How to optimise a strictly increasing stack based list

Question

So I am trying to solve https://leetcode.com/problems/daily-temperatures Basically given an array [30,40,50,60] we need to return the indices of the next increasing value so output would be [1,1,1,0] My algorithm is to

1. while end !=0 read from the array
2. if last element add 0 to output and stack
3. Else if temperature[end] > stack top add to stack and add stack top to be the temperature difference.
4. If temperature[end] <= stack top then we pop every element until this condition breaks and update the stack top and output.

I keep getting a time limit exceeded here, My understanding here is that the complexity is O(N). I am not sure how to optimise it further.

def dailyTemperatures(self, temperatures: List[int]) -> List[int]:
        output = []
        r = len(temperatures) - 1
        stack = []
        while r >= 0:
            if r == len(temperatures) - 1:
                stack.append(r)
                output.insert(0, 0)
            else:
                if temperatures[stack[-1]] > temperatures[r]:
                    output.insert(0, stack[-1]-r)
                    stack.append(r)
                else:
                    while stack and temperatures[stack[-1]] <= temperatures[r]:
                        stack.pop()
                    if len(stack) == 0:
                        output.insert(0, 0)
                        stack.append(r)
                    else:
                        output.insert(0, stack[-1]-r)
                        stack.append((r))

            r -= 1
        return output

Answer 1

An efficient implementation of a slow algorithm will still scale slowly. Optimizing the stack won't change the big-O. But I'll outline an idea using a different data structure for you to figure out.

In example1 of the problem you start with the array [73,74,75,71,69,72,76,73] . Let's arrange this in terms of maxes of ranges like so:

x = [
    [73,74,75,71,69,72,76,73],
    [   74,   75,   72,   76],
    [         75,         76],
    [                     76],
]

In other words x[i][j] gives the max of all elements from j * 2**i to (j+1) * 2**i - 1 .

Now to find the first rise after k we go "forward and down" until we find a block with a larger (or 0 if there is none) and then "up and forward" until we find where it is. Where:

while going forward and down at (i, j): if j is even: if j not at end of x[i]: move to (i, j+1) then test else: answer is 0 else: move to (i+1, j//2 + 1) then test

while going up and forward at (i, j) with 0 < i: if answer in range for (i-1, j+j): move to (i-1, j+j) else: move to (i-1, j+j+1)

For example if k was 2 we would do this.

start at (0, 2)
go f&d to (0, 3), check if 75 < x[0][3] (ie 71), stay f&d
go f&d to (1, 2), check if 75 < x[1][2] (ie 72), stay f&d
go f&d to (1, 3), check if 75 < x[1][3] (ie 76), switch to u&f
check if 75 < x[0][6] (ie 76) go u&f to (0, 6)

And now we know that the next one is at position 6. So we get 6 - 2 == 4 there.

What is the performance? The whole data structure is O(n) to build. Each lookup is at worst O(log(n)) . So doing the n checks is at worst O(n log(n)) . Which should be fast enough.

Answer 2

My Solution is

def dailyTemperatures(self, temperatures):
    res = []
    i = 0
    while i < len(temperatures) - 1:
        j = i + 1
        while True:
            if j >= len(temperatures):
                res.append(0)
                break
            if temperatures[j] <= temperatures[i]:
                j += 1
            else:
                res.append(j - i)
                break
        i += 1
    res.append(0)
    return res
    

Answer 3

After considerable testing, your answer IS linear. (And therefore better than what I suggested before.) However in order to meet their time limit you need to microptimize everything. Meaning get rid of every unneeded if , make sure your comparisons are the fastest possible, etc.

I would definitely say that leetcode set the time limit too restrictively for the problem and language performance.

def dailyTemperatures(self, temperatures: List[int]) -> List[int]:
    if 0 == len(temperatures):
        return []
    output = [0]
    r = len(temperatures) - 1
    stack = [r]
    r -= 1
    while r >= 0:
        while len(stack) and temperatures[stack[-1]] <= temperatures[r]:
            stack.pop()
        if len(stack) == 0:
            output.append(0)
        else:
            output.append(stack[-1]-r)
        stack.append((r))
        r -= 1
    output.reverse()
    return output