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sriramchandrk • Oct 16, 2008

# Programming Challenge - Try this (Triangle problem)

```            7
3   8
8   1   0
2   7   4   4
4   5   2   6   5   (Figure 1)```
Figure 1 shows a number triangle.
Write a program that calculates the highest sum of numbers passed on a route that starts at the top and ends somewhere on the base.

• Each step can go either diagonally down to the left or diagonally down to the right.
• The number of rows in the triangle is >1 but <=100.
• The numbers in the triangle, all integers, are between 0 and 99.
Input Data

Data about the number of rows in the triangle are first read from the INPUT.TXT file.

In our example, INPUT.TXT appears as follows:

5
7
3 8
8 1 0
2 7 4 4
4 5 2 6 5
Output Data

The highest sum is written as an integer in the OUTPUT.TXT file. In our example:
30

Note: This is taken from an olympiads exams.

You definitely will enjoy solving this

Thanks & Regards
Sriram
Kaustubh Katdare • Oct 16, 2008
Oh boy, this is interesting. Would love to see CEans cracking this one!

Shall move it to front page, soon.
prakash.athani • Oct 16, 2008
Hey Sriram,

Check this. This program does basically what you want.
Reply back & I can add support for error handling and INPUT.txt & OUTPUT.txt stuff.

```#include
#include

int main() {
int a[20],size=0,rows,sum,i,j,depth,height,left,right;
clrscr();

printf("Input the number of rows(>1 & <=100) :");
scanf("%d",&rows);

for(i=1;i<=rows;i++) {
printf("Input %d number(s) between 0 & 99 for row %d :",i,i);
for(j=1;j<=i;j++) {
scanf("%d",&a[size++]);
}
}

i=0;
sum=a[0];
depth=0;
height=rows-1;

while(depthright) {
sum=sum+left;
i=i+depth+1;
}
else {
sum=sum+right;
i=i+depth+2;
}//end of if

depth++;
}//end of while loop

printf("Highest sum : %d",sum);
getch();

return 0;

}```
sriramchandrk • Oct 17, 2008
The logic is wrong, its not working even for my data.

If there is a big number at the top level you are taking that direction what will it happen if from that route on all are small numbers!

for the data given by me it should give 30 as answer but your code gives 28.

It is taking this route 7 8 1 7 5=28
instead of 7 3 8 7 5=30 the correct route.

the list of possible paths for my given problem for reference

7 3 8 2 4=24
7 3 8 2 5=25
7 3 8 7 5=30
7 3 8 7 2=27
7 3 1 7 5=23
7 3 1 7 2=20
7 3 1 4 2=17
7 3 1 4 6=21
7 8 1 7 5=28
7 8 1 7 2=25
7 8 1 4 2=22
7 8 1 4 6=26
7 8 0 4 2=21
7 8 0 4 6=25
7 8 0 4 6=25
7 8 0 4 5=24
Big = 30

Prakash, let me know if you need any clarification regarding my comment.

Thanks & Regards
Sriram
Try the code:

```#include "stdio.h"

#define MAX_SUPPORTED_ROWS 100

int sum(int a[MAX_SUPPORTED_ROWS][MAX_SUPPORTED_ROWS], int row_count, int i, int j) {
int highest_sum = 0;
if(i == (row_count-1)) {
highest_sum = a[i][j];
} else {
int left_sum = sum(a, row_count, i + 1, j);
int right_sum = sum(a, row_count, i + 1, j + 1);
if(left_sum > right_sum) {
highest_sum = a[i][j] + left_sum;
} else {
highest_sum = a[i][j] + right_sum;
}
}
return highest_sum;
}

int main() {
int a[MAX_SUPPORTED_ROWS][MAX_SUPPORTED_ROWS] = {0};
int row_count = 0;
int i = 0, j = 0;

scanf("%d", &row_count);
if((row_count < 1) || (row_count > 100)) {
printf("Invalid row count");
return 0;
}

for(i = 0; i < row_count; i++) {
for(j = 0; j <= i; j++) {
scanf("%d", &a[i][j]);
if((a[i][j] < 0) || (a[i][j] > 99)) {
printf("Invalid values");
return 0;
}
}
}

printf("Row count: %d\n", row_count);
printf("Data:\n");
for(i = 0; i < row_count; i++) {
for(j = 0; j <= i; j++) {
printf("%d ", a[i][j]);
}
printf("\n");
}

int highest_sum = sum(a, row_count, 0, 0);
printf("Highest sum: %d\n", highest_sum);

return 0;
}```

Compile the file with above code and run as:
a.exe < input.txt > output.txt [on windows]
a.out < input.txt > output.txt [on linux]

Here,
a.exe or a.out are the executables generated after compilation
input.txt is the file containing input as specified in the problem statement
output.txt is the output file containing result

Kaustubh Katdare • Oct 17, 2008
Guys, do enclose your code in
` , [ / code ] tags (remove the spaces)`
sriramchandrk • Oct 17, 2008
You rock! my vote for you for Special CEan!

Prakash, is also on the way.

Thanks & Regards
Sriram
Thank you Sriram.

I would now like to take the problem to next level.

Modify the sample program given above (or write your one code) that not only print the highest sum but also print the exact number with their positions that sums to highest value, e.g., for the sample input data given in the problem statement, output should be:

Highest sum: 30
Data:
[1,1]: 7
[2,1]: 3
[3,1]: 8
[4,2]: 7
[5,2]: 5

sriramchandrk • Oct 17, 2008
Yes, that will be bit tricky as yours is recursive.
Go ahead, meanwhile let me think for some other Challenge.

Thanks & Regards
Sriram
No taker for the second part of the problem 😔

Ok, here is my solution.

```#include "stdio.h"

#define MAX_SUPPORTED_ROWS 100

int sum(int a[MAX_SUPPORTED_ROWS][MAX_SUPPORTED_ROWS], int pos[MAX_SUPPORTED_ROWS], int row_count, int i, int j) {
int highest_sum = 0;
int pos_left[MAX_SUPPORTED_ROWS] = { 0 };
int pos_right[MAX_SUPPORTED_ROWS] = { 0 };
int x = 0;

pos[i] = j;
if(i == (row_count-1)) {
highest_sum = a[i][j];
} else {
int left_sum = sum(a, pos_left, row_count, i + 1, j);
int right_sum = sum(a, pos_right, row_count, i + 1, j + 1);
if(left_sum > right_sum) {
highest_sum = a[i][j] + left_sum;
for(x = (i+1); x < row_count; x++) {
pos[x] = pos_left[x];
}
} else {
highest_sum = a[i][j] + right_sum;
for(x = (i+1); x < row_count; x++) {
pos[x] = pos_right[x];
}
}
}

return highest_sum;
}

int main() {
int a[MAX_SUPPORTED_ROWS][MAX_SUPPORTED_ROWS] = {0};
int pos[MAX_SUPPORTED_ROWS] = {0};
int row_count = 0;
int i = 0, j = 0;

scanf("%d", &row_count);
if((row_count < 1) || (row_count > 100)) {
printf("Invalid row count");
return 0;
}

for(i = 0; i < row_count; i++) {
for(j = 0; j <= i; j++) {
scanf("%d", &a[i][j]);
if((a[i][j] < 0) || (a[i][j] > 99)) {
printf("Invalid values");
return 0;
}
}
}

printf("Row count: %d\n", row_count);
printf("Data:\n");
for(i = 0; i < row_count; i++) {
for(j = 0; j <= i; j++) {
printf("%d ", a[i][j]);
}
printf("\n");
}

int highest_sum = sum(a, pos, row_count, 0, 0);
printf("\nHighest sum: %d\n", highest_sum);
printf("Data:\n");
for(i = 0; i < row_count; i++) {
printf("[%d,%d]: %d\n", i + 1, pos[i] + 1, a[i][pos[i]]);
}

return 0;
}
```