Problem: 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.

Submission attempts (in order):

import sys
input = sys.stdin.readline  
N = int(input())
xyh =[0]*N
for i in range(N):
    xyh[i] = tuple(int(i) for i in input().split())

from collections import defaultdict
H =defaultdict(set)
for x,y,h in xyh:
    for cx in range(101):
        for cy in range(101):
            xx =x -cx
            yy =y -cy
            if cx <=x and cy <=y:
                H[(cx,cy)].add( (h +xx +yy) )
            elif cx >x and cy <=y:
                 H[(cx,cy)].add( (h -xx +yy) )
            elif cx <=x and cy >y:
                 H[(cx,cy)].add( (h +xx -yy) )
            elif cx >x and cy >y:
                 H[(cx,cy)].add( (h -xx -yy) )
            

#H.sort(key =lambda x:x[1])
for k,v in H.items():
    if len(v)==1:
        if 0 <= v[0] <=10**9:
            print(*k,*v)
        elif v[0] <0:
            print(*k,0)
        elif 10**9 <v[0]:
            print(*k,10**9)


import sys
input = sys.stdin.readline  
N = int(input())
xyh =[0]*N
for i in range(N):
    xyh[i] = tuple(int(i) for i in input().split())

from collections import defaultdict
H =defaultdict(set)
for x,y,h in xyh:
    for cx in range(101):
        for cy in range(101):
            xx =x -cx
            yy =y -cy
            if cx <=x and cy <=y:
                H[(cx,cy)].add( (h +xx +yy) )
            elif cx >x and cy <=y:
                 H[(cx,cy)].add( (h -xx +yy) )
            elif cx <=x and cy >y:
                 H[(cx,cy)].add( (h +xx -yy) )
            elif cx >x and cy >y:
                 H[(cx,cy)].add( (h -xx -yy) )
            
print(xyh)
#H.sort(key =lambda x:x[1])
for k,v in H.items():
    if len(v)==1:
        print(*k,*v)


import sys
input = sys.stdin.readline  
N = int(input())
xyh =[0]*N
h_list =[0]*N

for i in range(N):
    x,y,h= (int(i) for i in input().split())
    xyh[i] =x,y,h
    h_list[i] =h

from bisect import bisect_right
xyh.sort(key =lambda x:x[2])
h_list.sort()
ind =bisect_right(h_list,0)
from collections import defaultdict
H =defaultdict(set)

for x,y,h in xyh[ind:]:
    for cx in range(101):
        for cy in range(101):
            xx =x -cx
            yy =y -cy
            if cx <=x and cy <=y:
                H[(cx,cy)].add( (h +xx +yy) )
            elif cx >x and cy <=y:
                H[(cx,cy)].add( (h -xx +yy) )
            elif cx <=x and cy >y:
                H[(cx,cy)].add( (h +xx -yy) )
            elif cx >x and cy >y:
                H[(cx,cy)].add( (h -xx -yy) )
            

#H.sort(key =lambda x:x[1])
if len(xyh[ind:]) ==1:
    print(*xyh[-1])
else:
    for k,v in H.items():
    
        if len(v)==1:
            vv =v.pop()
            if 0 <= vv :
                print(*k,vv)
            elif vv <0:
                print(*k,0)

Verdicts: Runtime Error

Wrong Answer

Accepted