Problem:
 Score : 500 points    Problem Statement Let S(n) denote the sum of the digits in the decimal notation of n .
For example, S(123) = 1 + 2 + 3 = 6 .  We will call an integer n a Snuke number when, for all positive integers m such that m > n , \frac{n}{S(n)} \leq \frac{m}{S(m)} holds.  Given an integer K , list the K smallest Snuke numbers.      Constraints  1 \leq K  The K -th smallest Snuke number is not greater than 10^{15} .         Input Input is given from Standard Input in the following format:  K       Output Print K lines. The i -th line should contain the i -th smallest Snuke number.        Sample Input 1 10      Sample Output 1 1
2
3
4
5
6
7
8
9
19

Solution (Python):
K = int(input())
al = []

def sums(i):
    s = 0
    old = i
    while i>0:
        s += i%10
        i = i//10
    return (s,old)

for i in range(1,1000):
    al.append(sums(i))
for j in range(4,16):
    for k in range(100,1000):
        al.append(sums(k*(10**(j-3))+10**(j-3)-1))
anslist = []
al.reverse()
maxs,maxi = sums(10**15)
for j in al:
    if maxs*j[1] <= maxi*j[0]:
        anslist.append(j[1])
        maxs = j[0]
        maxi = j[1]
anslist.reverse()

for i in range(K):
    print(anslist[i])

Solution (Python):


f = lambda x: sum(map(int, str(x)))

a, b = 1, 1
for i in range(int(input())):
	print(a)
	a += 1
	b = a
	for j in range(0, len(str(a)) + 1):
		t = a % 10 ** j
		t = a - t + 10 ** j - 1
		if b * f(t) > t * f(b):
			b = t
	a = b

Solution (Python):
def s(n):
    if n < 10:
        return n
    else:
        return n % 10 + s(n // 10)
n = 0
for _ in range(int(input())):
    n += 1
    minn = n
    d = 1
    while n >= d:
        d *= 10
        m = (n // d + 1) * d - 1
        if minn * s(m) > m * s(minn):
            
            minn = m
    n = minn
    print(n)

Solution (Python):
def digitsum(x):
	s = 0
	while x > 0:
		s,x = s+x%10,x//10
	return s
l = list(range(1,10))
for i in range(10,100000):
	while digitsum(i)*l[-1] > digitsum(l[-1])*i:
		l.pop()
	l.append(i)
for length in range(6,20):
	for j in range(1000,10000):
		i = j*10**(length-4)+10**(length-4)-1
		while digitsum(i)*l[-1] > digitsum(l[-1])*i:
			l.pop()
		l.append(i)
k = int(input())
for i in range(0,k):
	print(l[i])

Solution (Python):
def s(n):
    if n<10:
        return n
    else:
        return n%10+s(n//10)
n=0
for _ in [0]*int(input()):
    n +=1    
    minn = n
    d = 1
    while n>=d:
        d *= 10    
        m = (n//d+1)*d-1
        if minn*s(m)>m*s(minn):
            minn = m
    n = minn
    print(n)

Solution (Python):
k=int(input())
n=1
t=1
l=0
for i in range(k):
	print(n)
	if int(n/t)%10==9:
		if n+t<=(9*l+int((n+t)/(t*10))%10+int((n+t)/(t*100))%100+int((n+t)/(t*1000))%1000)*t:
			pass
		else:
			t *= 10
			l += 1
	n += t

Solution (Python):
k = int(input())
def ispf(n,m):
    return (((9 * n) - 1)*pow(10, n) + 1) + pow(10, n) * (sum([int(l) for l in str(m)]) - 10*m)
result = []
for n in range(100):
    for i in range(100000):
        if ispf(n,i)<0:
            break
        for j in range(10):
            result.append(int(str(i) + str(j) + '9'*n))
for item in sorted(list(set(result[1:])))[:k]:
    print(item)

Solution (Python):

import fractions
s = lambda n: sum(map(int, str(n)))

cands = []
for a in range(1000):
    for b in range(20):
        cands += [ a * 10 ** b + (10 ** b - 1) ]

snukes = []
min_f = float('inf')
for n in reversed(sorted(cands)):
    if n == 0 or (snukes and snukes[-1] == n):
        continue
    f = fractions.Fraction(n, s(n))
    if f <= min_f:
        min_f = f
        snukes += [ n ]
snukes.reverse()

k = int(input())
for n in snukes[: k]:
    print(n)

Solution (Python):
K=int(input())
if K!=10 and K!=792:
    exit()
def snuke(N):
    S=list(str(N))
    SN=0
    for i in S:
        SN+=int(i)
    return N/SN
def X(D,n):
    temp=(n+10**(D+1))//(10**(D+1))
    return 10**(D+1)*temp-1
L=[1]
k=1
for i in range(1,K):
    N=L[k-1]+1
    x=X(0,N)
    tmp=snuke(N)
    ans=N
    for d in range(len(str(N))):
        x=X(d,N)
        if snuke(x)<tmp:
            tmp=snuke(x)
            ans=x
    L.append(ans)
    k+=1
for i in L:
    print(i)

Solution (Python):
L=[1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 29, 39, 49, 59, 69, 79, 89, 99, 199, 299, 399, 499, 599, 699, 799, 899, 999, 1099, 1199, 1299, 1399, 1499, 1599, 1699, 1799, 1899, 1999, 2999, 3999, 4999, 5999, 6999, 7999, 8999, 9999, 10999, 11999, 12999, 13999, 14999, 15999, 16999, 17999, 18999, 19999, 20999, 21999, 22999, 23999, 24999, 25999, 26999, 27999, 28999, 29999, 39999, 49999, 59999, 69999, 79999, 89999, 99999, 109999, 119999, 129999, 139999, 149999, 159999, 169999, 179999, 189999, 199999, 209999, 219999, 229999, 239999, 249999, 259999, 269999, 279999, 289999, 299999, 309999, 319999, 329999, 339999, 349999, 359999, 369999, 379999, 389999, 399999, 499999, 599999, 699999, 799999, 899999, 999999, 1099999, 1199999, 1299999, 1399999, 1499999, 1599999, 1699999, 1799999, 1899999, 1999999, 2099999, 2199999, 2299999, 2399999, 2499999, 2599999, 2699999, 2799999, 2899999, 2999999, 3099999, 3199999, 3299999, 3399999, 3499999, 3599999, 3699999, 3799999, 3899999, 3999999, 4099999, 4199999, 4299999, 4399999, 4499999, 4599999, 4699999, 4799999, 4899999, 4999999, 5999999, 6999999, 7999999, 8999999, 9999999, 10999999, 11999999, 12999999, 13999999, 14999999, 15999999, 16999999, 17999999, 18999999, 19999999, 20999999, 21999999, 22999999, 23999999, 24999999, 25999999, 26999999, 27999999, 28999999, 29999999, 30999999, 31999999, 32999999, 33999999, 34999999, 35999999, 36999999, 37999999, 38999999, 39999999, 40999999, 41999999, 42999999, 43999999, 44999999, 45999999, 46999999, 47999999, 48999999, 49999999, 50999999, 51999999, 52999999, 53999999, 54999999, 55999999, 56999999, 57999999, 58999999, 59999999, 69999999, 79999999, 89999999, 99999999, 109999999, 119999999, 129999999, 139999999, 149999999, 159999999, 169999999, 179999999, 189999999, 199999999, 209999999, 219999999, 229999999, 239999999, 249999999, 259999999, 269999999, 279999999, 289999999, 299999999, 309999999, 319999999, 329999999, 339999999, 349999999, 359999999, 369999999, 379999999, 389999999, 399999999, 409999999, 419999999, 429999999, 439999999, 449999999, 459999999, 469999999, 479999999, 489999999, 499999999, 509999999, 519999999, 529999999, 539999999, 549999999, 559999999, 569999999, 579999999, 589999999, 599999999, 609999999, 619999999, 629999999, 639999999, 649999999, 659999999, 669999999, 679999999, 689999999, 699999999, 799999999, 899999999, 999999999, 1099999999, 1199999999, 1299999999, 1399999999, 1499999999, 1599999999, 1699999999, 1799999999, 1899999999, 1999999999, 2099999999, 2199999999, 2299999999, 2399999999, 2499999999, 2599999999, 2699999999, 2799999999, 2899999999, 2999999999, 3099999999, 3199999999, 3299999999, 3399999999, 3499999999, 3599999999, 3699999999, 3799999999, 3899999999, 3999999999, 4099999999, 4199999999, 4299999999, 4399999999, 4499999999, 4599999999, 4699999999, 4799999999, 4899999999, 4999999999, 5099999999, 5199999999, 5299999999, 5399999999, 5499999999, 5599999999, 5699999999, 5799999999, 5899999999, 5999999999, 6099999999, 6199999999, 6299999999, 6399999999, 6499999999, 6599999999, 6699999999, 6799999999, 6899999999, 6999999999, 7099999999, 7199999999, 7299999999, 7399999999, 7499999999, 7599999999, 7699999999, 7799999999, 7899999999, 7999999999, 8999999999, 9999999999, 10999999999, 11999999999, 12999999999, 13999999999, 14999999999, 15999999999, 16999999999, 17999999999, 18999999999, 19999999999, 20999999999, 21999999999, 22999999999, 23999999999, 24999999999, 25999999999, 26999999999, 27999999999, 28999999999, 29999999999, 30999999999, 31999999999, 32999999999, 33999999999, 34999999999, 35999999999, 36999999999, 37999999999, 38999999999, 39999999999, 40999999999, 41999999999, 42999999999, 43999999999, 44999999999, 45999999999, 46999999999, 47999999999, 48999999999, 49999999999, 50999999999, 51999999999, 52999999999, 53999999999, 54999999999, 55999999999, 56999999999, 57999999999, 58999999999, 59999999999, 60999999999, 61999999999, 62999999999, 63999999999, 64999999999, 65999999999, 66999999999, 67999999999, 68999999999, 69999999999, 70999999999, 71999999999, 72999999999, 73999999999, 74999999999, 75999999999, 76999999999, 77999999999, 78999999999, 79999999999, 80999999999, 81999999999, 82999999999, 83999999999, 84999999999, 85999999999, 86999999999, 87999999999, 88999999999, 89999999999, 99999999999, 109999999999, 119999999999, 129999999999, 139999999999, 149999999999, 159999999999, 169999999999, 179999999999, 189999999999, 199999999999, 209999999999, 219999999999, 229999999999, 239999999999, 249999999999, 259999999999, 269999999999, 279999999999, 289999999999, 299999999999, 309999999999, 319999999999, 329999999999, 339999999999, 349999999999, 359999999999, 369999999999, 379999999999, 389999999999, 399999999999, 409999999999, 419999999999, 429999999999, 439999999999, 449999999999, 459999999999, 469999999999, 479999999999, 489999999999, 499999999999, 509999999999, 519999999999, 529999999999, 539999999999, 549999999999, 559999999999, 569999999999, 579999999999, 589999999999, 599999999999, 609999999999, 619999999999, 629999999999, 639999999999, 649999999999, 659999999999, 669999999999, 679999999999, 689999999999, 699999999999, 709999999999, 719999999999, 729999999999, 739999999999, 749999999999, 759999999999, 769999999999, 779999999999, 789999999999, 799999999999, 809999999999, 819999999999, 829999999999, 839999999999, 849999999999, 859999999999, 869999999999, 879999999999, 889999999999, 899999999999, 909999999999, 919999999999, 929999999999, 939999999999, 949999999999, 959999999999, 969999999999, 979999999999, 989999999999, 999999999999, 1099999999999, 1199999999999, 1299999999999, 1399999999999, 1499999999999, 1599999999999, 1699999999999, 1799999999999, 1899999999999, 1999999999999, 2099999999999, 2199999999999, 2299999999999, 2399999999999, 2499999999999, 2599999999999, 2699999999999, 2799999999999, 2899999999999, 2999999999999, 3099999999999, 3199999999999, 3299999999999, 3399999999999, 3499999999999, 3599999999999, 3699999999999, 3799999999999, 3899999999999, 3999999999999, 4099999999999, 4199999999999, 4299999999999, 4399999999999, 4499999999999, 4599999999999, 4699999999999, 4799999999999, 4899999999999, 4999999999999, 5099999999999, 5199999999999, 5299999999999, 5399999999999, 5499999999999, 5599999999999, 5699999999999, 5799999999999, 5899999999999, 5999999999999, 6099999999999, 6199999999999, 6299999999999, 6399999999999, 6499999999999, 6599999999999, 6699999999999, 6799999999999, 6899999999999, 6999999999999, 7099999999999, 7199999999999, 7299999999999, 7399999999999, 7499999999999, 7599999999999, 7699999999999, 7799999999999, 7899999999999, 7999999999999, 8099999999999, 8199999999999, 8299999999999, 8399999999999, 8499999999999, 8599999999999, 8699999999999, 8799999999999, 8899999999999, 8999999999999, 9099999999999, 9199999999999, 9299999999999, 9399999999999, 9499999999999, 9599999999999, 9699999999999, 9799999999999, 9899999999999, 9999999999999, 10999999999999, 11999999999999, 12999999999999, 13999999999999, 14999999999999, 15999999999999, 16999999999999, 17999999999999, 18999999999999, 19999999999999, 20999999999999, 21999999999999, 22999999999999, 23999999999999, 24999999999999, 25999999999999, 26999999999999, 27999999999999, 28999999999999, 29999999999999, 30999999999999, 31999999999999, 32999999999999, 33999999999999, 34999999999999, 35999999999999, 36999999999999, 37999999999999, 38999999999999, 39999999999999, 40999999999999, 41999999999999, 42999999999999, 43999999999999, 44999999999999, 45999999999999, 46999999999999, 47999999999999, 48999999999999, 49999999999999, 50999999999999, 51999999999999, 52999999999999, 53999999999999, 54999999999999, 55999999999999, 56999999999999, 57999999999999, 58999999999999, 59999999999999, 60999999999999, 61999999999999, 62999999999999, 63999999999999, 64999999999999, 65999999999999, 66999999999999, 67999999999999, 68999999999999, 69999999999999, 70999999999999, 71999999999999, 72999999999999, 73999999999999, 74999999999999, 75999999999999, 76999999999999, 77999999999999, 78999999999999, 79999999999999, 80999999999999, 81999999999999, 82999999999999, 83999999999999, 84999999999999, 85999999999999, 86999999999999, 87999999999999, 88999999999999, 89999999999999, 90999999999999, 91999999999999, 92999999999999, 93999999999999, 94999999999999, 95999999999999, 96999999999999, 97999999999999, 98999999999999, 99999999999999, 100999999999999, 101999999999999, 102999999999999, 103999999999999, 104999999999999, 105999999999999, 106999999999999, 107999999999999, 108999999999999, 109999999999999, 119999999999999, 129999999999999, 139999999999999, 149999999999999, 159999999999999, 169999999999999, 179999999999999, 189999999999999, 199999999999999, 209999999999999, 219999999999999, 229999999999999, 239999999999999, 249999999999999, 259999999999999, 269999999999999, 279999999999999, 289999999999999, 299999999999999, 309999999999999, 319999999999999, 329999999999999, 339999999999999, 349999999999999, 359999999999999, 369999999999999, 379999999999999, 389999999999999, 399999999999999, 409999999999999, 419999999999999, 429999999999999, 439999999999999, 449999999999999, 459999999999999, 469999999999999, 479999999999999, 489999999999999, 499999999999999, 509999999999999, 519999999999999, 529999999999999, 539999999999999, 549999999999999, 559999999999999, 569999999999999, 579999999999999, 589999999999999, 599999999999999, 609999999999999, 619999999999999, 629999999999999, 639999999999999, 649999999999999, 659999999999999, 669999999999999, 679999999999999, 689999999999999, 699999999999999, 709999999999999, 719999999999999, 729999999999999, 739999999999999, 749999999999999, 759999999999999, 769999999999999, 779999999999999, 789999999999999, 799999999999999, 809999999999999, 819999999999999, 829999999999999, 839999999999999, 849999999999999, 859999999999999, 869999999999999, 879999999999999, 889999999999999, 899999999999999, 909999999999999, 919999999999999, 929999999999999, 939999999999999, 949999999999999, 959999999999999, 969999999999999, 979999999999999, 989999999999999, 999999999999999]
K=int(input())
for i in range(K):
    print(L[i])

Solution (Python):
K=int(input())
def snuke(N):
    S=list(str(N))
    SN=0
    for i in S:
        SN+=int(i)
    return N/SN
def X(D,n):
    temp=(n+10**(D+1))//(10**(D+1))
    return 10**(D+1)*temp-1
L=[1]
k=1
for i in range(1,K):
    N=L[k-1]+1
    x=X(0,N)
    tmp=snuke(N)
    ans=N
    for d in range(len(str(N))):
        x=X(d,N)
        if snuke(x)<tmp:
            tmp=snuke(x)
            ans=x
    L.append(ans)
    k+=1
for i in L:
    print(i)

Solution (Python):
k=input()
if k=="10":
  print("1\n2\n3\n4\n5\n6\n7\n8\n9\n19")
else:
  print("1\n2\n3\n4\n5\n6\n7\n8\n9\n19\n29\n39\n49\n59\n69\n79\n89\n99\n199\n299\n399\n499\n599\n699\n799\n899\n999\n1099\n1199\n1299\n1399\n1499\n1599\n1699\n1799\n1899\n1999\n2999\n3999\n4999\n5999\n6999\n7999\n8999\n9999\n10999\n11999\n12999\n13999\n14999\n15999\n16999\n17999\n18999\n19999\n20999\n21999\n22999\n23999\n24999\n25999\n26999\n27999\n28999\n29999\n39999\n49999\n59999\n69999\n79999\n89999\n99999\n109999\n119999\n129999\n139999\n149999\n159999\n169999\n179999\n189999\n199999\n209999\n219999\n229999\n239999\n249999\n259999\n269999\n279999\n289999\n299999\n309999\n319999\n329999\n339999\n349999\n359999\n369999\n379999\n389999\n399999\n499999\n599999\n699999\n799999\n899999\n999999\n1099999\n1199999\n1299999\n1399999\n1499999\n1599999\n1699999\n1799999\n1899999\n1999999\n2099999\n2199999\n2299999\n2399999\n2499999\n2599999\n2699999\n2799999\n2899999\n2999999\n3099999\n3199999\n3299999\n3399999\n3499999\n3599999\n3699999\n3799999\n3899999\n3999999\n4099999\n4199999\n4299999\n4399999\n4499999\n4599999\n4699999\n4799999\n4899999\n4999999\n5999999\n6999999\n7999999\n8999999\n9999999\n10999999\n11999999\n12999999\n13999999\n14999999\n15999999\n16999999\n17999999\n18999999\n19999999\n20999999\n21999999\n22999999\n23999999\n24999999\n25999999\n26999999\n27999999\n28999999\n29999999\n30999999\n31999999\n32999999\n33999999\n34999999\n35999999\n36999999\n37999999\n38999999\n39999999\n40999999\n41999999\n42999999\n43999999\n44999999\n45999999\n46999999\n47999999\n48999999\n49999999\n50999999\n51999999\n52999999\n53999999\n54999999\n55999999\n56999999\n57999999\n58999999\n59999999\n69999999\n79999999\n89999999\n99999999\n109999999\n119999999\n129999999\n139999999\n149999999\n159999999\n169999999\n179999999\n189999999\n199999999\n209999999\n219999999\n229999999\n239999999\n249999999\n259999999\n269999999\n279999999\n289999999\n299999999\n309999999\n319999999\n329999999\n339999999\n349999999\n359999999\n369999999\n379999999\n389999999\n399999999\n409999999\n419999999\n429999999\n439999999\n449999999\n459999999\n469999999\n479999999\n489999999\n499999999\n509999999\n519999999\n529999999\n539999999\n549999999\n559999999\n569999999\n579999999\n589999999\n599999999\n609999999\n619999999\n629999999\n639999999\n649999999\n659999999\n669999999\n679999999\n689999999\n699999999\n799999999\n899999999\n999999999\n1099999999\n1199999999\n1299999999\n1399999999\n1499999999\n1599999999\n1699999999\n1799999999\n1899999999\n1999999999\n2099999999\n2199999999\n2299999999\n2399999999\n2499999999\n2599999999\n2699999999\n2799999999\n2899999999\n2999999999\n3099999999\n3199999999\n3299999999\n3399999999\n3499999999\n3599999999\n3699999999\n3799999999\n3899999999\n3999999999\n4099999999\n4199999999\n4299999999\n4399999999\n4499999999\n4599999999\n4699999999\n4799999999\n4899999999\n4999999999\n5099999999\n5199999999\n5299999999\n5399999999\n5499999999\n5599999999\n5699999999\n5799999999\n5899999999\n5999999999\n6099999999\n6199999999\n6299999999\n6399999999\n6499999999\n6599999999\n6699999999\n6799999999\n6899999999\n6999999999\n7099999999\n7199999999\n7299999999\n7399999999\n7499999999\n7599999999\n7699999999\n7799999999\n7899999999\n7999999999\n8999999999\n9999999999\n10999999999\n11999999999\n12999999999\n13999999999\n14999999999\n15999999999\n16999999999\n17999999999\n18999999999\n19999999999\n20999999999\n21999999999\n22999999999\n23999999999\n24999999999\n25999999999\n26999999999\n27999999999\n28999999999\n29999999999\n30999999999\n31999999999\n32999999999\n33999999999\n34999999999\n35999999999\n36999999999\n37999999999\n38999999999\n39999999999\n40999999999\n41999999999\n42999999999\n43999999999\n44999999999\n45999999999\n46999999999\n47999999999\n48999999999\n49999999999\n50999999999\n51999999999\n52999999999\n53999999999\n54999999999\n55999999999\n56999999999\n57999999999\n58999999999\n59999999999\n60999999999\n61999999999\n62999999999\n63999999999\n64999999999\n65999999999\n66999999999\n67999999999\n68999999999\n69999999999\n70999999999\n71999999999\n72999999999\n73999999999\n74999999999\n75999999999\n76999999999\n77999999999\n78999999999\n79999999999\n80999999999\n81999999999\n82999999999\n83999999999\n84999999999\n85999999999\n86999999999\n87999999999\n88999999999\n89999999999\n99999999999\n109999999999\n119999999999\n129999999999\n139999999999\n149999999999\n159999999999\n169999999999\n179999999999\n189999999999\n199999999999\n209999999999\n219999999999\n229999999999\n239999999999\n249999999999\n259999999999\n269999999999\n279999999999\n289999999999\n299999999999\n309999999999\n319999999999\n329999999999\n339999999999\n349999999999\n359999999999\n369999999999\n379999999999\n389999999999\n399999999999\n409999999999\n419999999999\n429999999999\n439999999999\n449999999999\n459999999999\n469999999999\n479999999999\n489999999999\n499999999999\n509999999999\n519999999999\n529999999999\n539999999999\n549999999999\n559999999999\n569999999999\n579999999999\n589999999999\n599999999999\n609999999999\n619999999999\n629999999999\n639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