自下而上的动态编程

Question

I was trying to write a dynamic programming that counts the number of ways in which the road can be paved by using stones that are 2, 3, 5 meters. When I put 2, it gave me an error and starting from 2 to 20, it was supposed to give an output of

1, 1, 1, 3, 2, 5, 6, 8, 14, 16, 27, 36, 51, 77, 103, 155, 216, 309, 448

My code gives this result when I start the input from 3. Did I misunderstand something here?

def waysRoad(n):
    if n<0:
        return 0

    dp = [0] * (n+1)
    dp[0] = 1
    dp[1] = 0
    for i in range(2, n):
        sum = 0
        if i >=2:
            sum += dp[i-2]

        if i >=3:
            sum += dp[i-3]
        if i >=5:
            sum += dp[i-5]
        dp[i] = sum
    return dp[i]

Answer 1

To fill n-th list entry, you need to use loop limit n+1 :

for i in range(2, n + 1):

also it is worth to change return to

return dp[n]