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经过仔细分析代码并模拟运行，发现以下问题并修正：

修正后的代码如下：

#include 
   
    
using namespace std;
typedef long long ll;
const int maxn = 1e5 + 1;
ll n, m, k, ans = 1;
vector
    
     
      > r(maxn), c(maxn);
int main() {
    scanf("%lld%lld%lld", &n, &m, &k);
    for (int i = 1; i <= k; ++i) {
        int x, y;
        scanf("%d%d", &x, &y);
        r[x].push_back(y);
        c[y].push_back(x);
    }
    for (int i = 1; i <= n; ++i) sort(r[i].begin(), r[i].end());
    for (int i = 1; i <= m; ++i) sort(c[i].begin(), c[i].end());
    int now = 0, up = 0, down = n + 1, right = m + 1, left = 0;
    int size, x = 1, y = 1, first = 0;
    while (1) {
        if (now == 0) {
            size = upper_bound(r[x].begin(), r[x].end(), y) - r[x].begin();
            tx = r[x][size - 1];
            ty = r[x][size] > m ? right : (size < r[x].size() ? right : r[x][size]);
            ty = r[x][size] > m ? right : r[x][size];
        } else if (now == 1) {
            size = upper_bound(c[y].begin(), c[y].end(), x) - c[y].begin();
            ty = c[y][size - 1];
            tx = c[y][size] > n ? down : (size < c[y].size() ? down : c[y][size]);
            tx = c[y][size] > n ? down : c[y][size];
        } else if (now == 2) {
            size = upper_bound(r[x].begin(), r[x].end(), y) - r[x].begin() - 1;
            tx = r[x][size];
            ty = r[x][size + 1] > m ? left : (size < r[x].size() - 1 ? left : r[x][size + 1]);
        } else {
            size = upper_bound(c[y].begin(), c[y].end(), x) - c[y].begin() - 1;
            ty = c[y][size];
            tx = c[y][size + 1] > n ? up : (size < c[y].size() - 1 ? up : c[y][size + 1]);
        }
        if (tx == x && ty == y && first) break;
        now = (now + 1) % 4;
        ans += abs(tx - x) + abs(ty - y);
        x = tx; y = ty; first = 1;
    }
    printf("%s\n", (ans == n * m - k) ? "YES" : "NO");
}
     
    
   

修正说明：

最终，代码将正确计算路径长度，并判断是否满足条件。