Equilateral numbers

def eqnum(k):
    if k % 2 == 1:
        return k*((k+1)//2)
    else:
        return (k//2)*(k+1)
# print(eqnum(120000), 10**12)
# exit()
def binsearch(n, k0, k1):
    mid = (k0 + k1) // 2
    e = eqnum(mid)
    # print(n, k0, k1, e)
    if e == n:
        return mid
    elif k0 >= k1:
        if e > n:
            return k1-1
        else:
            return k1
    elif e > n:
        return binsearch(n, k0, mid-1)
    else:
        return binsearch(n, mid+1, k1)

n0 = int(input())
others = [([], 10**13, n0, 0)]
completed = []
while len(others):
    nums, k, n, c = others[0]
    others = others[1:]
    while(n):
        e = eqnum(k)
        e2 = eqnum(k-1)
        e3 = eqnum(k-2)
        if e2 >= 1 and 2*e2 <= n:
            nums2 = [x for x in nums]
            nums2.append(e2)
            nums2.append(e2)
            others.append([nums2, k-1, n-e2*2, c+2])
        if e3 >= 1 and 3*e3 <= n:
            nums3 = [x for x in nums]
            nums3.append(e3)
            nums3.append(e3)
            nums3.append(e3)
            others.append([nums3, k-2, n-e3*3, c+3])
        for l in range(k-3,k-100,-1):
            if l < 1:
                break
            eee = eqnum(l)
            if eee >= 1 and (k - l)*eee <= n:
                nums3 = [x for x in nums]
                for _ in range(k - l):
                    nums3.append(eee)
                others.append([nums3, l, n-(k - l) * eee, 0])
        if e <= n:
            c += 1
            n -= e
            nums.append(e)
        else:
            k = binsearch(n,1,k)
    # print(len(others))
    completed.append([x for x in nums])
mc = 10**12
mp = None
# print(len(completed), completed)
for c in completed:
    if len(c) < mc:
        mp = c
        mc = len(c)
        # print("val", c)
print(mc)
# print(len(mc), sum(nums), nums)
# print(c, sum(nums), nums)

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: WRONG ANSWER

Test 6

Verdict: TIME LIMIT EXCEEDED

Test 7

Verdict: WRONG ANSWER

Test 8

Verdict: WRONG ANSWER

Test 9

Verdict: TIME LIMIT EXCEEDED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: WRONG ANSWER

Test 12

Verdict: WRONG ANSWER