Binary String To Subsequences (Codeforces 1399D)
Tags: Greedy, data structures

You are given a binary string $$$s$$$ consisting of $$$n$$$ zeros and ones.Your task is to divide the given string into the minimum number of subsequences in such a way that each character of the string belongs to exactly one subsequence and each subsequence looks like "010101 ..." or "101010 ..." (i.e. the subsequence should not contain two adjacent zeros or ones).Recall that a subsequence is a sequence that can be derived from the given sequence by deleting zero or more elements without changing the order of the remaining elements. For example, subsequences of "1011101" are "0", "1", "11111", "0111", "101", "1001", but not "000", "101010" and "11100".You have to answer $$$t$$$ independent test cases.

Input: The first line of the input contains one integer $$$t$$$ ($$$1 \le t \le 2 \cdot 10^4$$$) — the number of test cases. Then $$$t$$$ test cases follow.The first line of the test case contains one integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the length of $$$s$$$. The second line of the test case contains $$$n$$$ characters '0' and '1' — the string $$$s$$$.It is guaranteed that the sum of $$$n$$$ does not exceed $$$2 \cdot 10^5$$$ ($$$\sum n \le 2 \cdot 10^5$$$).

Output: For each test case, print the answer: in the first line print one integer $$$k$$$ ($$$1 \le k \le n$$$) — the minimum number of subsequences you can divide the string $$$s$$$ to. In the second line print $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le k$$$), where $$$a_i$$$ is the number of subsequence the $$$i$$$-th character of $$$s$$$ belongs to.If there are several answers, you can print any.


Sample Inputs:
4
4
0011
6
111111
5
10101
8
01010000

Sample Outputs:
2
1 2 2 1 
6
1 2 3 4 5 6 
1
1 1 1 1 1 
4
1 1 1 1 1 2 3 4

Solution (Python):
import sys

def main():
    res = ''
    input = sys.stdin.readline
    print = sys.stdout.write
    t = int(input())
    for _ in range(t):
        n = int(input())
        s = input()
        zeros = []
        k_zeros = 0
        ones = []
        k_ones = 0
        nums = []
        k = 0
        for i in range(n):
            if s[i] == '1':
                k_ones += 1
                if k_zeros != 0:
                    k_zeros -= 1
                    nums.append(str(zeros[-1]))
                    ones.append(zeros[-1])
                    del zeros[-1]
                else:
                    k += 1
                    ones.append(k)
                    nums.append(str(k))
            else:
                k_zeros += 1
                if k_ones != 0:
                    k_ones -= 1
                    nums.append(str(ones[-1]))
                    zeros.append(ones[-1])
                    del ones[-1]
                else:
                    k += 1
                    zeros.append(k)
                    nums.append(str(k))
        res += str(k) + '\n' + ' '.join(nums) + '\n'
    print(res)
main()

Solution (Python):
import bisect
import collections
import math
import random
import sys
p2D = lambda x: print(*x, sep='\n')

def II():
    return int(sys.stdin.buffer.readline())

def MI():
    return map(int, sys.stdin.buffer.readline().split())

def LI():
    return list(map(int, sys.stdin.buffer.readline().split()))

def LLI(rows_number):
    return [LI() for _ in range(rows_number)]

def BI():
    return sys.stdin.buffer.readline().rstrip()

def SI():
    return sys.stdin.buffer.readline().rstrip().decode()

def li():
    return [int(i) for i in input().split()]

def lli(rows):
    return [li() for _ in range(rows)]

def si():
    return input()

def ii():
    return int(input())

def ins():
    return input().split()

def drank(d, processing, da, rank):
    tmp = 10 ** 9
    if len(d[da]) == 1:
        return 1
    for di in d[da]:
        if processing[di - 1] == 0:
            processing[di - 1] = 1
            tmp = min(tmp, drank(d, processing, di, rank))
            processing[di - 1] = 0
    rank[da - 1] = tmp + 1
    return tmp + 1

def binary_search(n, a):
    l = len(a)
    low = 0
    high = l - 1
    while high >= low:
        mid = (high + low) // 2
        if a[mid] == n:
            return mid
        elif a[mid] > n:
            high = mid - 1
        else:
            low = mid + 1
    return -1

def solve():
    n = II()
    s = SI()
    postive = []
    negetive = []
    pneutrals = []
    nneutrals = []
    x = 1
    ans = []
    for i in range(n):
        if s[i] == '1':
            if negetive:
                z = negetive.pop()
                nneutrals.append(z)
            elif pneutrals:
                z = pneutrals.pop()
                postive.append(z)
            else:
                z = x
                postive.append(x)
                x += 1
            ans.append(z)
        else:
            if postive:
                z = postive.pop()
                pneutrals.append(z)
            elif nneutrals:
                z = nneutrals.pop()
                negetive.append(z)
            else:
                z = x
                negetive.append(x)
                x += 1
            ans.append(z)
    print(len(postive) + len(negetive) + len(pneutrals) + len(nneutrals))
    return ' '.join(map(str, ans))

def main():
    for _ in range(II()):
        sys.stdout.write(str(solve()) + '\n')
if __name__ == '__main__':
    main()

Solution (Python):
from collections import deque

def solve():
    t = int(input())
    for cs in range(1, t + 1):
        n = int(input())
        s = input().strip()
        (p0, p1) = (deque(), deque())
        ans = [0] * n
        cnt = 0
        for i in range(n):
            if s[i] == '1':
                if p0:
                    ans[i] = p0.popleft()
                else:
                    cnt += 1
                    ans[i] = cnt
                p1.append(ans[i])
            else:
                if p1:
                    ans[i] = p1.popleft()
                else:
                    cnt += 1
                    ans[i] = cnt
                p0.append(ans[i])
        print(cnt)
        print(' '.join(map(str, ans)))
if __name__ == '__main__':
    solve()