BFS

#include <iostream>
#include <queue>
using namespace std;
const int N = 1010;
int graph[N][N];
bool st[N][N];
typedef pair<int, int> pii;
int n;
int dic[8][2] = {
    {-1, -1}, {-1, 0}, {-1, 1}, {0, -1},
    {0, 1}, {1, -1}, {1, 0}, {1, 1}
};
void bfs(int x, int y, bool& is_peak, bool& is_valley){
    queue<pii> qu;
    qu.push({x, y});
    st[x][y] = true;
    while(!qu.empty()){
        pii now = qu.front();
        qu.pop();
        for(int i = 0; i < 8; i ++ ){
            int xx = now.first + dic[i][0];
            int yy = now.second + dic[i][1];
            if(xx < 0 || xx >= n || yy < 0 || yy >= n)  continue;
            if(graph[xx][yy] > graph[now.first][now.second])    is_peak = false;
            if(graph[xx][yy] < graph[now.first][now.second])    is_valley = false;
            if(graph[xx][yy] == graph[now.first][now.second] && !st[xx][yy]){
                qu.push({xx, yy});
                st[xx][yy] = true;
            }
        }
    }
}
int main(){
    cin >> n;
    for(int i = 0; i < n; i ++ ){
        for(int j = 0; j < n; j ++ ){
            cin >> graph[i][j];
        }
    }
    int peak, valley;
    peak = valley = 0;
    for(int i = 0; i < n; i ++ ){
        for(int j = 0; j < n; j ++ ){
            if(st[i][j])    continue;
            bool is_peak, is_valley;
            is_peak = is_valley = true;
            bfs(i, j, is_peak, is_valley);
            if(is_peak) peak ++ ;
            if(is_valley)   valley ++ ;
        }
    }
    cout << peak << " " << valley << endl;
    return 0;
}

DFS

#include <iostream>
using namespace std;
const int N = 1E3 + 10;
int graph[N][N];
bool vis[N][N];
int n;
bool is_peak, is_valley;
int dx[8] = {-1, -1, 0, 1, 1, 1, 0, -1};
int dy[8] = {0, -1, -1, -1, 0, 1, 1, 1};
void read(){
    cin >> n;
    for(int i = 0; i < n; i ++ ){
        for(int j = 0; j < n; j ++ )    cin >> graph[i][j];
    }
}
void dfs(int x, int y){
    for(int i = 0; i < 8; i ++ ){
        int xx = x + dx[i], yy = y + dy[i];
        if(xx < 0 || xx >= n || yy < 0 || yy >= n)  continue;
        if(graph[xx][yy] > graph[x][y]) is_peak = false;
        else if(graph[xx][yy] < graph[x][y])    is_valley = false;
        else{
            if(vis[xx][yy]) continue;
            vis[xx][yy] = true;
            dfs(xx, yy);
        }
    }
}
int main(){
    read();
    int peak = 0, valley = 0;
    for(int i = 0; i < n; i ++ ){
        for(int j = 0; j < n; j ++ ){
            if(vis[i][j])   continue;
            is_peak = true, is_valley = true;
            vis[i][j] = true;
            dfs(i, j);
            peak += is_peak;
            valley += is_valley;
        }
    }
    cout << peak << ' ' << valley << endl;
    return 0;
}