1
5 1 3
1 2 3 5 4

#include <bits/stdc++.h>
using namespace std;
#define ll long long int
#define debug(x) cout << #x << ' ' << x << endl;
#define fastio() ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
#define exe(k,n) for(int i=k;i<n;i++)
#define exec(n) for(int i=0;i<n;i++)
#define endl '\n'
#define ss second
#define ff first
#define pb push_back
#define hii cout << "Hi\n";
#define int long long int
const int inf = 1e18;
const int N = 2*1e5+10;
bool is_sorted(vector<int> &v)
{
    for(int i=0;i<(int)v.size() -1;i++)
    {
        if(v[i]>v[i+1])return false;
    }
    return true;
}
signed main() 
{   fastio();       
    int T=1;
    cin >>T;
    while(T--)
    {   
        int n,x,y;
        cin >> n >> x >> y;
        vector<int> v(n);
        exec(n) cin >> v[i];
        int flag=1;
        vector<int> ind;
        for(int i=0;i<n-1;i++)
        {
            if(v[i]>v[i+1])
            {
                flag=0;
                ind.pb(i);
            }
        }
        if(x>y)swap(x,y);
        if(x<=y)
        {
            if(ind.size()==1)
            {
                int a=ind.back();
                if(a)
                {
                    swap(v[a],y);
                    if(is_sorted(v))flag=1;
                    swap(v[a],y);
                }
                swap(v[a],x);
                if(is_sorted(v))flag=1;
                swap(v[a],x);
                if(a<n-1)
                {
                    swap(v[a+1],x);
                    if(is_sorted(v))flag=1;
                    swap(v[a+1],x);
                }
                swap(v[a+1],y);
                if(is_sorted(v))flag=1;
                swap(v[a+1],y);
                //5 2 2 
                //1 2 3 5 4
                if(a)
                {
                    swap(v[a-1],x);
                    swap(v[a],y);
                    if(is_sorted(v))flag=1;
                    swap(v[a-1],x);
                    swap(v[a],y);
                }
                //5 4 4
                //1 2 4 5 3
                if(a<n-1)
                {
                    swap(v[a],x);
                    swap(v[a+1],y);
                    if(is_sorted(v))flag=1;
                    swap(v[a],x);
                    swap(v[a+1],y);
                }
                //5 5 5
                //1 2 5 3 4
                //1 2 5 4 3 
                if(a<n-2)
                {
                    swap(v[a+1],x);
                    swap(v[a+2],y);
                    if(is_sorted(v))flag=1;
                    swap(v[a+1],x);
                    swap(v[a+2],y);                    
                }
            }
            else if(ind.size()==2)
            {
                int a=ind[0];
                int b=ind[1];
                vector<int>temp[4];
                exec(4)temp[i]=v;
                temp[0][a]=x;
                temp[0][b]=y;
                temp[1][a+1]=x;
                temp[1][b]=y;
                temp[2][a]=x;
                temp[2][b+1]=y;
                temp[3][a+1]=x;
                temp[3][b+1]=y;
                exec(4)
                {
                    if(is_sorted(temp[i]))flag=1;
                }
            }
        }
        if(flag) cout << "Yes";
        else cout << "No";
        cout << endl;
    }   

 return 0;   
} 

If you remove an edge, the optimal answer will always be adjacent to the removed edge.

Try something similar to rerooting dp, calculate answer for all the houses using prefix sums.