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Competition Arena > MagicSquare

MagicSquare

SRM 188 · 2004-03-25 · by legakis

SRM 188 · 2004-03-25 · by legakis · Simple Math
Class Name: MagicSquare
Return Type: int
Method Name: missing
Arg Types: (vector<int>)
Problem Statement

Problem Statement

A magic square is a 3x3 array of numbers, such that the sum of each row, column, and diagonal are all the same. For example: 


    8 1 6
    3 5 7
    4 9 2

In this example, all rows, columns, and diagonals sum to 15.

You will be given a int[] representing the nine numbers of a magic square, listed left-to-right, top-to-bottom. However, one of these numbers will be replaced by a -1. Write a method to determine which number was removed. For example, if the 7 was removed from the magic square above, you would be given { 8, 1, 6, 3, 5, -1, 4, 9, 2 }, and your program should return 7.

The completed magic square will consist of exactly 9 distinct positive integers.

Constraints

  • square will contain exactly 9 elements.
  • Each element of square will either be -1 or be between 1 and 100, inclusive.
  • Exactly one element of square will be -1.
  • The eight elements of square that are not -1 will be distinct.
  • The input will be such that a number between 1 and 100, inclusive, can be found to complete the magic square, and it will not be equal to any of the other 8 numbers in the square.
Examples
0)
{ 8, 1, 6, 3, 5, -1, 4, 9, 2 }
Returns: 7

This is the example from the problem statement.

1)
{ -1, 1, 6, 3, 5, 7, 4, 9, 2 }
Returns: 8

The same square, but this time with the number 8 removed.

2)
{ 5, 15, 13, 19, 11, 3, 9, 7, -1 }
Returns: 17

The missing number is 17.

3)
{ 5, 15, -1, 19, 11, 3, 9, 7, 17 }
Returns: 13

13

4)
{ 5, 15, 13, 19, 11, 3, -1, 7, 17 }
Returns: 9

9

Submissions are judged against all 18 archived test cases, of which 5 are shown here. Case numbers match the judge’s.

Coding Area

Language: C++17 · define a public class MagicSquare with a public method int missing(vector<int> square) · 18 test cases · 2 s / 256 MB per case

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