Resultant Vector Magnitude

Statement

Goal

The resultant vector of two or more vectors originating from the same location is simply the sum of the components of the vectors also originating from the same point. This can also be referred to as vector addition.

In this puzzle you must sum the i, j , and k components of each 3-dimensional vector to create the resultant vector, and from there you must calculate the magnitude of the resultant vector using a derivation of the Pythagorean Theorem which is the square-root of the sum of the components squared.

√(i² + j² + k²)

The result is to be an integer expression of the magnitude such that any decimal values are truncated after the calculation.

Input

Line 1: An integer N for the number of vectors.
NextN lines: A string containing the i, j, k components represented with integers ranging from -100 to 100. The integer precedes the component label.

Output

Line 1: A string of the resultant vector formatted in a similar manner to the input vectors.
Line 2: The integer representation of the magnitude of the resultant vector.

Constraints

-100 <= i <= 100
-100 <= j <= 100
-100 <= k <= 100

Example

Input

2
1i 1j 1k
1i 1j 1k

Output

2i 2j 2k
3

Game modes

Fastest, Shortest

Test cases

2 Vectors Test

Input

2 1i 1j 1k 1i 1j 1k

Output

2i 2j 2k 3

2 Vectors Validator Validator

Input

2 2i 2j 2k 2i 2j 2k

Output

4i 4j 4k 6

1 Vector Test

Input

1 5i 3j 10k

Output

5i 3j 10k 11

1 Vector Validator Validator

Input

1 7i 9j 0k

Output

7i 9j 0k 11

Negative Components Test

Input

3 -3i -8j -15k -14i 4j -25k 8i 12j 55k

Output

-9i 8j 15k 19

Negative Components Validator Validator

Input

3 -6i 9j -2k 2i -77j 6k 0i 0j 0k

Output

-4i -68j 4k 68

Lots of Vectors Test

Input

13 5i 12j 1k -5i 0j 1k 5i -54j 1k -66i 32j -1k 7i -9j 0k 7i 12j 13k -25i -6j 44k -3i 0j -21k 0i -11j -7k 6i 45j -10k -8i 15j -2k 27i 11j -1k -41i -13j -9k

Output

-91i 34j 9k 97

Lots of Vectors Validator Validator

Input

13 4i 12j 1k -5i 0j 1k 5i -54j 1k -66i 32j -1k 7i -9j 0k 7i 12j 13k -25i -6j 44k -3i 0j -21k 0i -11j -7k 6i 45j -10k -8i 15j -2k 27i 11j -1k -41i -13j -9k

Output

-92i 34j 9k 98

Solution language

Solution

Stub generator input

Comments

12 Comments

BoatBuilder Unnamed CodinGamer

about 4 years ago

✅ Approved the contribution. Comment: good CoC to learn or revise about vectors.

zakacat Unnamed CodinGamer

Thanks!

FredericLocquet Unnamed CodinGamer

✅ Approved the contribution. Comment: Good review of the vectors ! Easy and can be done in less than 10 minutes. Nice clash. My solution in python : n = int(input()) vector_sum = [0,0,0] for i in range(n): vector = list(map(int,input().replace("i","").replace("j","").replace("k","").split(" "))) for i in range(3): vector_sum[i] += vector[i] print("{0}i {1}j {2}k".format(*vector_sum)) print(int(sum(x**2 for x in vector_sum)**.5))

Jogginho Unnamed CodinGamer

✅ Approved the contribution. Comment: Un Puzzle réalisable par tous avec une vrai possibilité de faire la différence en terme de rapidité

over 4 years ago

Please correct a typing error in test 7 : 6i 45j- 10k is this 6i 45j -10k ?

Good Catch! Thanks. That was a typo that I have now fixed.

5DN1L Unnamed CodinGamer

1. Semi-similar clash exists: https://www.codingame.com/... 2. The inputs and the outputs are quite a mess there without the "+" signs to separate each component of i, j and k. Just visually unpleasant to me.

Hmm, I'll take that into consideration. Maybe I will add that the player needs to calculate the magnitude, as well. I will also think about adding the plus signs or cleaning it up somehow.