Problem:


Score : 300 points

Problem Statement

Given are positive integers N, M, Q, and Q quadruples of integers ( a_i , b_i , c_i , d_i ).

Consider a sequence A satisfying the following conditions:

A is a sequence of N positive integers.

1 \leq A_1 \leq A_2 \le \cdots \leq A_N \leq M.

Let us define a score of this sequence as follows:

The score is the sum of d_i over all indices i such that A_{b_i} - A_{a_i} = c_i. (If there is no such i, the score is 0.)

Find the maximum possible score of A.

Constraints

All values in input are integers.

2 ≤ N ≤ 10

1 \leq M \leq 10

1 \leq Q \leq 50

1 \leq a_i < b_i \leq N ( i = 1, 2, ..., Q )

0 \leq c_i \leq M - 1 ( i = 1, 2, ..., Q )

(a_i, b_i, c_i) \neq (a_j, b_j, c_j) (where i \neq j)

1 \leq d_i \leq 10^5 ( i = 1, 2, ..., Q )

Input

Input is given from Standard Input in the following format:

N M Q
a_1 b_1 c_1 d_1
:
a_Q b_Q c_Q d_Q

Output

Print the maximum possible score of A.

Sample Input 1

3 4 3
1 3 3 100
1 2 2 10
2 3 2 10

Sample Output 1

110

When A = \{1, 3, 4\}, its score is 110. Under these conditions, no sequence has a score greater than 110, so the answer is 110.

Sample Input 2

4 6 10
2 4 1 86568
1 4 0 90629
2 3 0 90310
3 4 1 29211
3 4 3 78537
3 4 2 8580
1 2 1 96263
1 4 2 2156
1 2 0 94325
1 4 3 94328

Sample Output 2

357500

Sample Input 3

10 10 1
1 10 9 1

Sample Output 3

1



Sample input:
3 4 3
1 3 3 100
1 2 2 10
2 3 2 10


Sample output:
110

Submission status: Accepted

Solution code:
from collections import deque

N,M,Q = map(int,input().split())
QUERY = [0]*Q
for i in range(Q):
    QUERY[i] = tuple(map(int,input().split()))

ans = 0
D = deque()
D.append(-1)
D.append(1)
dlen = 2
A = deque()
Alen = 0
while dlen != 0:
    f = D.pop()
    dlen -= 1
    if f == -1:
        A.pop()
        Alen -= 1
        continue
    A.append(f)
    Alen += 1
    if Alen == N:
        e = 0
        for a,b,c,d in QUERY:
            a -= 1
            b -= 1
            if A[b] - A[a] == c:
                e += d
        ans = max(ans,e)
    else:
        for AA in range(A[-1],M+1):
            D.append(-1)
            D.append(AA)
            dlen += 2

print(ans)

Submission status: Accepted

Solution code:
N, M, Q =  map(int, input().split())
List = [list(map(int, input().split())) for _ in range(Q)]
A = [1 for _ in range(N)]
ans = 0

nCr = {}
def cmb(n, r):
    if r == 0 or r == n: return 1
    if r == 1: return n
    if (n,r) in nCr: return nCr[(n,r)]
    nCr[(n,r)] = cmb(n-1,r) + cmb(n-1,r-1)
    return nCr[(n,r)]

def new_A(A):
  for i in range(N):
    if A[N-i-1] < M:
      A[N-i-1] += 1
      break
    elif A[N-i-1] == M and A[N-i-2] < M:
      A[N-i-2] += 1
      for x in range(N-i-1, N):
        A[x] = A[N-i-2]
      break
  return A

for j in range(cmb(N+M-1, N)):
  sum = 0
  for k in range(Q):
    if A[List[k][1]-1] - A[List[k][0]-1] == List[k][2]:
      sum += List[k][3]
  if ans < sum:
    ans = sum
  A = new_A(A)
print(ans)

Submission status: Accepted

Solution code:
edges=[]
N,M,Q=map(int,input().split())
conditions=[]
for i in range(Q):
    a,b,c,d=map(int,input().split())
    conditions.append([a,b,c,d])
for i in range(M):
    edges.append(list(range(i+1,M+1)))
A=[]
score=0
score_list=[]
def dfs(x,N,M):
    A.append(x)
    score=0
    if len(A)<N:
        for i in edges[x-1]:
            dfs(i,N,M)
            if i==edges[x-1][-1]:
                A.pop()
    elif len(A)==N:
        for i in range(Q):
            if A[conditions[i][1]-1]-A[conditions[i][0]-1]==conditions[i][2]:
                score+=conditions[i][3]
            if i==Q-1:
                score_list.append(score)                
        A.pop()
dfs(1,N,M)


print(max(score_list))

Submission status: Accepted

Solution code:
import itertools
n,m,q = map(int,input().split())
inputList = []
for i in range(1,q+1):
    abcd = list(map(int,input().split()))
    inputList.append(abcd)
AList =  list(itertools.combinations_with_replacement(range(1,m+1), n))
PointList = []
for array in AList:
    point = 0
    for iList in inputList:
        if array[iList[1]-1] - array[iList[0]-1] == iList[2]:
            point = point + iList[3]
    PointList.append(point)
print(max(PointList))

Submission status: Accepted

Solution code:
import copy

arrays = []
n,m,q = 0,0,0

def main():
    global n, m, q
    global arrays
    n, m, q = map(int, input().split())
    abcd = [list(map(int, input().split())) for _ in range(q)]
    ans = 0
    dfs([], 1)
    for array in arrays:
        tmp = 0
        for i in range(q):
            if array[abcd[i][1]-1] - array[abcd[i][0]-1] == abcd[i][2]:
                tmp += abcd[i][3]
        ans = max(ans, tmp)
    print(ans)

def dfs(stack, i):
    stack.append(i)
    if len(stack) == n:
        arrays.append(copy.deepcopy(stack))
        if i < m:
            stack.pop()
            dfs(copy.deepcopy(stack), i + 1)
        return
    dfs(copy.deepcopy(stack), i)
    if i < m:
        stack.pop()
        dfs(copy.deepcopy(stack), i + 1)

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import sys
def main():
    input = sys.stdin.readline
    N,M,Q=map(int, input().split())
    ABCD=[tuple(map(int, input().split())) for _ in range(Q)]

    def f(l):
        res=0
        for a,b,c,d in ABCD:
            if l[b]-l[a]==c: res+=d
        return res

    ans=0
    stk=[[1]]
    while stk:
        l=stk.pop()
        if len(l)==N+1:
            ans = max(ans, f(l))
        else:
            for i in range(l[-1],M+1):
                stk.append(l+[i])
    print(ans)

if __name__ == '__main__':
    main()

Submission status: Accepted

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, M, Q = R()
    ABCD = [R() for i in range(Q)]
    task = [([1], 1)]
    ans = 0
    while task:
        l, max_val = task.pop()
        if len(l) == N+1:
            tmp = 0
            for a, b, c, d in ABCD:
                if l[b] - l[a] == c:
                    tmp += d
            ans = max(ans, tmp)
        else:
            for i in range(max_val, M+1):
                task.append((l+[i], max(i, max_val)))
    
    print(ans)

    #%%
    # 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()

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10**9)

n, m, q = map(int, input().split())
val = [list(map(int, input().split())) for _ in range(q)]
ans = 0

def dfs(A):
  global ans
  if len(A) == n+1:
    score = 0
    for a,b,c,d in val:
      if A[b]-A[a] == c:
        score += d
    ans = max(ans, score)
  else:
    A.append(A[-1])
    while(A[-1] <= m):
      dfs(A.copy())
      A[-1] += 1
A = [1]
dfs(A)
print(ans)

Submission status: Accepted

Solution code:
def makeSeqList(N,M,curList,res):
    if len(curList)==N:
        res.append(curList.copy())
        return

    for i in range(1,M+1):
        if len(curList)!=0 and i<curList[-1]:
            continue
        curList.append(i)
        makeSeqList(N,M,curList,res)
        del curList[-1]

def main():
    N,M,Q=map(int,input().split())
    quadList=[]
    for _ in range(Q):
        quadList.append(list(map(int,input().split())))
    res=[]
    makeSeqList(N,M,[],res)
    ans=-1
    for sequence in res:
        summ=0
        for q in quadList:
            if (sequence[q[1]-1]-sequence[q[0]-1])==q[2]:
                summ+=q[3]
        ans=max(ans,summ)
    print(ans)

if __name__=='__main__':
    main()

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
from itertools import combinations_with_replacement
import copy
def f(A, x, N, M, A_list):
    if len(A) == N:
        A_list.append(A)
        return
    A.append(x)
    for i in range(x, M+1):
        A_copy = copy.copy(A)
        f(A_copy, i, N, M, A_list)
def main():
    N, M, Q = map(int, input().split())
    q_list = []
    for _ in range(Q):
        a, b, c, d = map(int, input().split())
        q_list.append((a, b, c, d))
    # A = combinations_with_replacement(range(1, M+1), N)
    A_list = []
    f([], 1, N, M, A_list)
    ans = 0
    for Ai in A_list:
        v = 0
        Ai = list(map(int, Ai))
        for a, b, c, d in q_list:
            if Ai[b-1]-Ai[a-1] == c:v += d
        ans = max(ans, v)
    print(ans)
if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
N, M, Q = list(map(int, input().split()))
a = [0]*Q
b = [0]*Q
c = [0]*Q
d = [0]*Q
for i in range(Q):
  a[i], b[i], c[i], d[i] = list(map(int, input().split()))
li = [1]*11
ans = 0

def countup(l, n, m):
  l[n] += 1
  if l[n] > m:
    if n == 0:
      return
    countup(l, n-1, m)
    l[n] = l[n-1]
  return

while(li[0]==1):
  pt = 0
  for i in range(Q):
    if (li[b[i]]-li[a[i]]==c[i]):
      pt += d[i]
  ans = max(ans, pt)
  countup(li, N, M)

print(ans)

Submission status: Accepted

Solution code:
import itertools
N,M,Q = map(int, input().split())
a = [0]*Q
b = [0]*Q
c = [0]*Q
d = [0]*Q
for i in range(Q):
    a[i],b[i],c[i],d[i] = map(int, input().split())

ans = 0

for L in list(itertools.combinations_with_replacement(range(1,M+1),N)):
    now = 0
    for i in range(Q):
        if L[b[i]-1] - L[a[i]-1] == c[i]:
            now += d[i]
    ans = max(ans, now)

print(ans)

Submission status: Accepted

Solution code:
import sys
import os
import math
import bisect
import collections
import itertools

ii = lambda: int(sys.stdin.buffer.readline().rstrip())
il = lambda: list(map(int, sys.stdin.buffer.readline().split()))
fl = lambda: list(map(float, sys.stdin.buffer.readline().split()))
iln = lambda n: [int(sys.stdin.buffer.readline().rstrip()) for _ in range(n)]

iss = lambda: sys.stdin.buffer.readline().decode().rstrip()
sl = lambda: list(map(str, sys.stdin.buffer.readline().decode().split()))
isn = lambda n: [sys.stdin.buffer.readline().decode().rstrip() for _ in range(n)]

lcm = lambda x, y: x * y / math.gcd(x, y)

MOD = 10 ** 9 + 7
MAX = float('inf')


def main():
    if os.getenv("LOCAL"):
        sys.stdin = open("input.txt", "r")

    N, M, Q = il()
    abcd = [il() for _ in range(Q)]

    ret = 0
    for i in itertools.combinations_with_replacement(range(1, M + 1), N):
        tmp = 0
        for a, b, c, d in abcd:
            if i[b - 1] - i[a - 1] == c: tmp += d

        ret = max(ret, tmp)

    print(ret)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import sys
import copy
from collections import deque


def main():
    N, M, Q = map(int, input().split())
    ABCD = [[int(_) for _ in input().split()] for i in range(Q)]

    seq_list = make_sequence(N, M)
    
    max_score = 0
    for i_seq in seq_list:
        score = 0
        for a, b, c, d in ABCD:
            if (i_seq[b-1] - i_seq[a-1]) == c:
                score += d
        
        max_score = max(max_score, score)

    print(max_score)
    return


def make_sequence(N, M):
    seq_list = []
    sequence = [-1] * N

    seq_deque = deque()
    now_ele = 0
    for i in range(M):
        sequence[0] = i
        now_seq = copy.copy(sequence)
        seq_deque.append([now_ele, now_seq])

    while len(seq_deque) > 0:
        pre_ele ,pre_seq = seq_deque.popleft()
        if pre_seq[-1] != -1:
            seq_list.append(pre_seq)
            continue

        end_ele = M - sum(pre_seq[0:pre_ele+1])
        for i in range(end_ele):
            pre_seq[pre_ele+1] = i
            now_seq = copy.copy(pre_seq)
            seq_deque.append([pre_ele+1 ,now_seq])

    for i_seq in seq_list:
        now_value = 1
        for i, i_value in enumerate(i_seq):
            now_value += i_value
            i_seq[i] = now_value

    return seq_list


if __name__ == '__main__':
    main()
    sys.exit(0)

Submission status: Accepted

Solution code:
import sys
import os
import math
import bisect
import collections
import itertools

ii = lambda: int(sys.stdin.buffer.readline().rstrip())
il = lambda: list(map(int, sys.stdin.buffer.readline().split()))
fl = lambda: list(map(float, sys.stdin.buffer.readline().split()))
iln = lambda n: [int(sys.stdin.buffer.readline().rstrip()) for _ in range(n)]

iss = lambda: sys.stdin.buffer.readline().decode().rstrip()
sl = lambda: list(map(str, sys.stdin.buffer.readline().decode().split()))
isn = lambda n: [sys.stdin.buffer.readline().decode().rstrip() for _ in range(n)]

lcm = lambda x, y: x * y / math.gcd(x, y)

MOD = 10 ** 9 + 7
MAX = float('inf')


def f(A, B, x):
    return math.floor(A * x / B) - A * math.floor(x / B)


def main():
    if os.getenv("LOCAL"):
        sys.stdin = open("input.txt", "r")

    N, M, Q = il()
    abcd = [il() for _ in range(Q)]

    ret = 0
    for i in itertools.combinations_with_replacement(range(1, M + 1), N):
        tmp = 0
        for a, b, c, d in abcd:
            if i[b - 1] - i[a - 1] == c: tmp += d

        ret = max(ret, tmp)

    print(ret)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import itertools

n, m, q = map(int, input().split())
abcd = [tuple(map(int, input().split())) for _ in range(q)]
ans = 0
for com in itertools.combinations_with_replacement(range(1, m + 1), n):
    score = sum([d for a, b, c, d in abcd if com[b-1] - com[a-1] == c])
    if ans < score:
        ans = score
print(ans)

Submission status: Accepted

Solution code:
N, M, Q = map(int, input().split())
ABCD = [tuple(map(int, input().split())) for _ in range(Q)]
ans, A = 0, [1] * (N - 1) + [0]
while A != [M] * N:
    if A[N - 1] < M:
        A[N - 1] += 1
    else:
        c = N - 2
        while A[c] == M:
            c -= 1
        A[c] += 1
        for i in range(c + 1, N):
            A[i] = A[c]
    ans = max(ans, sum([d for a, b, c, d in ABCD if A[b - 1] - A[a - 1] == c]))
print(ans)

Submission status: Accepted

Solution code:
import itertools
 
n, m, q = map(int, input().split())
abcd = [list(map(int, input(). split())) for _ in range(q)]
 
points = []
for able in itertools.combinations_with_replacement(range(1, m+1), n):
    point = 0
    for a, b, c, d in abcd:
        if able[b-1] - able[a-1] == c:
            point += d
    points.append(point)
 
print(max(points))

Submission status: Accepted

Solution code:
def Array_list(array_list,m,n):
    if n == 0:
        return array_list
    else:
        array_list_next = []
        for array in array_list:
            for i in range(array[len(array)-1],m+1):
                array_list_next.append(array+[i])
        return Array_list(array_list_next,m,n-1)

def main():
    N,M,Q = map(int,input().split())
    abcd = [list(map(int,input().split())) for _ in range(Q)]

    L = [[i] for i in range(1,M+1)]
    array_list = Array_list(L,M,N)

    ans,tmp = 0,0
    for array in array_list:
        tmp = 0
        for a,b,c,d in abcd:
            if array[b-1] - array[a-1] == c:
                tmp += d
        ans = max(tmp,ans)

    print(ans)

if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
import sys
import itertools
import numpy as np


read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
N, M, Q = map(int, readline().split())
A = np.array(list(itertools.combinations_with_replacement(range(1, M + 1), N)))
n = len(A)
score = np.zeros(n, np.int32)
m = map(int, read().split())
for a, b, c, d in zip(m, m, m, m):
    cond = A[:, b - 1] - A[:, a - 1] == c
    score += d * cond
print(score.max())

Submission status: Accepted

Solution code:
import itertools
n,m,q=map(int,input().split())
a=[0 for i in range(q)]
b=[0 for i in range(q)]
c=[0 for i in range(q)]
d=[0 for i in range(q)]
for i in range(q):
    a[i],b[i],c[i],d[i]=map(int,input().split())
    b[i]-=1;a[i]-=1
ans=0
for seq in itertools.combinations_with_replacement(range(m),n):
    tmp = 0
    for i in range(q):
        if seq[b[i]]-seq[a[i]]==c[i]:
            tmp+=d[i]
    ans=max(ans,tmp)
print(ans)

Submission status: Accepted

Solution code:
import itertools
N,M,Q = map(int,input().split())
L = [list(map(int,input().split())) for _ in range(Q)]
data = list(range(1,M+1))
A=list(itertools.combinations_with_replacement(data,N))
max_score = 0

for Ai in A:
  x = 0
  for a,b,c,d in L:
    if Ai[b-1] - Ai[a-1] == c:
      x += d
  max_score = max(max_score,x)

print(max_score)