PROJECT EULER SOLUTION # 67

Solution to problem number 67 of Project Euler.

Question # 67

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.

3
7 4
2 4 6
8 5 9 3

That is, 3 + 7 + 4 + 9 = 23.
Find the maximum total from top to bottom in triangle.txt (right click and 'Save Link/Target As...'), a 15K text file containing a triangle with one-hundred rows.

NOTE: This is a much more difficult version of Problem 18. It is not possible to try every route to solve this problem, as there are 2⁹⁹altogether! If you could check one trillion (10¹²) routes every second it would take over twenty billion years to check them all. There is an efficient algorithm to solve it. ;o)

Solution # 67

/***********************************************************************************************************/

#include<stdio.h>

#include<conio.h>

#include<stdlib.h>

#include<time.h>

int get_sum(int *);

int main()

{

       FILE *f;

       int arr[100][100],max1[100],max2[100],i=0,j=0,maximum=0;

      

       f=fopen("D:/e.txt","r");

       i=0;

       for(i=0;i<100;i++)

              for(j=0;j<=i;j++)

              {

                     fscanf(f,"%d",&arr[i][j]);

              }

       for(i=0;i<100;i++)

       {

              for(j=0;j<=i;j++)

              {

                     if(i==0)

                     {

                           max1[j]=arr[i][j];

                           continue;

                     }

                     else if((j-1)<0)

                           max2[j]=arr[i][j]+max1[j];

                     else if(j==i)

                           max2[j]=arr[i][j]+max1[j-1];

                     else

                           max2[j]=arr[i][j]+((max1[j-1]>max1[j])?max1[j-1]:max1[j]);          

              }

              if(i==0)

                     continue;

                    

              for(j=0;j<=i;j++)

                     max1[j]=max2[j];

       }

      

       for(i=0;i<100;i++)

              if(maximum<max2[i])

                     maximum=max2[i];

       printf("Answer = %d\n\n",maximum);

      

       printf("\nEXECUTION TIME = %f\n",clock()/(float)CLK_TCK);

       system("pause");

}

/***********************************************************************************************************/