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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.

Input

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.

Output

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

Sample Input

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

Output for Sample Input

12
no solution

题目大意：在一个集合中求出最大的d，d=a+b+c，a,b,c,d属于这个集合。

解析：这题可以把 a+b+c=d，转换为 a+b = d-c，这样就可以减少循环的次数。其中d和c用for来遍历，a+b用二分来查找出相应的值。

#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
const int N = 1005;
int n;
int num[N];
void solve() {
    int t;
    for(int d = n-1; d >= 0; d--) {
        for(int c = n-1; c >= 0; c--) {
            if(c == d) {
                continue;
            }
            t = num[d] - num[c];
            int a = 0, b = c-1;
            while(a < b) {
                if(num[a] + num[b] == t) {
                    printf("%d\n",num[d]);
                    return ;
                }else if(num[a] + num[b] < t) {
                    a++;
                }else {
                    b--;
                }
            }
        }   
    }
    printf("no solution\n");
}
int main() {
    while(scanf("%d",&n) != EOF && n) {
        for(int i = 0; i < n; i++) {
            scanf("%d",&num[i]);
        }
        sort(num,num+n);
        solve();
    }
    return 0;
}