[Golang] Number spiral diagonals - Problem 28 - Project Euler
source link: http://siongui.github.io/2018/10/24/go-number-spiral-diagonals-problem-28-project-euler/
Go to the source link to view the article. You can view the picture content, updated content and better typesetting reading experience. If the link is broken, please click the button below to view the snapshot at that time.
[Golang] Number spiral diagonals - Problem 28 - Project Euler
October 24, 2018
Problem: [1]
Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:
21 22 23 24 25
20 7 8 9 10
19 6 1 2 11
18 5 4 3 12
17 16 15 14 13
It can be verified that the sum of the numbers on the diagonals is 101.
What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?
Solution:
669171001
First take a look at the four numbers on the diagonals of N x N square. for example, 3 5 7 9 on 3 x 3 square. The difference is 2 on the numbers. So the difference is n-1 on N x N square. We use this observation to calculate all numbers on the diagonals and hence the sum of them.
package main
import (
"fmt"
)
func main() {
sum := 1
nextNumberInDiagoal := 1
for j := 2; j < 1001; j += 2 {
for i := 0; i < 4; i++ {
nextNumberInDiagoal += j
sum += nextNumberInDiagoal
//fmt.Println(nextNumberInDiagoal)
}
}
fmt.Println(sum)
}
Test on:
References:
Recommend
About Joyk
Aggregate valuable and interesting links.
Joyk means Joy of geeK