Found a coin problem on the internet that can be considered two-dimensional, and the idea is a bit like using an expansion method.
//============================================================================
// Name : The Candyman Can.cpp
// Date : 2013/4/10 下午6:40:00
// Author : GCA
//============================================================================
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <climits>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <cctype>
#include <utility>
using namespace std;
#ifdef ONLINE\_JUDGE
#define ll "%lld"
#else
#define ll "%I64d"
#endif
typedef unsigned int uint;
typedef long long int Int;
#define Set(a,s) memset(a,s,sizeof(a))
#define Write(w) freopen(w,"w",stdout)
#define Read(r) freopen(r,"r",stdin)
#define Pln() printf("\\n")
#define I\_de(x,n)for(int i=0;i<n;i++)printf("%d ",x\[i\]);Pln()
#define De(x)printf(#x"%d\\n",x)
#define For(i,x)for(int i=0;i<x;i++)
#define CON(x,y) x##y
#define Pmz(dp,nx,ny)for(int hty=0;hty<ny;hty++){for(int htx=0;htx<nx;htx++){\\
printf("%d ",dp\[htx\]\[hty\]);}Pln();}
#define M 1005
#define PII pair<int,int\>
#define PB push\_back
#define oo INT\_MAX
#define Set\_oo 0x3f
#define Is\_debug true
#define debug(...) if(Is\_debug)printf("DEBUG: "),printf(\_\_VA\_ARGS\_\_)
#define FOR(it,c) for(\_\_typeof((c).begin()) it=(c).begin();it!=(c).end();it++)
#define eps 1e-6
bool xdy(double x,double y){return x>y+eps;}
bool xddy(double x,double y){return x>y-eps;}
bool xcy(double x,double y){return x<y-eps;}
bool xcdy(double x,double y){return x<y+eps;}
int min3(int x,int y,int z){
int tmp=min(x,y);
return min(tmp,z);
}
int max3(int x,int y,int z){
int tmp=max(x,y);
return max(tmp,z);
}
int n,cost\[M\];
int sum=0;
int dp\[M\]\[M\];
int maxd(int i,int j){
int k=sum-i-j;
return max3(abs(k-i),abs(i-j),abs(j-k));
}
int main() {
ios\_base::sync\_with\_stdio(0);
int test,ff=0;
scanf("%d",&test);
while(test--){
sum=0;
Set(dp,0);
dp\[0\]\[0\]=1;
scanf("%d",&n);
for(int i=0;i<n;i++){
scanf("%d",&cost\[i\]);
sum+=cost\[i\];
}
for(int i=0;i<n;i++){
for(int j=sum;j>=0;j--){
for(int k=sum;k>=0;k--){
if(dp\[j\]\[k\]){
dp\[j+cost\[i\]\]\[k\]=1;
dp\[j\]\[k+cost\[i\]\]=1;
}
}
}
}
int minsum=oo;
for(int i=0;i<=sum;i++){
for(int j=0;j<=sum;j++){
if(dp\[i\]\[j\])
minsum=min(maxd(i,j),minsum);
}
}
printf("Case %d: ",++ff);
printf("%d\\n",minsum);
}
}