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: 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
    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)]
    XYH.sort(key=itemgetter(2), reverse=True)
    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 max(hans-abs(xans-x)-abs(yans-y), 0) != h:
                        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: Accepted

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

xx, yy, hh = next(l for l in L if l[2] >= 1)
for Cx in range(101):
    for Cy in range(101):
        H = hh + abs(xx - Cx) + abs(yy - Cy)
        for x, y, h in L:
            if h != max(H - abs(x - Cx) - abs(y - Cy), 0):
                break
        else:
            print(Cx, Cy, H)
            quit()

Submission status: Accepted

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 get_H(Cx, Cy):
    for x, y, h in L:
        if h > 0:
            return abs(x - Cx) + abs(y - Cy) + h


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


N = int(input())

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

for Cx in range(101):
    for Cy in range(101):
        H = get_H(Cx, Cy)
        if check_H(Cx, Cy, H):
            print('{} {} {}'.format(Cx, Cy, H))
            exit(0)

Submission status: Accepted

Solution code:
N=int(input())
xyh=[list(map(int,input().split()[:3])) for _ in range(N)]

#hが0以外の要素をみつける
ax, ay, ah = list(filter(lambda x: x[2], xyh))[0]

for x in range(101):
    for y in range(101):
        H=ah+abs(ax-x)+abs(ay-y)
        if all(max(H-abs(t[0]-x)-abs(t[1]-y),0) == t[2] for t in xyh):
            print(x,y,H)

Submission status: Accepted

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)
            if all(hi == max(H - abs(cx - xi) - abs(cy - yi), 0) for xi, yi, hi in xyh):
                return " ".join([str(cx), str(cy), str(H)])


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

Submission status: Accepted

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:
        if h == 0:
            continue
        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: Accepted

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 xyh[k][2] == 0:
        if cnt > h:
          continue
      if h != cnt:
        flag = False
    if flag:
      print(i, j, h)
      exit(0)

Submission status: Accepted

Solution code:
n = int(input())

x = [0 for i in range(n)]
y = [0 for i in range(n)]
h = [0 for i in range(n)]

k = 0

for i in range(n):
    x[i], y[i], h[i] = map(int, input().split())
    if h[i] > 0:
        k = i

ansx = -1
ansy = -1
ansh = -1

for cx in range(101):
    for cy in range(101):
        H = h[k] + abs(x[k] - cx) + abs(y[k] - cy)
        flag = True
        for i in range(n):
            if max(H - abs(x[i] - cx) - abs(y[i] - cy), 0) != h[i]:
                flag = False
                break
        if flag:
            ansx = cx
            ansy = cy
            ansh = H
            break
    if ansx >= 0:
        break

print(ansx, ansy, ansh)

Submission status: Accepted

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


for cx in range(101):
    for cy in range(101):
        for i in range(n):
            ch = h[i] + abs(x[i] - cx) + abs(y[i] - cy)
            if all(h[j] == max(ch - abs(x[j] - cx) - abs(y[j] - cy), 0) for j in range(n)):
                print(cx, cy, ch)
                exit()

Submission status: Accepted

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,y,h=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()

Submission status: Accepted

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 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: Accepted

Solution code:
A=abs
_,*p=[list(map(int,t.split()[::-1]))for t in open(0)]
h,y,x=max(p)
r=range(101)
for i in r:
 for j in r:H=h+A(x-j)+A(y-i);print(*(j,i,H)*all(u==max(H-A(s-j)-A(t-i),0)for u,t,s in p))

Submission status: Accepted

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

Submission status: Accepted

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

Submission status: Accepted

Solution code:
n=int(input())

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

for inp in range(n):
    x,y,h=map(int,input().split())
    if h != 0:
        cnt+=1
        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)

if cnt==1:
    for i in range(101):
        for q in range(101):
            if L[i][q]=={0,1}:
                print(str(i)+" "+str(q)+" "+"1")
                break
else:  
    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: Accepted

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:
			if d[p]!=0:
				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: Accepted

Solution code:
N = int(input())

L = []
for i in range(N):
    x, y, h = map(int, input().split())
    L.append([x, y, h])
    if h != 0:
        idx = i


for i in range(101):
    for j in range(101):
        H = L[idx][2] + abs(L[idx][0]-i) + abs(L[idx][1]-j)
        for k in range(N):
            if L[k][2] == max(H - abs(L[k][0]-i) - abs(L[k][1]-j), 0):
                pass
            else:
                break
            if k == N-1:
                ansx = i
                ansy = j
                ansh = H

print(ansx, ansy, ansh)

Submission status: Accepted

Solution code:
N = int(input())
P = [list(map(int, input().split())) for i in range(N)]
C = [[0]*101 for i in range(101)]
P.sort(key=lambda x:x[2], reverse=True)
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: Accepted

Solution code:
A=abs
_,*p=[list(map(int,t.split()[::-1]))for t in open(0)]
h,y,x=sorted(p)[-1]
r=range(101)
for i in r:
 for j in r:H=h+A(x-j)+A(y-i);print(*(j,i,H)*all(u==max(H-A(s-j)-A(t-i),0)for u,t,s in p))

Submission status: Accepted

Solution code:
#!/usr/bin/env python3
#ABC112 C

import sys
import math
import bisect
sys.setrecursionlimit(1000000000)
from heapq import heappush, heappop
from collections import defaultdict
from itertools import accumulate
from collections import Counter
from collections import deque
from operator import itemgetter
from itertools import permutations
mod = 10**9 + 7
inf = float('inf')
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))

n = I()
xyh = [LI() for _ in range(n)]
maxh = 0
for x,y,h in xyh:
    maxh = max(maxh,h)
for H in range(maxh,maxh+201):
    for cx in range(101):
        for cy in range(101):
            for x,y,h in xyh:
                if h != max(H-abs(x-cx)-abs(y-cy),0):
                    break
            else:
                print(cx,cy,H)
                quit()

Submission status: Accepted

Solution code:
def c_pyramid():
    N = int(input())
    Pos = [[int(i) for i in input().split()] for j in range(N)]
    # 与えられた情報から頂点座標を一意に得られるので、h=0にならない
    x, y, h = sorted(Pos, key=lambda x: x[2])[-1]
    # 中心座標を全探索
    for cx in range(101):
        for cy in range(101):
            # 頂点の高さ height を決めたとき、すべての座標の情報と一致するか？
            height = h + abs(x - cx) + abs(y - cy)  # 定義式から逆算
            if all(h_i == max(height - abs(x_i - cx) - abs(y_i - cy), 0)
                   for x_i, y_i, h_i in Pos):
                return '{} {} {}'.format(cx, cy, height)  # すべて一致した。これが解
    return None

print(c_pyramid())

Submission status: Accepted

Solution code:
A=abs
_,*p=[list(map(int,t.split()))for t in open(0)]
for t in p:
 if t[2]:x,y,h=t
r=range(101)
for i in r:
 for j in r:H=h+A(x-j)+A(y-i);print(*(j,i,H)*all(u==max(H-A(s-j)-A(t-i),0)for s,t,u in p))

Submission status: Accepted

Solution code:
A=abs
_,*p=[list(map(int,t.split()))for t in open(0)]
for t in p:
 if t[2]:x,y,h=t
for I in range(10201):j,i=I//101,I%101;H=h+A(x-j)+A(y-i);print(*(j,i,H)*all(u==max(H-A(s-j)-A(t-i),0)for s,t,u in p))

Submission status: Accepted

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

for cx in range(101):
	for cy in range(101):
		ch = None
		for x, y, h in XYH:
			if 0 < h:
				ch = h + abs(x - cx) + abs(y - cy)
				if 0 < ch:
					break
		else:
			continue
		for x, y, h in XYH:
			th = max(0, ch - abs(x - cx) - abs(y - cy))
			if th != h:
				break
		else:
			print(cx, cy, ch)
			exit()

Submission status: Accepted

Solution code:
from operator import itemgetter
import sys
input = sys.stdin.readline
def inpl(): return list(map(int, input().split()))

N = int(input())
Q = sorted([inpl() for _ in range(N)], key=itemgetter(2), reverse=True)

for cx in range(101):
    for cy in range(101):
        ch = abs(cx - Q[0][0]) + abs(cy - Q[0][1]) + Q[0][2]
        for x, y, h in Q:
            if h != max(ch - abs(x-cx) - abs(y-cy), 0):
                break
        else:
            print(cx, cy, ch)

Submission status: Accepted

Solution code:
import sys

stdin = sys.stdin

sn = lambda : stdin.readline().rstrip()
an = lambda : list(map(int, stdin.readline().split()))
ni = lambda : int(sn())

n = ni()
xyz = [0] * n
for i in range(n):
  xyz[i] = an()

xyz.sort(key = lambda x: x[2])

sx, sy, sh = xyz[-1]
for Cy in range(101):
  for Cx in range(101):
    H = sh + abs(sx - Cx) + abs(sy - Cy)
    if all(h == max(H - abs(x - Cx) - abs(y - Cy), 0) for x, y, h in xyz):
      print(Cx, Cy, H)
      exit()

Submission status: Accepted

Solution code:
A=abs
_,*p=[list(map(int,t.split()))for t in open(0)]
x,y,h=[t for t in p if t[2]][0]
for I in range(10201):j,i=I//101,I%101;H=h+A(x-j)+A(y-i);print(*(j,i,H)*all(u==max(H-A(s-j)-A(t-i),0)for s,t,u in p))

Submission status: Accepted

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

for x0 in range(101):
    for y0 in range(101):
        a = -1
        ok = True
        for x, y, h in XYH:
            if h == 0:
                continue
            if a == -1:
                a = abs(x-x0) + abs(y-y0) + h
                continue
            if a != abs(x-x0) + abs(y-y0) + h:
                ok = False
                break
        for x, y, h in XYH:
            if h != max(a- abs(x0-x) - abs(y0-y), 0):
                ok = False
        if ok:
            print(x0, y0, a)
            break
    if ok:
        break