一个一个模拟：超时

// 模拟
#include <iostream>

using namespace std;
typedef long long ll;
int x, y;
int a;
int b;//起始位置

int isFit(int xx, int yy){
    if(xx == a){//   纵向
        if(x != a)  return -1;
        int sm = max(yy, b);
        int xm = yy + b - sm;
        if(y >= xm && y <= sm){
            return abs(y-b);
        }else{
            return -1;
        }
    }else if(yy == b){ //横向
        if(y != b)  return -1;
        int yb = max(a, xx);
        int zb = a + xx - yb; 
        if(x >= zb && x <= yb){
            return abs(x-a);
        }else{
            return -1;
        }
    }else{
        return -1;
    }
}

int dy[4] = {0, 1, 0, -1};
int dx[4] = {-1, 0, 1, 0};//左 上 右 下
int main(){
    cin >> x >> y;
    ll sum = 0;

    for(int i = 0;  ; i ++ ){ // 走的次数  
    //从第0 次开始 ，走的步数（i/2 + 1）,方向i%4
        int xx = a + dx[i%4]*(i/2+1);
        int yy = b + dy[i%4]*(i/2+1);
        int res = isFit(xx, yy);
        if(res != -1){  //在这条直线上面
            sum += res;
            break;
        }else{
            sum += i/2+1;
            a = xx;
            b = yy;
        }
    }
    cout << sum << endl;
    return 0;
}

找规律

#include <iostream>

using namespace std;
typedef long long ll;
int main(){
    int x, y;
    cin >> x >> y;
    //判断在哪个方向上的边
    ll sum = 0;
    if(y >= abs(x)){  //上
        //端点   y >= 0
        int n = y;
        sum = ((ll)2*n*(2*n-1)) + x + n;
    }else if(x >= abs(y)){  //左
        int n = x;
        sum = ((ll)4*n*n) + n - y;
    }else if(-y+1 >= -x){ //下
        int n = -y;
        sum = (ll)2*n*(2*n+1) + n - x;
    }else{
        //x <= 0
        int n = abs(x);
        sum = (ll)(2*n-1)*(2*n-1) + y + n - 1;
    }
    cout << sum << endl;
    return 0;
}