Project Euler:problem 5-gon Ring

Consider the following "magic" 3-gon ring, filled with the numbers 1 to 6, and all line adding to nine.

Working clockwise, and starting from the group of three with the numerically lowest external node (4,3,2 in this Example), each solution can is described uniquely. For example, the above solution can is described by the set:4,3,2; 6,2,1; 5,1,3.

It is possible to complete the ring with four different totals:9, ten, one, and 12. There is eight solutions in total.

Total	Solution Set
9	4,2,3; 5,3,1; 6,1,2
9	4,3,2; 6,2,1; 5,1,3
10	2,3,5; 4,5,1; 6,1,3
10	2,5,3; 6,3,1; 4,1,5
11	1,4,6; 3,6,2; 5,2,4
11	1,6,4; 5,4,2; 3,2,6
12	1,5,6; 2,6,4; 3,4,5
12	1,6,5; 3,5,4; 2,4,6

By concatenating All group it is possible to form 9-digit strings; The maximum string for a 3-gon ring is 432621513.

Using the numbers 1 to ten, and depending on arrangements, it's possible to form 16-and 17-digit strings. What's the maximum 16-digit string for a "magic" 5-gon ring?

The a0 of the most outer ring is the smallest number in the outer ring, so the a0<=6, at the same time, makes the string the largest, so a0=6, while the other number of the outer ring is 7,8,9,10 respectively.

The number of 1+2+3+...+9+10=55 inner rings is 1,2,3,4,5, and the 14 of each row is counted.

So what line A0 is in, the other two numbers are 8, and 6,7 are in the outer ring, so these two numbers can only be 5 and 3.

#include <iostream> #include <string> #include <vector> #include <algorithm>using namespace std ; int main () {int a[7] = {1, 2, 4, 7, 8, 9,};int b[2] = {3, 5};string tmp,res;do{for (int i = 0; i < 2; i++) {if (a [0] + b[i] + a[1] = && a[1] + a[2] + a[3] = = && A[3] + a[4] + a[5] = [+] && a[5] + a[6] + b [(i + 1)% 2] = =) {cout << "6" << B[i] << b[(i + 1)% 2] << endl;cout << a[0] << b[( i + 1)% 2] << a[1] << endl;cout << a[2] << a[1] << a[3] << endl;cout << a[4] &l t;< a[3] << a[5] << endl;cout << a[6] << a[5] << b[i] << endl;cout << Endl;} }} while (Next_permutation (A, A + 7)), System ("pause"); return 0;}

Stole a lazy, output two sets of results

Apparently that big 6531031914842725.

Copyright NOTICE: This article for Bo Master original article, without Bo Master permission not reproduced.

Project Euler:problem 5-gon Ring