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.

Submission attempts (in order):
#
# abc167 c
#
import sys
from io import StringIO
import unittest
from collections import deque


class TestClass(unittest.TestCase):
    def assertIO(self, input, output):
        stdout, stdin = sys.stdout, sys.stdin
        sys.stdout, sys.stdin = StringIO(), StringIO(input)
        resolve()
        sys.stdout.seek(0)
        out = sys.stdout.read()[:-1]
        sys.stdout, sys.stdin = stdout, stdin
        self.assertEqual(out, output)

    def test_入力例_1(self):
        input = """3 3 10
60 2 2 4
70 8 7 9
50 2 3 9"""
        output = """120"""
        self.assertIO(input, output)

    def test_入力例_2(self):
        input = """3 3 10
100 3 1 4
100 1 5 9
100 2 6 5"""
        output = """-1"""
        self.assertIO(input, output)

    def test_入力例_3(self):
        input = """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"""
        output = """1067"""
        self.assertIO(input, output)


def resolve_bit():
    N, M, X = map(int, input().split())
    CA = [list(map(int, input().split())) for _ in range(N)]

    ans = float("inf")
    for bit in range(1 << N):
        S = [0]*(M+1)
        for i, ca in enumerate(CA):
            if (1 << i) & bit == 1 << i:
                S = list(map(sum, zip(S, ca)))
        for s in S[1:]:
            if s < X:
                break
        else:
            ans = min(ans, S[0])

    if ans == float("inf"):
        ans = -1

    print(ans)


def resolve():
    global N, M, X, CA
    N, M, X = map(int, input().split())
    CA = [list(map(int, input().split())) for _ in range(N)]

    b = deque()
    ans = dfs(0, b)
    if ans == float("inf"):
        ans = -1

    print(ans)


def dfs(n, B):
    if n == N:
        S = [0]*(M+1)
        for i, ca in enumerate(CA, 1):
            if i in B:
                S = list(map(sum, zip(S, ca)))
        for s in S[1:]:
            if s < X:
                return float("inf")
        else:
            return S[0]

    ans = float("inf")
    B.append(n+1)
    tmp = dfs(n+1, B)
    ans = min(ans, dfs(n+1, B))
    B.pop()
    ans = min(ans, dfs(n+1, B))

    return ans


if __name__ == "__main__"    ans = min(ans, tmp):
    # unittest.main()
    resolve()


#
# abc167 c
#
import sys
from io import StringIO
import unittest
from collections import deque


class TestClass(unittest.TestCase):
    def assertIO(self, input, output):
        stdout, stdin = sys.stdout, sys.stdin
        sys.stdout, sys.stdin = StringIO(), StringIO(input)
        resolve()
        sys.stdout.seek(0)
        out = sys.stdout.read()[:-1]
        sys.stdout, sys.stdin = stdout, stdin
        self.assertEqual(out, output)

    def test_入力例_1(self):
        input = """3 3 10
60 2 2 4
70 8 7 9
50 2 3 9"""
        output = """120"""
        self.assertIO(input, output)

    def test_入力例_2(self):
        input = """3 3 10
100 3 1 4
100 1 5 9
100 2 6 5"""
        output = """-1"""
        self.assertIO(input, output)

    def test_入力例_3(self):
        input = """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"""
        output = """1067"""
        self.assertIO(input, output)


def resolve():
    N, M, X = map(int, input().split())
    CA = [list(map(int, input().split())) for _ in range(N)]

    ans = float("inf")
    for bit in range(1 << N):
        S = [0]*(M+1)
        for i, ca in enumerate(CA):
            if (1 << i) & bit == 1 << i:
                S = list(map(sum, zip(S, ca)))
        if min(S[1:]) < X:
        	break
        ans = min(ans, S[0])

    if ans == float("inf"):
        ans = -1

    print(ans)


if __name__ == "__main__":
    # unittest.main()
    resolve()


#
# abc167 c
#
import sys
from io import StringIO
import unittest
from collections import deque


class TestClass(unittest.TestCase):
    def assertIO(self, input, output):
        stdout, stdin = sys.stdout, sys.stdin
        sys.stdout, sys.stdin = StringIO(), StringIO(input)
        resolve()
        sys.stdout.seek(0)
        out = sys.stdout.read()[:-1]
        sys.stdout, sys.stdin = stdout, stdin
        self.assertEqual(out, output)

    def test_入力例_1(self):
        input = """3 3 10
60 2 2 4
70 8 7 9
50 2 3 9"""
        output = """120"""
        self.assertIO(input, output)

    def test_入力例_2(self):
        input = """3 3 10
100 3 1 4
100 1 5 9
100 2 6 5"""
        output = """-1"""
        self.assertIO(input, output)

    def test_入力例_3(self):
        input = """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"""
        output = """1067"""
        self.assertIO(input, output)


def resolve():
    N, M, X = map(int, input().split())
    CA = [list(map(int, input().split())) for _ in range(N)]

    ans = float("inf")
    for bit in range(1 << N):
        S = [0]*(M+1)
        for i, ca in enumerate(CA):
            if (1 << i) & bit == 1 << i:
                S = list(map(sum, zip(S, ca)))
        if min(S[1:]) >= X:
            ans = min(ans, S[0])

    if ans == float("inf"):
        ans = -1

    print(ans)


def resolve_dfs():
    global N, M, X, CA
    N, M, X = map(int, input().split())
    CA = [list(map(int, input().split())) for _ in range(N)]

    b = deque()
    ans = dfs(0, b)
    if ans == float("inf"):
        ans = -1

    print(ans)


def dfs(n, B):
    if n == N:
        S = [0]*(M+1)
        for i, ca in enumerate(CA, 1):
            if i in B:
                S = list(map(sum, zip(S, ca)))
        if min(S[1:]) < X:
            return float("inf")
        else:
            return S[0]

    ans = float("inf")
    B.append(n+1)
    ans = min(ans, dfs(n+1, B))
    B.pop()
    ans = min(ans, dfs(n+1, B))

    return ans


if __name__ == "__main__":
    # unittest.main()
    resolve()


Verdicts: Runtime Error

Wrong Answer

Accepted