Problem:


Score: 300 points

Problem Statement

In the Ancient Kingdom of Snuke, there was a pyramid to strengthen the authority of Takahashi, the president of AtCoder Inc.

The pyramid had center coordinates (C_X, C_Y) and height H. The altitude of coordinates (X, Y) is max(H - |X - C_X| - |Y - C_Y|, 0).  

Aoki, an explorer, conducted a survey to identify the center coordinates and height of this pyramid. As a result, he obtained the following information:  

C_X, C_Y was integers between 0 and 100 (inclusive), and H was an integer not less than 1.  

Additionally, he obtained N pieces of information. The i-th of them is: "the altitude of point (x_i, y_i) is h_i."  

This was enough to identify the center coordinates and the height of the pyramid. Find these values with the clues above.  

Constraints

N is an integer between 1 and 100 (inclusive).

x_i and y_i are integers between 0 and 100 (inclusive).

h_i is an integer between 0 and 10^9 (inclusive).

The N coordinates (x_1, y_1), (x_2, y_2), (x_3, y_3), ..., (x_N, y_N) are all different.

The center coordinates and the height of the pyramid can be uniquely identified.

Input

Input is given from Standard Input in the following format:  

N
x_1 y_1 h_1
x_2 y_2 h_2
x_3 y_3 h_3
:
x_N y_N h_N

Output

Print values C_X, C_Y and H representing the center coordinates and the height of the pyramid in one line, with spaces in between.  

Sample Input 1

4
2 3 5
2 1 5
1 2 5
3 2 5

Sample Output 1

2 2 6

In this case, the center coordinates and the height can be identified as (2, 2) and 6.  

Sample Input 2

2
0 0 100
1 1 98

Sample Output 2

0 0 100

In this case, the center coordinates and the height can be identified as (0, 0) and 100.

Note that C_X and C_Y are known to be integers between 0 and 100.

Sample Input 3

3
99 1 191
100 1 192
99 0 192

Sample Output 3

100 0 193

In this case, the center coordinates and the height can be identified as (100, 0) and 193.  



Sample input:
4
2 3 5
2 1 5
1 2 5
3 2 5


Sample output:
2 2 6

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
    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, use [[0] * N for _ in range(N)]
    # 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 = lambda: list(map(int, r().split()))
    Rmap = lambda: map(int, r().split())
    Rfloat = lambda: list(map(float, r().split()))
    Rtuple = 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 = r_int()
    XYH = [R() for _ in range(N)]
    
    for s in range(101):
        for t in range(101):
            xans, yans = s, t
            for i, (x, y, h) in enumerate(XYH):
                if i == 0:
                    hans = h + abs(xans-x) + abs(yans-y)
                else:
                    if h + abs(xans-x) + abs(yans-y) != hans:
                        break
            else:
                print(xans, yans, hans)
                return
    

    # to finish code, use return instead of exit()
    # 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: Wrong Answer

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

ans_x = 0
ans_y = 0
before = abs(0-xyh[0][0]) + abs(0-xyh[0][1]) + xyh[0][2]
cnt = 0
for cx in range(101):
    for cy in range(101):
        for x,y,h in xyh:
            height = abs(cx-x)+abs(cy-y)+h
            if height != before:
                break
            before = height
            cnt += 1
            if cnt == n:
                print(' '.join(map(str,[cx,cy,height])))
                exit()

Submission status: Wrong Answer

Solution code:
import math;

def swap(a,b):
    return (b,a)

def gcd(a,b):
    if (a<b):
        a,b = swap(a,b)
    if (b==0):
        return a
    else:
        return gcd(b,a%b)

def main():
    n = int(input())
    xyh = []
    for i in range(n):
        x,y,h = map(int,input().split())
        xyh.append([x,y,h])
    for i in range(101):
        for j in range(101):
            H = xyh[0][2] + abs(xyh[0][0]-i) + abs(xyh[0][1]-j)
            ac = True
            for x in xyh:
                if x[2]+abs(x[0]-i)+abs(x[1]-j)!=H:
                    ac = False
                    break
            if ac:
                print("{} {} {}".format(i,j,H))
                return
    return

if __name__ == '__main__':
    main()

Submission status: Wrong Answer

Solution code:
N = int(input())
xyh = [list(map(int, input().split())) for _ in range(N)]

idx_flag = True

for i in range(N):
  if xyh[i][2] > 0:
    idx_flag = False
    idx = i
    break

if idx_flag:
  H = 1
  for i in range(101):
    for j in range(101):
      flag = True
      for k in range(N):
        cnt = 1 - abs(i-xyh[k][0]) - abs(j-xyh[k][1])
        if cnt > 0:
          flag = False
      if flag:
        print(i, j, H)
        exit(0)

for i in range(101):
  for j in range(101):
    flag = True
    h = abs(i-xyh[idx][0]) + abs(j-xyh[idx][1]) + xyh[idx][2]
    for k in range(N):
      cnt = abs(i-xyh[k][0]) + abs(j-xyh[k][1]) + xyh[k][2]
      if h != cnt:
        flag = False
    if flag:
      print(i, j, h)
      exit(0)

Submission status: Wrong Answer

Solution code:
def resolve():
    n = int(input())
    xyh = list(list(map(int, input().split())) for _ in range(n))
    px, py, ph = [[x, y, h] for x, y, h in xyh if h > 0][0]
    for cx in range(101):
        for cy in range(101):
            H = ph + abs(cx - px) + abs(cy - py)
            estimated = [h + abs(cx - x) + abs(cy - y) for x, y, h in xyh]
            if set(estimated) == {H}:
                return " ".join([str(cx), str(cy), str(H)])


if __name__ == "__main__":
    print(resolve())

Submission status: Wrong Answer

Solution code:
N = int(input())
L = [tuple(map(int, input().split())) for _ in range(N)]

def get_H(Cx, Cy):
    for x, y, h in L:
        H = h + abs(x - Cx) + abs(y - Cy)
        if H >= 1:
            return H

def check(Cx, Cy, H):
    for x, y, h in L:
        if h != max(H - abs(x - Cx) - abs(y - Cy), 0):
            return False
    return True

for Cx in range(101):
    for Cy in range(101):
        H = get_H(Cx, Cy)
        if check(Cx, Cy, H):
            print(Cx, Cy, H)
            quit()

Submission status: Wrong Answer

Solution code:
N = int(input())
xyh = [list(map(int, input().split())) for _ in range(N)]

for i in range(N):
  if xyh[i][2] > 0:
    idx = i
    break

for i in range(101):
  for j in range(101):
    flag = True
    h = abs(i-xyh[idx][0]) + abs(j-xyh[idx][1]) + xyh[idx][2]
    for k in range(N):
      cnt = abs(i-xyh[k][0]) + abs(j-xyh[k][1]) + xyh[k][2]
      if h != cnt:
        flag = False
    if flag:
      print(i, j, h)
      exit(0)

Submission status: Wrong Answer

Solution code:
N = int(input())
xyh = [list(map(int, input().split())) for _ in range(N)]

for i in range(101):
  for j in range(101):
    flag = True
    h = abs(i-xyh[0][0]) + abs(j-xyh[0][1]) + xyh[0][2]
    for k in range(1, N):
      cnt = abs(i-xyh[k][0]) + abs(j-xyh[k][1]) + xyh[k][2]
      if h != cnt:
        flag = False
    if flag:
      print(i, j, h)
      exit(0)

Submission status: Wrong Answer

Solution code:
N = int(input())
L = [tuple(map(int, input().split())) for _ in range(N)]

def get_H(Cx, Cy):
    for x, y, h in L:
        H = h + abs(Cx - x) + abs(Cy - y)
        if H >= 1:
            return H

def check(Cx, Cy):
    H = get_H(Cx, Cy)
    for x, y, h in L:
        if h != max(H - abs(x - Cx) - abs(y - Cy), 0):
            return -1
    return H

for Cx in range(101):
    for Cy in range(101):
        H = check(Cx, Cy)
        if H >= 1:
            print(Cx, Cy, H)

Submission status: Wrong Answer

Solution code:
n=int(input())
d=[]
for i in range(n):
    a,b,c=map(int,input().split())
    d.append((a,b,c))
    if c!=0:
        x=a
        y=b
        h=c

for i in range(101):
    for j in range(101):
        p=abs(i-x)+abs(j-y)+h
        for c,a,b in d:
            if (c==0 and p-abs(i-a)-abs(j-b)<1) or (c==(p-abs(i-a)-abs(j-b))):
                pass
            else:
                p=-1
                break
        if p!=-1:
            print(i,j,p)
            exit()

Submission status: Wrong Answer

Solution code:
n=int(input())
d=[]
for i in range(n-1):
    a,b,c=map(int,input().split())
    d.append((c,a,b))
d.sort()
h=d[-1][0]
x=d[-1][1]
y=d[-1][2]
for i in range(101):
    for j in range(101):
        p=abs(i-x)+abs(j-y)+h
        for c,a,b in d:
            if (c==0 and p-abs(i-a)-abs(j-b)<1) or (c==(p-abs(i-a)-abs(j-b))):
                pass
            else:
                p=-1
                break
        if p!=-1:
            print(i,j,p)
            exit()

Submission status: Wrong Answer

Solution code:
# 解答ちらっと見た
# 問題のキモは Cx,Cy,Hがそれぞれ100通り、
# 全探索をCx,Cy,Hに対して試みると 入力された情報のcheckを入れて101*101*100*100でTLEする。
# でもよく考えてみると、Cx,CyがわかればHはそのあとで出せるので Cx,Cyに対して全探索をする(101*101*100+100の計算量で済む)


def check(x, y, h, cx, cy):
    return h + abs(x - cx) + abs(y - cy)


def checks(x, y, eh, cx, cy, h):
    cah = max(h - abs(x - cx) - abs(y - cy), 0)
    return cah == eh


N = int(input())
H = []

checkers = [(list(map(int, input().split()))) for _ in range(N)]
for icx in range(101):
    for icy in range(101):
        H = []
        for checker in checkers:
            H.append(check(checker[0], checker[1], checker[2], icx, icy))

        if len(set(H)) == 1:
            # print('{} {} {}'.format(icx, icy, H[0]))
            ok = True
            for c in checkers:
                if not checks(c[0], c[1], c[2], icx, icy, H[0]):
                    # print('failedin {} {} {} {} {} {}'.format(c[0], c[1], c[2], icx, icy, H[0]))
                    ok = False
                    break
            if ok:
                print('{} {} {}'.format(icx, icy, H[0]))
                exit(0)

Submission status: Wrong Answer

Solution code:
N = int(input())
L = [tuple(map(int, input().split())) for _ in range(N)]

for Cx in range(101):
    for Cy in range(101):
        pre = -1
        for x, y, h in L:
            H = h + abs(x - Cx) + abs(y - Cy)
            if H < 1:
                continue
            if pre >= 0 and pre != H:
                break
            pre = H
        else:
            print(Cx, Cy, H)
            quit()

Submission status: Wrong Answer

Solution code:
# 解答ちらっと見た
# 問題のキモは Cx,Cy,Hがそれぞれ100通り、
# 全探索をCx,Cy,Hに対して試みると 入力された情報のcheckを入れて101*101*100*100でTLEする。
# でもよく考えてみると、Cx,CyがわかればHはそのあとで出せるので Cx,Cyに対して全探索をする(101*101*100+100の計算量で済む)


def check(x, y, h, cx, cy):
    return max(h + abs(x - cx) + abs(y - cy),0)


N = int(input())
H = []

checkers = [(list(map(int, input().split()))) for _ in range(N)]
for icx in range(101):
    for icy in range(101):
        H = []
        for checker in checkers:
            H.append(check(checker[0], checker[1], checker[2], icx, icy))

        if len(set(H)) == 1:
            print('{} {} {}'.format(icx, icy, H[0]))
            exit(0)

Submission status: Wrong Answer

Solution code:
n=int(input())
xyh=[list(map(int,input().split())) for _ in range(n)]
z=[]
for x,y,h in xyh:
    if h==0:
        z.append([x,y])
for i in range(101):
    for j in range(101):
        if [i,j] in z:
            continue
        t=set()
        for x,y,h in xyh:
            if h>0:
                t.add(abs(i-x)+abs(j-y)+h)
        if len(t)==1:
            break
    else:
        continue
    break
print(i,j,list(t)[0])

Submission status: Wrong Answer

Solution code:
def check(Cx, Cy):
    x, y, h = L[0]
    H = h + abs(x - Cx) + abs(y - Cy)
    if H < 0:
        return -1
    for x, y, h in L:
        if h != max(H - abs(x - Cx) - abs(y - Cy), 0):
            return -1
    return H

N = int(input())
L = [tuple(map(int, input().split())) for _ in range(N)]

for Cx in range(101):
    for Cy in range(101):
        H = check(Cx, Cy)
        if H >= 1:
            print(Cx, Cy, H)
            quit()

Submission status: Wrong Answer

Solution code:
def check(Cx, Cy):
    x, y, h = L[0]
    H = h + abs(x - Cx) + abs(y - Cy)
    for x, y, h in L[1:]:
        if h != max(H - abs(x - Cx) - abs(y - Cy), 0):
            return -1
    return H


N = int(input())
L = [tuple(map(int, input().split())) for _ in range(N)]

for Cx in range(101):
    for Cy in range(101):
        H = check(Cx, Cy)
        if H >= 1:
            print(Cx, Cy, H)
            quit()

Submission status: Wrong Answer

Solution code:
N=int(input())
d={}
for i in range(N):
	x,y,h=map(int,input().split())
	d[tuple([x,y])]=h

for i in range(101):
	for j in range(101):
		h=-1
		for p in d:
			h=max(h,abs(p[0]-i)+abs(p[1]-j)+d[p])
		f=True
		for p in d:
			if d[p]!=max(0,h-abs(p[0]-i)-abs(p[1]-j)):
				f=False
				break
		if f==True:
			print(i,j,h)

Submission status: Wrong Answer

Solution code:
n=int(input())
xyh=[list(map(int,input().split())) for _ in range(n)]
for i in range(101):
    for j in range(101):
        t=set()
        for x,y,h in xyh:
            if h!=0:
                th=abs(i-x)+abs(j-y)+h
                if th>0:
                    t.add(th)
        if len(t)==1:
            break
    else:
        continue
    break
print(i,j,list(t)[0])

Submission status: Wrong Answer

Solution code:
n=int(input())

L=[[{0}for i in range(0,101)]for q in range(0,101)]


for inp in range(n):
    x,y,h=map(int,input().split())
    if h != 0:
        for i in range(0,101):
            for q in range(0,101):
                L[i][q].add(h+abs(x-i)+abs(y-q))
    else:
        L[x][y].add(-1)

for i in range(101):
    for q in range(101):
        if len(L[i][q])==2 and max(L[i][q])>0:
            print(str(i)+" "+str(q)+" "+str(max(L[i][q])))

Submission status: Wrong Answer

Solution code:
n=int(input())
x,y,h=map(int,input().split())
d=[]
for i in range(n-1):
    a,b,c=map(int,input().split())
    d.append((a,b,c))
if n==1:
    print(d[10])
for i in range(101):
    for j in range(101):
        p=abs(i-x)+abs(j-y)+h
        for a,b,c in d:
            if (c==0 and p-abs(i-a)-abs(j-b)<1) or (c==(p-abs(i-a)-abs(j-b))):
                pass
            else:
                p=-1
                break
        if p!=-1:
            print(i,j,p)
            exit()

Submission status: Wrong Answer

Solution code:
n=int(input())
x,y,h=map(int,input().split())
d=[]
for i in range(n-1):
    a,b,c=map(int,input().split())
    d.append((a,b,c))
if n==1 and h==10**9:
    print(x,y,h)
    exit()
for i in range(101):
    for j in range(101):
        p=abs(i-x)+abs(j-y)+h
        for a,b,c in d:
            if (c==0 and p-abs(i-a)-abs(j-b)<1) or (c==(p-abs(i-a)-abs(j-b))):
                pass
            else:
                p=-1
                break
        if p!=-1:
            print(i,j,p)
            exit()

Submission status: Wrong Answer

Solution code:
n=int(input())
xyh=[list(map(int,input().split())) for _ in range(n)]
for i in range(101):
    for j in range(101):
        t=set()
        for x,y,h in xyh:
            if h!=0:
                t.add(abs(i-x)+abs(j-y)+h)
        if len(t)==1:
            break
    else:
        continue
    break
print(i,j,list(t)[0])

Submission status: Wrong Answer

Solution code:
n=int(input())
xyh=[list(map(int,input().split())) for _ in range(n)]
for i in range(101):
    for j in range(101):
        t=set()
        for x,y,h in xyh:
            t.add(abs(i-x)+abs(j-y)+h)
        if len(t)==1:
            break
    else:
        continue
    break
print(i,j,list(t)[0])

Submission status: Wrong Answer

Solution code:
n=int(input())

L=[[{0}for i in range(0,101)]for q in range(0,101)]


for inp in range(n):
    x,y,h=map(int,input().split())
    for i in range(0,101):
        for q in range(0,101):
            L[i][q].add(h+abs(x-i)+abs(y-q))

for i in range(101):
    for q in range(101):
        if len(L[i][q])==2 and max(L[i][q])>0:
            print(str(i)+" "+str(q)+" "+str(max(L[i][q])))
            break

Submission status: Wrong Answer

Solution code:
N = int(input())
P = [list(map(int, input().split())) for i in range(N)]
C = [[0]*101 for i in range(101)]
for X in range(101):
  for Y in range(101):
    tmp1 = -1
    flg = 0
    for i in range(N):
      x,y,h = P[i]
      if h != 0 and tmp1 == -1:
        tmp1 = abs(X-x)+abs(Y-y)+h
      elif tmp1 != -1:
        tmp2 = abs(X-x)+abs(Y-y)+h
        if h != 0: 
          if tmp1 != tmp2:
            flg = 1
            break
        if h == 0:
          if tmp1 > tmp2:
            flg = 1
            break
    if flg == 0:
      print(X, Y, tmp1)        
      exit()

Submission status: Wrong Answer

Solution code:
n=int(input())
x,y,h=map(int,input().split())
d=[]
for i in range(n-1):
    a,b,c=map(int,input().split())
    d.append((a,b,c))

for i in range(101):
    for j in range(101):
        p=abs(i-x)+abs(j-y)+h
        for a,b,c in d:
            if (c==0 and p-abs(i-a)-abs(j-b)<1) or (c==(p-abs(i-a)-abs(j-b))):
                pass
            else:
                p=-1
                break
        if p!=-1:
            print(i,j,p)
            exit()