# Problem C - Sumsets

Problem C - Sumsets

## Problem C - Sumsets

Given S, a set of integers, find the largest d such that a + b + c = d where a, b, c, and d are distinct elements of S.

Several S, each consisting of a line containing an integer 1 <= n <= 1000 indicating the number of elements in S, followed by the elements of S, one per line. Each element of S is a distinct integer between -536870912 and +536870911 inclusive. The last line of input contains 0.

For each S, a single line containing d, or a single line containing "no solution".

``````5
2
3
5
7
12
5
2
16
64
256
1024
0
``````

``````12
no solution
``````

``````#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <ctype.h>

int c,i,j,k,n,wn;

char w[10001][100], buf[1000];

int main(){

while (1 == scanf("%d",&n)) {
if (c++) printf("\n");
wn = 0;
for (;;) {
if (1 != scanf("%[^a-zA-Z]",buf)) break;
if (1 != scanf("%[a-zA-Z]",buf)) break;
if (!strcmp(buf,"EndOfText")) break;
for (i=0;buf[i];i++) buf[i] = tolower(buf[i]);
strcpy(w[wn++],buf);
}
qsort(w,wn,100,strcmp);
strcpy(w[wn++],"***");
strcpy(buf,"\$\$\$");
for (i=j=0;i<wn;i++) {
if (strcmp(buf,w[i])) {
if (strcmp(buf,"\$\$\$") && k == n) printf("%s\n",buf),j=1;
strcpy(buf,w[i]);
k = 0;
}
k++;
}
if (!j) printf("There is no such word.\n");
}
}``````

``````#include<stdio.h>
#include<iostream>
#include<algorithm>
using namespace std;
int n,num[1005];

void solve()
{
for(int d=n-1;d>=0;d--)
{
for(int c=n-1;c>=0;c--)
{
if(c==d)
{
continue;
}
int t=num[d]-num[c];
int a=0,b=c-1;
while(a<b)
{
if(num[a]+num[b]==t)
{
cout<<num[d]<<endl;
return ;
}
else
if(num[a]+num[b]<t)
{
a++;
}
else
{
b--;
}
}
}
}

cout<<"no solution"<<endl;
}
int main()
{

while((cin>>n),n)
{
for(int i=0;i<n;i++)
cin>>num[i];
sort(num,num+n);
solve();
}

return 0;
}
``````