Solution to
problem number 61 of Project Euler.
Question # 61
Triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers are
all figurate (polygonal) numbers and are generated by the following formulae:|
Triangle
|
|
P3,n=n(n+1)/2
|
|
1, 3, 6, 10, 15, ...
|
|
Square
|
|
P4,n=n2
|
|
1, 4, 9, 16, 25, ...
|
|
Pentagonal
|
|
P5,n=n(3n
 1)/2 |
|
1, 5, 12, 22, 35, ...
|
|
Hexagonal
|
|
P6,n=n(2n
 1) |
|
1, 6, 15, 28, 45, ...
|
|
Heptagonal
|
|
P7,n=n(5n
 3)/2 |
|
1, 7, 18, 34, 55, ...
|
|
Octagonal
|
|
P8,n=n(3n
 2) |
|
1, 8, 21, 40, 65, ...
|
- The set is cyclic, in that the last two digits of each number is the first two digits of the next number (including the last number with the first).
- Each polygonal type: triangle (P3,127=8128), square (P4,91=8281), and pentagonal (P5,44=2882), is represented by a different number in the set.
- This is the only set of 4-digit numbers with this property.
Solution # 61
/**********************************************************************/
#include<math.h>
#include<stdio.h>
#include<stdlib.h>
int
arr[6]={0};
int
isTriangle(int);
int
isSquare(int);
int
isPentagonal(int);
int
isHexagonal(int);
int
isHeptagonal(int);
int
isOctagonal(int);
int
isAnyPolygonal(int);
int
isAnySquare(int,int,int,int,int,int);
int
isAnyTriangle(int,int,int,int,int,int);
int
isAnyPentagonal(int,int,int,int,int,int);
int
isAnyHexagonal(int,int,int,int,int,int);
int
isAnyHeptagonal(int,int,int,int,int,int);
int
isAnyOctagonal(int,int,int,int,int,int);
int
main()
{
int i,a,b,c,e,d,f,flag=0;
for(a=1000;a<10000;a++)
if(isAnyPolygonal(a))
for(b=1000;b<10000;b++)
if(a%100==(b/100)
&& isAnyPolygonal(b))
for(c=1000;c<10000;c++)
if(b%100==(c/100)
&& isAnyPolygonal(c))
for(d=1000;d<10000;d++)
if(c%100==(d/100) &&
isAnyPolygonal(d))
for(e=1000;e<10000;e++)
if(d%100==(e/100)
&& isAnyPolygonal(e))
for(f=1000;f<10000;f++)
if(e%100==(f/100)
&& f%100==(a/100) && isAnyPolygonal(f))
{
flag=0;
for(i=0;i<6;i++)
arr[i]=0;
//printf("%d
%d %d %d %d %d\n",a,b,c,d,e,f);
isAnyTriangle(a,b,c,d,e,f);
isAnySquare(a,b,c,d,e,f);
isAnyPentagonal(a,b,c,d,e,f);
isAnyHexagonal(a,b,c,d,e,f);
isAnyHeptagonal(a,b,c,d,e,f);
isAnyOctagonal(a,b,c,d,e,f);
for(i=0;i<6;i++)
flag+=arr[i];
if(flag==6)
{
printf("%d %d %d %d %d
%d",a,b,c,d,e,f);
printf(" sum = %d\n",(a+b+c+e+d+f));
printf("Lavish done!!!\n");
exit(1);
}
}
return 0;
}
int
isAnyPolygonal(int n)
{
if(isTriangle(n) || isSquare(n) ||
isPentagonal(n) || isHexagonal(n) || isHeptagonal(n) || isOctagonal(n))
return 1;
return 0;
}
int
isAnyTriangle(int a,int b,int c,int d,int e,int f)
{
if(isTriangle(a))
{
arr[0]=1;
return 1;
}
if(isTriangle(b))
{
arr[1]=1;
return 1;
}
if(isTriangle(c))
{
arr[2]=1;
return 1;
}
if(isTriangle(d))
{
arr[3]=1;
return 1;
}
if(isTriangle(e))
{
arr[4]=1;
return 1;
}
if(isTriangle(f))
{
arr[5]=1;
return 1;
}
return 0;
}
int
isAnySquare(int a,int b,int c,int d,int e,int f)
{
if(isSquare(a))
{
arr[0]=1;
return 1;
}
if(isSquare(b))
{
arr[1]=1;
return 1;
}
if(isSquare(c))
{
arr[2]=1;
return 1;
}
if(isSquare(d))
{
arr[3]=1;
return 1;
}
if(isSquare(e))
{
arr[4]=1;
return 1;
}
if(isSquare(f))
{
arr[5]=1;
return 1;
}
return 0;
}
int
isAnyPentagonal(int a,int b,int c,int d,int e,int f)
{
if(isPentagonal(a))
{
arr[0]=1;
return 1;
}
if(isPentagonal(b))
{
arr[1]=1;
return 1;
}
if(isPentagonal(c))
{
arr[2]=1;
return 1;
}
if(isPentagonal(d))
{
arr[3]=1;
return 1;
}
if(isPentagonal(e))
{
arr[4]=1;
return 1;
}
if(isPentagonal(f))
{
arr[5]=1;
return 1;
}
return 0;
}
int
isAnyHexagonal(int a,int b,int c,int d,int e,int f)
{
if(isHexagonal(a))
{
arr[0]=1;
return 1;
}
if(isHexagonal(b))
{
arr[1]=1;
return 1;
}
if(isHexagonal(c))
{
arr[2]=1;
return 1;
}
if(isHexagonal(d))
{
arr[3]=1;
return 1;
}
if(isHexagonal(e))
{
arr[4]=1;
return 1;
}
if(isHexagonal(f))
{
arr[5]=1;
return 1;
}
return 0;
}
int
isAnyHeptagonal(int a,int b,int c,int d,int e,int f)
{
if(isHeptagonal(a))
{
arr[0]=1;
return 1;
}
if(isHeptagonal(b))
{
arr[1]=1;
return 1;
}
if(isHeptagonal(c))
{
arr[2]=1;
return 1;
}
if(isHeptagonal(d))
{
arr[3]=1;
return 1;
}
if(isHeptagonal(e))
{
arr[4]=1;
return 1;
}
if(isHeptagonal(f))
{
arr[5]=1;
return 1;
}
return 0;
}
int
isAnyOctagonal(int a,int b,int c,int d,int e,int f)
{
if(isOctagonal(a))
{
arr[0]=1;
return 1;
}
if(isOctagonal(b))
{
arr[1]=1;
return 1;
}
if(isOctagonal(c))
{
arr[2]=1;
return 1;
}
if(isOctagonal(d))
{
arr[3]=1;
return 1;
}
if(isOctagonal(e))
{
arr[4]=1;
return 1;
}
if(isOctagonal(f))
{
arr[5]=1;
return 1;
}
return 0;
}
int
isTriangle(int n)
{
int i;
for(i=0;i<n;i++)
if(n*2==(i*(i+1)))
return 1;
return 0;
}
int
isSquare(int n)
{
if((int)sqrt(n)==sqrt(n))
return
1;
return 0;
}
int
isPentagonal(int n)
{
int i;
for(i=0;i<n;i++)
if(n*2==(i*(3*i-1)))
return 1;
return 0;
}
int
isHexagonal(int n)
{
int i;
for(i=0;i<n;i++)
if(n==(i*(2*i-1)))
return 1;
return 0;
}
int
isHeptagonal(int n)
{
int i;
for(i=0;i<n;i++)
if(n*2==(i*(5*i-3)))
return 1;
return 0;
}
int
isOctagonal(int n)
{
int i;
for(i=0;i<n;i++)
if(n==(i*(3*i-2)))
return 1;
return 0;
}
/**********************************************************************/
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