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	HanSF hANsf

搬运于2025-08-24 21:17:53，当前版本为作者最后更新于2025-03-18 13:14:48，作者可能在搬运后再次修改，您可在原文处查看最新版

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以下是正文

题目传送门

很明显，这道题是一个大分类讨论，根据题意，我们只需要区区 $C_{7}^4 = 35$ 个 if 语句就可以判断出所有情况。

#include <bits/stdc++.h>
#define int long long
using namespace std;
struct node{
    int x,y,z;
}tmp[105];
bool cmp(node a,node b){
    if(a.x!=b.x) return a.x<b.x;
    if(a.y!=b.y) return a.y<b.y;
    return a.z<b.z;
}
int tot = 0;
void check(int a1,int a2,int a3){  // 判断是否合法。
    if(a1<0||a2<0||a3<0) return;
    if(a1+a2>a3&&a2+a3>a1&&a1+a3>a2&&a1<=a2&&a2<=a3) tmp[++tot] = {a1,a2,a3};
}
signed main(){
    ios::sync_with_stdio(false);
    cin.tie(0);cout.tie(0);
    int x[5];cin>>x[1]>>x[2]>>x[3]>>x[4];
    sort(x+1,x+5);
    if(x[1]+x[2]==x[4]){ //1
        int a1 = x[1],a2 = x[2],a3 = x[3];
        check(a1,a2,a3);
    }
    if(x[1]+x[3]==x[4]){ //2
        int a1 = x[1],a2 = x[2],a3 = x[3];
        check(a1,a2,a3);
    }
    if(x[2]+x[3]==x[4]){ //3
        int a1 = x[1],a2 = x[2],a3 = x[3];
        check(a1,a2,a3);
    }
    if(x[1]+x[2]+x[3]==x[4]){ //4
        int a1 = x[1],a2 = x[2],a3 = x[3];
        check(a1,a2,a3);
    }
    if(x[1]+x[2]==x[3]){ //5
        int a1 = x[1],a2 = x[2],a3 = x[4]-x[1];
        check(a1,a2,a3);
    }
    if(x[1]+x[2]==x[3]){ //6
        int a1 = x[1],a2 = x[2],a3 = x[4]-x[2];
        check(a1,a2,a3);
    }
    if(x[1]+x[2]==x[3]){ //7
        int a1 = x[1],a2 = x[2],a3 = x[4]-x[3];
        check(a1,a2,a3);
    }
    if(x[3]-x[1]==x[4]-x[2]){ //8
        int a1 =  x[1],a2 = x[2],a3 = x[3]-x[1];
        check(a1,a2,a3);
    }
    if(x[2]+x[3]==x[4]){ //9
        int a1 = x[1],a2 = x[2],a3 = x[3]-x[1];
        check(a1,a2,a3);
    }
    if(x[1]+x[3]==x[4]){ //10
        int a1 = x[1],a2 = x[2],a3 = x[3]-x[2];
        check(a1,a2,a3);
    }
    if(x[1]+x[2]==x[4]){ //11
        int a1 = x[1],a2 = x[3]-x[1],a3 = x[2];
        check(a1,a2,a3);
    }
    if(x[2]+x[3]-x[1]==x[4]){ //12
        int a1 = x[1],a2 = x[3]-x[1],a3 = x[2];
        check(a1,a2,a3);
    }
    if(x[2]+x[3]==x[4]){ //13
        int a1 = x[1],a2 = x[3]-x[1],a3 = x[2];
        check(a1,a2,a3);
    }
    if(x[1]+x[2]==x[3]){ //14
        int a1 = x[1],a2 = x[4]-x[2],a3 = x[2];
        check(a1,a2,a3);
    }
    if(x[1]+x[2]==x[3]){ //15
        int a1 = x[1],a2 = x[4]-x[3],a3 = x[2];
        check(a1,a2,a3);
    }
    if(x[1]+x[3]==x[4]){ //16
        int a1 = x[1],a2 = x[4]-x[1]-x[2],a3 = x[2];
        check(a1,a2,a3);
    }
    if(x[2]+x[3]-x[1]*2==x[4]){ //17
        int a1 = x[1],a2 = x[2]-x[1],a3 = x[3]-x[1];
        check(a1,a2,a3);
    }
    if(x[2]+x[3]-x[1]==x[4]){ //18
        int a1 = x[1],a2 = x[2]-x[1],a3 = x[3]-x[1];
        check(a1,a2,a3);
    }
    if(x[1]+x[3]==x[4]){ //19
        int a1 = x[1],a2 = x[2]-x[1],a3 = x[4]-x[2];
    }
    if(x[1]+x[3]==x[4]){ //20
        int a1 = x[1],a2 = x[4]-x[2],a3 = x[2]-x[1];
        check(a1,a2,a3);
    }
    if(x[3]-x[1]==x[4]-x[2]){ //21
        int a1 = x[3]-x[1],a2 = x[1],a3 = x[2];
        check(a1,a2,a3);
    }
    if(x[1]+x[2]==x[4]){ //22
        int a1 = x[3]-x[1],a2 = x[1],a3 = x[2];
        check(a1,a2,a3);
    }
    if(x[2]+x[3]==x[4]){ //23
        int a1 = x[3]-x[1],a2 = x[1],a3 = x[2];
        check(a1,a2,a3);
    }
    if(x[1]+x[2]==x[4]){ //24
        int a1 = x[3]-x[2],a2 = x[1],a3 = x[2];
        check(a1,a2,a3);
    }
    if(x[1]+x[3]==x[4]) { //25
        int a1 = x[3]-x[2],a2 = x[1],a3 = x[2];
        check(a1,a2,a3);
    }
    if(x[1]+x[2]==x[3]){ //26
        int a1 = x[4]-x[3],a2 = x[1],a3 = x[2];
        check(a1,a2,a3);
    }
    if(x[2]+x[4]-x[1]*2==x[3]){ //27
        int a1 = x[2]-x[1],a2 = x[1],a3 = x[4]-x[1];
        check(a1,a2,a3);
    }
    if(x[1]+x[3]==x[4]){ //28
        int a1 = x[2]-x[1],a2 = x[1],a3 = x[4]-x[2];
        check(a1,a2,a3);
    }
    if(x[2]+x[3]-x[1]==x[4]){ //29
        int a1 = x[2]-x[1],a2 = x[1],a3 = x[3]-x[1];
        check(a1,a2,a3);
    }
    if(x[1]+x[2]==x[4]){ //30
        int a1 = x[4]-x[3],a2 = x[1],a3 = x[3]-x[1];
        check(a1,a2,a3);
    }
    if(x[3]+x[4]-x[1]*2==x[2]){ //31
        int a1 = x[3]-x[1],a2 = x[4]-x[1],a3 = x[1];
        check(a1,a2,a3);
    }
    if(x[1]+x[2]==x[4]){ //32
        int a1 = x[3]-x[1],a2 = x[4]-x[3],a3 = x[1];
        check(a1,a2,a3);
    }
    if(x[1]+x[2]==x[4]){ //33
        int a1 = x[4]-x[3],a2 = x[3]-x[1],a3 = x[1];
        check(a1,a2,a3);
    }
    if(x[2]+x[3]-x[1]==x[4]){ //34
        int a1 = x[4]-x[3],a2 = x[3]-x[1],a3 = x[1];
        check(a1,a2,a3);
    }
    if(x[1]+x[2]+x[3]==x[4]*2){ //35
        int a1 = (x[1]+x[2]-x[3])/2,a2 = (x[1]-x[2]+x[3])/2,a3 = (x[2]-x[1]+x[3])/2;
        check(a1,a2,a3);
    }
    sort(tmp+1,tmp+tot+1,cmp); // 排序，用来去重。
    cout<<tmp[1].x<<" "<<tmp[1].y<<" "<<tmp[1].z<<'\n';
    for(int i=2;i<=tot;i++){
        if(tmp[i].x!=tmp[i-1].x||tmp[i].y!=tmp[i-1].y||tmp[i].z!=tmp[i-1].z){  // 去重
            cout<<tmp[i].x<<" "<<tmp[i].y<<" "<<tmp[i].z<<'\n';
        }
    }
    return 0;
}

AC 记录。