Sums of Digits (Codeforces 509C)
Tags: Implement, dp

Vasya had a strictly increasing sequence of positive integers a1, ..., an. Vasya used it to build a new sequence b1, ..., bn, where bi is the sum of digits of ai's decimal representation. Then sequence ai got lost and all that remained is sequence bi.Vasya wonders what the numbers ai could be like. Of all the possible options he likes the one sequence with the minimum possible last number an. Help Vasya restore the initial sequence.It is guaranteed that such a sequence always exists.

Input: The first line contains a single integer number n (1 ≤ n ≤ 300).Next n lines contain integer numbers b1, ..., bn  — the required sums of digits. All bi belong to the range 1 ≤ bi ≤ 300.

Output: Print n integer numbers, one per line — the correct option for numbers ai, in order of following in sequence. The sequence should be strictly increasing. The sum of digits of the i-th number should be equal to bi. If there are multiple sequences with least possible number an, print any of them. Print the numbers without leading zeroes.


Sample Inputs:
3
1
2
3

3
3
2
1

Sample Outputs:
1
2
3

3
11
100

Solution (Python):
(digs, a, le) = ([0] * 333, 0, 0)
for _ in range(int(input())):
    b = int(input())
    (delta, a) = (b - a, b)
    for (i, d) in enumerate(digs):
        if d < 9 and 0 < delta <= 9 * i + 9 - d:
            break
        delta += d
        digs[i] = 0
    digs[i] += 1
    le = max(le, i)
    (i, delta) = divmod(delta - 1, 9)
    digs[:i] = [9] * i
    digs[i] += delta
    print(''.join(map(str, digs[le::-1])))

Solution (Python):
t = [0] * 400
x = k = 0
for q in range(int(input())):
    y = int(input())
    (d, x) = (y - x, y)
    j = 0
    while d < 1 or t[j] > min(8, 9 * j + 9 - d):
        d += t[j]
        t[j] = 0
        j += 1
    t[j] += 1
    k = max(k, j)
    (a, b) = divmod(d - 1, 9)
    t[:a] = [9] * a
    t[a] += b
    print(''.join(map(str, t[k::-1])))

Solution (Python):
def fill9(x, u):
    k = x // 9
    for i in range(k):
        u[i] = 9
    if x % 9:
        u[k] = x % 9
        return k + 1
    else:
        return k
n = input()
n = int(n)
u = [0 for i in range(300 // 9 * 150 + 150)]
k = 1
for i in range(n):
    x = input()
    x = int(x)
    t = k - 1
    while t >= 0:
        if u[t] + 9 * t < x:
            t = fill9(x, u)
            if t > k:
                k = t
            break
        elif u[t] >= x:
            t += 1
            u[t] += 1
            x -= 1
            while u[t] == 10:
                u[t] = 0
                t += 1
                u[t] += 1
                x += 9
            if t + 1 > k:
                k = t + 1
            for t in range(fill9(x, u), t):
                u[t] = 0
            break
        else:
            x -= u[t]
            t -= 1
    v = [str(j) for j in u[k - 1:-len(u) - 1:-1]]
    print(''.join(v))