Problem:


Score : 300 points

Problem

Takahashi, who is a novice in competitive programming, wants to learn M algorithms.
Initially, his understanding level of each of the M algorithms is 0.

Takahashi is visiting a bookstore, where he finds N books on algorithms.
The i-th book (1\leq i\leq N) is sold for C_i yen (the currency of Japan). If he buys and reads it, his understanding level of the j-th algorithm will increase by A_{i,j} for each j (1\leq j\leq M).
There is no other way to increase the understanding levels of the algorithms.

Takahashi's objective is to make his understanding levels of all the M algorithms X or higher. Determine whether this objective is achievable. If it is achievable, find the minimum amount of money needed to achieve it.

Constraints

All values in input are integers.

1\leq N, M\leq 12

1\leq X\leq 10^5

1\leq C_i \leq 10^5

0\leq A_{i, j} \leq 10^5

Input

Input is given from Standard Input in the following format:

N M X
C_1 A_{1,1} A_{1,2} \cdots A_{1,M}
C_2 A_{2,1} A_{2,2} \cdots A_{2,M}
\vdots
C_N A_{N,1} A_{N,2} \cdots A_{N,M}

Output

If the objective is not achievable, print -1; otherwise, print the minimum amount of money needed to achieve it.

Sample Input 1

3 3 10
60 2 2 4
70 8 7 9
50 2 3 9

Sample Output 1

120

Buying the second and third books makes his understanding levels of all the algorithms 10 or higher, at the minimum cost possible.

Sample Input 2

3 3 10
100 3 1 4
100 1 5 9
100 2 6 5

Sample Output 2

-1

Buying all the books is still not enough to make his understanding levels of all the algorithms 10 or higher.

Sample Input 3

8 5 22
100 3 7 5 3 1
164 4 5 2 7 8
334 7 2 7 2 9
234 4 7 2 8 2
541 5 4 3 3 6
235 4 8 6 9 7
394 3 6 1 6 2
872 8 4 3 7 2

Sample Output 3

1067



Sample input:
3 3 10
60 2 2 4
70 8 7 9
50 2 3 9


Sample output:
120

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') # 26
    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]

    class SegTree:
        """
        ref: https://qiita.com/takayg1/items/c811bd07c21923d7ec69
        init(init_val, ide_ele): 配列init_valで初期化 O(N)
        update(k, x): k番目の値をxに更新 O(logN)
        query(l, r): 区間[l, r)をsegfuncしたものを返す O(logN)
        """
        def __init__(self, init_val, segfunc, ide_ele):
            """
            init_val: 配列の初期値
            segfunc: 区間にしたい操作
            ide_ele: 単位元
            n: 要素数
            num: n以上の最小の2のべき乗
            tree: セグメント木(1-index)
            """
            n = len(init_val)
            self.segfunc = segfunc
            self.ide_ele = ide_ele
            self.num = 1 << (n - 1).bit_length()
            self.tree = [ide_ele] * 2 * self.num
            # 配列の値を葉にセット
            for i in range(n):
                self.tree[self.num + i] = init_val[i]
            # 構築していく
            for i in range(self.num - 1, 0, -1):
                self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1])

        def update(self, k, x):
            """
            k番目の値をxに更新
            k: index(0-index)
            x: update value
            """
            k += self.num
            self.tree[k] = x
            while k > 1:
                self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1])
                k >>= 1

        def query(self, l, r):
            """
            [l, r)のsegfuncしたものを得る
            l: index(0-index)
            r: index(0-index)
            """
            res = self.ide_ele
            l += self.num
            r += self.num
            while l < r:
                if l & 1:
                    res = self.segfunc(res, self.tree[l])
                    l += 1
                if r & 1:
                    res = self.segfunc(res, self.tree[r - 1])
                l >>= 1
                r >>= 1
            return res

    # ************ Graph ************
    # Graph: https://en.wikipedia.org/wiki/Directed_graph
    # 最短経路問題: https://ja.wikipedia.org/wiki/%E6%9C%80%E7%9F%AD%E7%B5%8C%E8%B7%AF%E5%95%8F%E9%A1%8C
    
    # 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]

    # Warshall Floyd O(V**3)
    def warshall_floyd(number_vertex, XYD, shift_one_for_vertex=False):
        # ref: https://juppy.hatenablog.com/entry/2018/11/01/%E8%9F%BB%E6%9C%AC_python_%E5%85%A8%E7%82%B9%E5%AF%BE%E6%9C%80%E7%9F%AD%E7%B5%8C%E8%B7%AF%E6%B3%95%EF%BC%88%E3%83%AF%E3%83%BC%E3%82%B7%E3%83%A3%E3%83%AB%E3%83%95%E3%83%AD%E3%82%A4%E3%83%89%E6%B3%95
        # number_vertex: len(vertex)
        # XYD: list of distance from x to y
        # shift_one_for_vertex: XYDの値が1~Nの時(0~N-1でない時)に調整するフラグ。
        # d[i][j]: iからjへの最短距離
        d = [[float("inf")]*number_vertex for i in range(number_vertex)]
        for x, y, dist in XYD:
            if shift_one_for_vertex:
                x = x - 1
                y = y - 1
            d[x][y] = dist
            d[y][x] = dist
        for i in range(number_vertex):
            d[i][i] = 0 # distance of same vertex is 0
        for k in range(number_vertex):
            for i in range(number_vertex):
                for j in range(number_vertex):
                    d[i][j] = min(d[i][j],d[i][k] + d[k][j])
        return d


    """ 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, X = R()
    CA = [R() for _ in range(N)]
    ans = INF
    for i in range(2**N):
        bin_str = bin(i)
        cost = 0
        unde = [0] * M
        for j in range(N):
            if bin_str[-j-1] == 'b':
                break
            if bin_str[-j-1] == '1':
                for k in range(M+1):
                    if k == 0:
                        cost += CA[j][k]
                    else:
                        unde[k-1] += CA[j][k]
        for each_unde in unde:
            if each_unde < X:
                break
        else:
            ans = min(cost, ans)
    if ans == INF:
        print(-1)
    else:
        print(ans)
        

        
    
    
    # 小文字をカウントしたリストを持つセグ木で行けそう。

    
    # a = [14, 5, 9, 13, 7, 12, 11, 1, 7, 8]
    


    #%%
    # 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:
N, M, X = map(int, input().split())
CA = []
for _ in range(N):
    tmp = list(map(int, input().split()))
    CA.append(tmp)

ans = -1
for i in range(2**N):
    tmp_cost = 0
    tmp_X = [0]*(M+1)
    for j in range(N):
        if ((i >> j) & 1):
            for k in range(M+1):
                tmp_X[k] += CA[j][k]
    for j in range(1, M+1):
        if tmp_X[j] < X:
            break
    else:
        if ans == -1:
            ans = tmp_X[0]
        else:
            ans = min(ans, tmp_X[0])
print(ans)

Submission status: Accepted

Solution code:
import numpy as np

n, m, x = map(int, input().split())
ca = np.array([list(map(int, input().split())) for _ in range(n)])

pattern = []
for i in range(2 ** n):
    temp = [0] * n
    for j in range(n):
        if (i >> j) & 1:
            temp[j] = 1
    pattern.append(temp)

ans = 10 ** 10
for p in pattern:
    check = [0] * (m + 1)
    for i in range(n):
        if p[i] == 1:
            check += ca[i]
    flag = True
    for a in check[1:]:
        if a < x:
            flag = False
            break
    if flag:
        ans = min(ans, check[0])

print(ans) if ans != 10 ** 10 else print(-1)

Submission status: Accepted

Solution code:
n,m,x=map(int,input().split())
CA=[list(map(int,input().split())) for _ in range(n)]

res=10**7

for i in range(2**n):
	money=0
	under=[0]*m
	
	for j in range(n):
		if i>>j&1:
			money+=CA[j][0]
			for k in range(m):
				under[k]+=CA[j][k+1]
		
	if min(under)>=x:
		res=min(res,money)

if res==10**7:
	print("-1")
else:
	print(res)

Submission status: Accepted

Solution code:
# coding:utf-8

import sys
import math
import time
#import numpy as np
import collections
from collections import deque
from collections import Counter
import queue
import copy
import bisect
import heapq
import itertools



#sys.setrecursionlimit(10**7)
#N, Q = map(int, input().split())
#G = [list(input()) for i in range(H)]
#INF = V * 10001
#A = [int(i) for i in input().split()]
#AB = [list(map(int, input().split())) for _ in range(K)]

N, M, X = map(int,input().split())
Book = [list(map(int, input().split())) for _ in range(N)]
Alg = [0]*M
money = 10**8
temp = 0
flag = True
ans = 0

for i in range(2**N):
    for j in range(N):
        if((i >> j) & 1):
            temp += Book[j][0]
            for k in range(M):
                Alg[k] += Book[j][k+1]
    for l in range(M):
        #print(Alg)
        if(Alg[l] < X):
            flag = False
            break
    if(flag):
        money = min(money,temp)
    flag = True
    temp = 0
    for m in range(len(Alg)):
        Alg[m] = 0

if(money==10**8):
    print(-1)
else:
    print(money)

Submission status: Accepted

Solution code:
n, m, x = map(int, input().split())
a = []
max_sum = [0 for _ in range(m)]
price_sum = 0
for i in range(n):
    input_list = list(map(int, input().split()))
    a.append([input_list[0], input_list[1:]])
    price_sum += input_list[0]
    for j in range(m):
        max_sum[j] += input_list[j + 1]

flag = 0
for j in range(m):
    if max_sum[j] < x:
        flag = 1
if flag:
    print(-1)
else:
    min_price = price_sum
    for pattern in range(1, 2 ** n):
        flag = 0
        now_price = price_sum
        now_sum = max_sum.copy()
        # print(bin(pattern))
        for i in range(n):
            if pattern & 1 << i:
                now_price -= a[i][0]
                for j in range(m):
                    now_sum[j] -= a[i][1][j]

        # print(now_price, now_sum)
        for j in range(m):
            if now_sum[j] < x:
                flag = 1
        if not flag and now_price < min_price:
            min_price = now_price

    print(min_price)

Submission status: Accepted

Solution code:
#!/usr/bin/env python3
import sys
from itertools import product


def solve(N, M, X, C, A):
    L = list(product([True, False], repeat=N))
    mn = 100000000000
    for l in L:
        cst = 0
        rikai = [0 for _ in range(M)]
        for i in range(N):
            if l[i]:
                cst += C[i]
                for j in range(M):
                    rikai[j] += A[i][j]
        tf = True
        for j in range(M):
            if rikai[j] < X:
                tf = False
                break
        if tf:
            mn = min(mn, cst)
    if mn == 100000000000:
        print(-1)
    else:
        print(mn)
    return

# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    M = int(next(tokens))  # type: int
    X = int(next(tokens))  # type: int
    C = [0 for _ in range(N)]
    A = [[0 for _ in range(M)] for _ in range(N)]
    for i in range(N):
        C[i] = int(next(tokens))
        for j in range(M):
            A[i][j] = int(next(tokens))
    solve(N, M, X, C, A)

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import numpy as np

N, M, X = map(int, input().split())

C = [0] * N
A = np.zeros((N, M), np.int64)
for i in range(N):
    Y = [int(k) for k in input().split()]
    C[i] = Y[0]
    A[i, :] = Y[1:]
ans = float('inf')
for bits in range(1 << N):
    sum = 0
    U = np.zeros(M, np.int64)
    for i in range(N):
        if (bits >> i) & 1:
            sum += C[i]
            U += A[i, :]
    if np.count_nonzero(U >= X) == M:
        ans = min(ans, sum)
print(ans if ans != float('inf') else -1)

Submission status: Accepted

Solution code:

n, m, x = map(int,input().split())
array = [[int(x) for x in input().split()] for y in range(n)]

ans = float("inf")
for i in range(2**n):
    tmp = [0 for x in range(m)]
    tmp_cost = 0
    bits = format(i, "b").zfill(n)
    for j in range(n):
        bit = bits[j]
        if bit == "1":
            tmp_cost += array[j][0]
            for k in range(m):
                tmp[k] += array[j][1+k]
    for l in tmp:
        if l < x:
            break
    else:
        ans = min(ans, tmp_cost)
print(ans if ans != float("inf") else -1)

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10000000)
INF = 10 ** 10
ans = INF


def rec(A, C, X, idx, ability, sum_):
    if idx == len(A):
        for i in range(len(ability)):
            if ability[i] < X:
                break
        else:
            global ans
            ans = min(sum_, ans)
    else:
        # not buy
        rec(A, C, X, idx+1, ability, sum_)
        M = len(A[0])
        import copy 
        new_ability = copy.copy(ability)
        for i in range(M):
            new_ability[i] += A[idx][i]
        rec(A, C, X, idx+1, new_ability, sum_+C[idx])


def main():
    N, M, X = map(int, input().split())
    C = []
    A = []
    for i in range(N):
        lists = [int(c) for c in input().split()]
        ci = lists[0]
        ai = lists[1:]
        C.append(ci)
        A.append(ai)

    ability = [0] * M
    rec(A, C, X, 0, ability, 0)

    if ans == INF:
        print(-1)
    else:
        print(ans)
    

    
    



if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import numpy as np
import itertools

N, M, X = map(int, input().split())
CA = []
cost = 12 * (10**5) + 1

for _ in range(N):
  CA.append(list(map(int, input().split())))

for T in itertools.product([1,0], repeat = N):
  Flag = True
  ans = np.zeros(M+1)
  for i in range(N):
    if T[i] == 1:
      ans += np.array(CA[i])

  for j in range(1, M+1):
    if ans[j] < X:
      Flag = False
      break
  
  if Flag:
    cost = min(cost, ans[0])

if cost == 12 * (10**5) + 1:
  print(-1)
else:
  print(int(cost))

Submission status: Accepted

Solution code:
import numpy as np


def main():
    n, m, x = map(int, input().split())
    cas = np.array([list(map(int, input().split())) for _ in range(n)])

    ans = -1
    for i in range(2 ** n):
        if i == 0:
            continue
        books = []
        for j in range(n):
            if ((i >> j) & 1):
                books.append(cas[j])

        books = np.array(books)
        if np.all(np.sum(books[:, 1:], axis=0) >= x):
            ans_temp = np.sum(books[:, 0])
            if ans == -1:
                ans = ans_temp
            else:
                ans = min(ans, ans_temp)
    print(ans)


if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
import itertools
from collections import defaultdict
import collections
import sys
sys.setrecursionlimit(200000)
mod = 1000000007

n, m, x = map(int, input().split())
ca = [list(map(int, input().split())) for i in range(n)]

ans = mod
for i in range(2 ** n):
    alg = [0] * (m+1)
    switch = [0] * n
    for j in range(n):
        if((i >> j) & 1):
            switch[j] = 1
    for k in range(n):
        for l in range(m + 1):
            if switch[k] == 1:
                alg[l] += ca[k][l]
    for y in range(m+1):
        if y != 0:
            if x > alg[y]:
                break
        if y == m:
            ans = min(ans, alg[0])

if ans == mod:
    print("-1")
else:
    print(ans)

Submission status: Accepted

Solution code:
from itertools import groupby, accumulate, product, permutations, combinations
def solve():
    N, M, X = map(int, input().split())
    A = [list(map(int, input().split())) for _ in range(N)]
    ans = 10**9
    for p in product([0,1],repeat=N):
        cost = 0
        for i in range(N):
            if p[i]==1:
                cost += A[i][0]
        for j in range(1,M+1):
            und = 0
            for i in range(N):
                if p[i]==1:
                    und += A[i][j]
            if und<X:
                break
        else:
            ans = min(ans,cost)
    if ans == 10**9:
        return -1
    return ans
print(solve())

Submission status: Accepted

Solution code:
import copy
n, m, x = map(int, input().split())
c, a = [], []

for i in range(n):
    temp = list(map(int, input().split()))
    c.append(temp[0])
    a.append(temp[1:])

# print(c, a)
ans = 10**10

def isClear(arr):
    return all(val >= x for val in arr)

def solve(idx, price, arr):
    global ans
    if idx == n:
        if isClear(arr):
            # print('clear:', arr)
            ans = min(ans, price)
        return

    # Read
    temp = copy.deepcopy(arr)
    for i in range(m):
        temp[i] += a[idx][i]

    solve(idx + 1, price + c[idx], temp)

    # Not read
    solve(idx + 1, price, arr)

score = [0]*m
solve(0, 0, score)

if ans == 10**10:
    print(-1)
else:
    print(ans)