)
                    index = trend.index(elbow)
                    prev.extend(trend[1:index+1])
                    yield prev
                    prev = trend[index:]
                    prev_dir = trend_dir
            else:
                prev = trend
                prev_dir = trend_dir
            trend = [number]
    if len(trend) > 1:
        if prev:
            prev.extend(trend[1:])
            yield prev
        else:
            yield trend


data = [100, 99, 90, 79, 62, 94, 88, 75, 80, 72, 74, 87, 84, 90]
print(*trends(data))