by hansang:

#include<bits/stdc++.h>
using namespace std;
const int N=45, M=1620;
int a[N], f[2][M][M];
bool pd(int i, int j, int k){
	if(i+j<=k || abs(i-j)>=k) return 0;
	if(i+k<=j || abs(i-k)>=j) return 0;
	if(j+k<=i || abs(k-j)>=i) return 0;
	if((i<=0) || (j<=0) || (k<=0)) return 0;
	return 1;
}
double calc(double i, double j, double k){
	double p=(i+j+k)/2;
	double res=sqrt(p*(p-i)*(p-j)*(p-k))*100.0;
	return res;
}
int main(){
	int n, sum=0; scanf("%d", &n);
	for(int i=1; i<=n; i++){
		scanf("%d", &a[i]);
		sum+=a[i];
	}
	double ans=0;
	memset(f, 0, sizeof(f)); f[0][0][0]=1;
	for(int i=1; i<=n; i++){
		for(int j=0; j<=sum/2; j++){
			for(int k=0; k<=sum/2; k++) if(f[(i-1)&1][j][k]){
				f[i&1][j+a[i]][k]=1;
				f[i&1][j][k+a[i]]=1;
				f[i&1][j][k]=1; 
				
				int t=sum-k-j-a[i];
				if(pd(j+a[i], k, t)) ans=max(ans, calc(j+a[i], k, t));
				if(pd(j, k+a[i], t)) ans=max(ans, calc(j, k+a[i], t));
			}
		}
	}
	printf("%d\n", (!ans)? -1: (int)ans);
	return 0;
}

by hansang:

#include<bits/stdc++.h>
using namespace std;
const int N=45, M=1620;
int a[N], f[2][M][M];
bool pd(int i, int j, int k){
	if(i+j<=k || abs(i-j)>=k) return 0;
	if(i+k<=j || abs(i-k)>=j) return 0;
	if(j+k<=i || abs(k-j)>=i) return 0;
	if((i<=0) || (j<=0) || (k<=0)) return 0;
	return 1;
}
double calc(double i, double j, double k){
	double p=(i+j+k)/2;
	double res=sqrt(p*(p-i)*(p-j)*(p-k))*100.0;
	return res;
}
int main(){
	int n, sum=0; scanf("%d", &n);
	for(int i=1; i<=n; i++){
		scanf("%d", &a[i]);
		sum+=a[i];
	}
	double ans=0;
	memset(f, 0, sizeof(f)); f[0][0][0]=1;
	for(int i=1; i<=n; i++){
		for(int j=0; j<=sum/2; j++){
			for(int k=0; k<=sum/2; k++) if(f[(i-1)&1][j][k]){
				f[i&1][j+a[i]][k]=1;
				f[i&1][j][k+a[i]]=1;
				f[i&1][j][k]=1; 
				
				int t=sum-k-j-a[i];
				if(pd(j+a[i], k, t)) ans=max(ans, calc(j+a[i], k, t));
				if(pd(j, k+a[i], t)) ans=max(ans, calc(j, k+a[i], t));
			}
		}
	}
	printf("%d\n", (!ans)? -1: (int)ans);
	return 0;
}