赛时交了三发，写了两发 DFS 一发 BFS，赛后调了一会没调出来

BFS 直接改造 DFS 而成，$\color{green}\texttt{AC 38}\color{red}\texttt{ WA 19}$

#include <bits/stdc++.h>
#define endl '\n'
typedef long long ll;
using namespace std;

const int N = 1e3 + 10;
char graph[N][N];
bool vis[N][N];
int sblockx = 0, sblocky = 0;
int ANS = 0x7fffffff;
int n, m;
queue<pair<pair<int, int>, pair<bool, int>>> q;

void bfs()
{
    q.push({{sblockx, sblocky}, {0, 0}});
    q.push({{sblockx, sblocky}, {1, 0}});
    while (!q.empty())
    {
        int i = q.front().first.first;
        int j = q.front().first.second;
        bool isodd = q.front().second.first;
        int ans = q.front().second.second;
        q.pop();   
        if (graph[i][j] == 'G')
        {
            ANS = min(ANS, ans);
            continue;
        }
        if (isodd)
        {
            isodd = !isodd;
            if (!vis[i][j + 1] && 1 <= j + 1 && j + 1 <= m)
            {
                vis[i][j + 1] = true;
                q.push({{i, j + 1}, {isodd, ans + 1}});
            }
            if (!vis[i][j - 1] && 1 <= j - 1 && j - 1 <= m)
            {
                vis[i][j - 1] = true;
                q.push({{i, j - 1}, {isodd, ans + 1}});
            }
        }
        else
        {
            isodd = !isodd;
            if (!vis[i + 1][j] && 1 <= i + 1 && i + 1 <= n)
            {
                vis[i + 1][j] = true;
                q.push({{i + 1, j}, {isodd, ans + 1}});
            }
            if (!vis[i - 1][j] && 1 <= i - 1 && i - 1 <= n)
            {
                vis[i - 1][j] = true;
                q.push({{i - 1, j}, {isodd, ans + 1}});
            }
        }
    }
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    cin >> n >> m;
    for (int i = 1; i <= n; i++)
    {
        for (int j = 1; j <= m; j++)
        {
            cin >> graph[i][j];
            if (graph[i][j] == '#')
            {
                vis[i][j] = true;
            }
            if (graph[i][j] == 'S')
            {
                sblockx = i;
                sblocky = j;
            }
        }
    }
    
    bfs();

    cout << (ANS == 0x7fffffff ? -1 : ANS) << endl;
    return 0;
}