Problem:


Score : 600 points

Problem Statement

There is a game that involves three variables, denoted A, B, and C.

As the game progresses, there will be N events where you are asked to make a choice.
Each of these choices is represented by a string s_i. If s_i is AB, you must add 1 to A or B then subtract 1 from the other; if s_i is AC, you must add 1 to A or C then subtract 1 from the other; if s_i is BC, you must add 1 to B or C then subtract 1 from the other.

After each choice, none of A, B, and C should be negative.

Determine whether it is possible to make N choices under this condition. If it is possible, also give one such way to make the choices.

Constraints

1 \leq N \leq 10^5

0 \leq A,B,C \leq 10^9

N, A, B, C are integers.

s_i is AB, AC, or BC.

Input

Input is given from Standard Input in the following format:

N A B C
s_1
s_2
:
s_N

Output

If it is possible to make N choices under the condition, print Yes; otherwise, print No.

Also, in the former case, show one such way to make the choices in the subsequent N lines. The (i+1)-th line should contain the name of the variable (A, B, or C) to which you add 1 in the i-th choice.

Sample Input 1

2 1 3 0
AB
AC

Sample Output 1

Yes
A
C

You can successfully make two choices, as follows:

In the first choice, add 1 to A and subtract 1 from B. A becomes 2, and B becomes 2.

In the second choice, add 1 to C and subtract 1 from A. C becomes 1, and A becomes 1.

Sample Input 2

3 1 0 0
AB
BC
AB

Sample Output 2

No

Sample Input 3

1 0 9 0
AC

Sample Output 3

No

Sample Input 4

8 6 9 1
AC
BC
AB
BC
AC
BC
AB
AB

Sample Output 4

Yes
C
B
B
C
C
B
A
A



Sample input:
2 1 3 0
AB
AC


Sample output:
Yes
A
C

Submission status: Wrong Answer

Solution code:
# -*- coding: utf-8 -*-
abc = ["A","B","C"]

def calculate(x,y, q1,q2):
    flag = 0
    ans = ""
    if x == 1 and y == 1:
        if q1 == q2:
            y -= 1
            x += 1
            #print(y)
            if y < 0:
                print("No")
                flag = 1
                return(x, y, ans, flag)
            ans = abc[q1[0]]

        elif q2 != "":
            t = set(q1) & set(q2)
            s = set(q1) - t
            #print(t,s)
            if t < s:
                y -= 1
                x += 1
                #print(y)
                if y < 0:
                    print("No")
                    flag = 1
                    return(x, y, ans, flag)
                ans = abc[q1[0]]
            else:
                x -= 1
                y += 1
                ans = ""
                #print(x)
                if x < 0:
                    print("No")
                    flag = 1
                    return(x, y, ans, flag)
                ans = abc[q1[1]]

    elif x <= y:
        y -= 1
        x += 1
        #print(y)
        if y < 0:
            print("No")
            flag = 1
            return(x, y, ans, flag)
        ans = abc[q1[0]]
    else:
        x -= 1
        y += 1
        ans = ""
        #print(x)
        if x < 0:
            print("No")
            flag = 1
            return(x, y, ans, flag)
        ans = abc[q1[1]]
    return (x, y, ans, flag)

def main():
    N, A, B, C  =  [int(i) for i in input().split()]
    s = []
    for i in range(N):
        t = input()
        if t == "AB":
            s.append([0,1])
        if t == "AC":
            s.append([0,2])
        if t == "BC":
            s.append([1,2])
    #print(s)
    answers  = []
    for i, q1 in enumerate(s):
        ans = ""
        f = 0
        q2 = ""
        if i+1 != N:
            q2 = s[i+1]

        if q1 == [0,1]:
            #print(1)
            A, B, ans, f = calculate(A,B,q1,q2)
        if q1 == [1,2]:
            #print(2)
            B, C, ans,f  = calculate(B,C,q1,q2)
        if q1 == [0,2]:
            #print(3)
            A, C, ans,f  = calculate(A,C,q1,q2)
        answers.append(ans)
        if f == 1:
            return
    print("Yes")

    for a in answers:
        print(a)
if __name__ == "__main__":
    main()

Submission status: Wrong Answer

Solution code:
# -*- coding: utf-8 -*-
abc = ["A","B","C"]

def calculate(x,y, b, e):
    flag = 0
    ans = ""
    if x <= y:
        y -= 1
        x += 1
        #print(y)
        if y < 0:
            print("No")
            flag = 1
            return(x, y, ans, flag)
        ans = abc[b]
    else:
        x -= 1
        y += 1
        ans = ""
        #print(x)
        if x < 0:
            print("No")
            flag = 1
            return(x, y, ans, flag)
        ans = abc[e]
    return (x, y, ans, flag)

def main():
    N, A, B, C  =  [int(i) for i in input().split()]
    s = []
    for i in range(N):
        t = input()
        if t == "AB":
            s.append([0,1])
        if t == "AC":
            s.append([0,2])
        if t == "BC":
            s.append([1,2])
    #print(s)
    answers  = []
    for ss in s:
        ans = ""
        f = 0
        if ss == [0,1]:
            #print(1)
            A, B, ans, f = calculate(A,B,0,1)
        if ss == [1,2]:
            #print(2)
            B, C, ans,f  = calculate(B,C,1,2)
        if ss == [0,2]:
            #print(3)
            A, C, ans,f  = calculate(A,C,0,2)
        answers.append(ans)
        if f == 1:
            return
    print("Yes")

    for a in answers:
        print(a)
if __name__ == "__main__":
    main()

Submission status: Wrong Answer

Solution code:
# -*- coding: utf-8 -*-
abc = ["A","B","C"]

def calculate(x,y, b, e):
    flag = 0
    ans = ""
    if x <= y:
        y -= 1
        x += 1
        #print(y)
        if y < 0:
            print("No")
            flag = 1
            return(x, y, ans, flag)
        ans = abc[b]
    else:
        x -= 1
        y += 1
        ans = ""
        #print(x)
        if x < 0:
            print("No")
            flag = 1
            return(x, y, ans, flag)
        ans = abc[e]
    return (x, y, ans, flag)

def main():
    N, A, B, C  =  [int(i) for i in input().split()]
    s = []
    for i in range(N):
        t = input()
        if t == "AB":
            s.append([0,1])
        if t == "AC":
            s.append([0,2])
        if t == "BC":
            s.append([1,2])
    #print(s)
    answers  = []
    for ss in s:
        ans = ""
        f = 0
        if ss == [0,1]:
            #print(1)
            A, B, ans, f = calculate(A,B,0,1)
        if ss == [1,2]:
            #print(2)
            B, C, ans,f  = calculate(B,C,1,2)
        if ss == [0,2]:
            #print(3)
            A, C, ans,f  = calculate(A,C,0,2)
        answers.append(ans)
        if f == 1:
            return

    for a in answers:
        print(a)
if __name__ == "__main__":
    main()

Submission status: Wrong Answer

Solution code:
def main(sample_file = ''):

    """ convenient functions
    # for i, a in enumerate(iterable)
    # q, mod = divmod(a, b)
    # divmod(x, y) returns the tuple (x//y, x%y)
    # Higher-order function: reduce(operator.mul, xyz_count, 1)
    # manage median(s) using two heapq https://atcoder.jp/contests/abc127/tasks/abc127_f
    """

    """convenient decorator
    # @functools.lru_cache():
    # to facilitate use of recursive function
        # ex:
        # from functools import lru_cache
        # import sys
        # sys.setrecursionlimit(10**9)
        # @lru_cache(maxsize=None)
        # def fib(n):
        #     if n < 2:
        #         return n
        #     return fib(n-1) + fib(n-2)
        # print(fib(1000))
    """
    
    # import numpy as np
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product # https://docs.python.org/ja/3/library/itertools.html
    # accumulate() returns iterator! to get list: list(accumulate())
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  # prime factor
        b, e = 2, 0  # base, exponent
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):   
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        # TODO: How should I do when n - r is negative?
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict # https://docs.python.org/ja/3/library/collections.html#collections.deque
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest # https://docs.python.org/ja/3/library/heapq.html
    from copy import deepcopy, copy # https://docs.python.org/ja/3/library/copy.html
    import operator
    from operator import itemgetter #sort 
    # ex1: List.sort(key=itemgetter(1))
    # ex2: sorted(tuples, key=itemgetter(1,2))
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd # Deprecated since version 3.5: Use math.gcd() instead.
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    # first create factorial_list
    # fac_list = mod_factorial_list(n)
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    AtoZ = list('abcdefghijklmnopqrsruvwxyz')
    modpow = lambda a, n, p = MOD: pow(a, n, p) # Recursive function in python is slow!
    def modinv(a, p = MOD):
        # evaluate reciprocal using Fermat's little theorem:
        # a**(p-1) is identical to 1 (mod p) when a and p is coprime
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        # fac_list = modfactorial_list(100)
        # print(modcomb(100, 5, modfactorial_list(100)))
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    # Graph: https://en.wikipedia.org/wiki/Directed_graph
    # Bellman-Ford: O(|V||E|). Use this if there exists an edge with negative length in the graph
    # After N steps, the shortest path has converded if there doesn't exist an cycle of edges with negative
    # Watch out: d[N] == d[2*N] doesn't necessarily mean the graph doesn't have negative cycle
    # ref: https://www.youtube.com/watch?v=1Z6ofKN03_Y

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    """ initialize variables and set inputs
    # initialize variables
        # to initialize list, use [0] * n
        # to initialize two dimentional array:
            # ex) [[0] * N for _ in range(N)]
            # ex2) dp = [[0] * (N+1) for _ in range(W*2)]
    # set inputs
        # put inputs between specific values (almost as quickly)
        # ex) S = [-INF] + [int(r()) for _ in range(A)] + [INF]
        # open(0).read() is sometimes useful:
        # ex) n, m, *x = map(int, open(0).read().split())
        #     min(x[::2]) - max(x[1::2])
        # ex2) *x, = map(int, open(0).read().split())
        #     don't forget to add comma after *x if only one variable is used
    # preprocessing
        # transpose = [x for x in zip(*data)]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [(1, 4, 7), (2, 5, 8), (3, 6, 9)]
        # flat = [flatten for inner in data for flatten in inner]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [1, 2, 3, 4, 5, 6, 7, 8, 9]
    # calculate and output
        # output pattern
        # ex1) print(*l) => when l = [2, 5, 6], printed 2 5 6
    """

    # functions to read input
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    r_float = lambda: float(r())
    R = lambda: list(map(int, r().split()))
    R_str = lambda: r().split()
    R_map = lambda: map(int, r().split())
    R_float = lambda: list(map(float, r().split()))
    R_tuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    # single int: int(r())
    # single string: r()
    # single float: float(r())
    # line int: R()
    # line string: r().split()
    # line (str, int, int): [j if i == 0 else int(j) for i, j in enumerate(r().split())]
    # lines int: [R() for _ in range(n)]
    """

    # for test
    if sample_file:
        sys.stdin = open(sample_file)
        
    # ----------------------------------
    # main
    #%%
    N, A, B, C = R()
    S = [r() for _ in range(N)]
    ABC = [A, B, C]
    d = {'AB': (0, 1), 'AC': (0, 2), 'BC': (1, 2)}
    ans = []
    if A == B == C == 0:
        print('NO')
    elif A + B + C == 1:
        for s in S:
            s0, s1 = d[s]
            if ABC[s0] == ABC[s1] == 0:
                print('NO')
                return
            if ABC[s0] == 0:
                ABC[s0] += 1
                ABC[s1] -= 1
                ans.append(s[0])
            else:
                ABC[s0] -= 1
                ABC[s1] += 1
                ans.append(s[1])
        print('Yes')
        for i in ans:
            print(i)
    else:
        for i, s in enumerate(S):
            s0, s1 = d[s]
            if ABC[s0] == ABC[s1] == 0:
                print('NO')
                return
            if i == N - 1:
                if ABC[s0] == 0:
                    ans.append(s[0])
                else:
                    ans.append(s[1])
                print('Yes')
                for i in ans:
                    print(i)
                return
            else:
                if ABC[s0] == 0:
                    ans.append(s[0])
                    ABC[s0] += 1
                    ABC[s1] -= 1
                elif ABC[s1] == 0:
                    ans.append(s[1])
                    ABC[s1] += 1
                    ABC[s0] -= 1
                else:
                    # both are more than 0
                    s0_next, s1_next = d[S[i+1]]
                    if s0 == s0_next and s1 == s1_next:
                        ans.append(s[0])
                        ABC[s0] += 1
                        ABC[s1] -= 1
                    elif s0 == s0_next or s0 == s1_next:
                        ans.append(s[0])
                        ABC[s0] += 1
                        ABC[s1] -= 1
                    else: # s1 == s0_next or s1 == s1_next:
                        ans.append(s[1])
                        ABC[s1] += 1
                        ABC[s0] -= 1

    #%%
    # end of main
    # ----------------------------------

    """memo: how to use defaultdict of list
    # initialize
    Dic = defaultdict(list)
    # append / extend
    Dic[x].append(y)
    # three methods for loop: keys(), values(), items()
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    # to make binary digits text
    >>> a = 5
    >>> bin_str_a = format(a, '#06b')
    >>> print(bin_str_a)
    0b0101 # first 2 strings (='0b') indicates it is binary
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()