图论03

101. 孤岛的总面积

#include <iostream>
#include <vector>
#include <queue>

using namespace std;
int dirt[4][2] = {0, 1, 1, 0, -1, 0, 0, -1};

void bfs(vector<vector<int>> &grid, int x, int y) {
    queue<pair<int, int>> que;
    que.push({x, y});
    grid[x][y] = 0;
    while (!que.empty()) {
        pair<int, int> cur = que.front();
        que.pop();
        int curx = cur.first, cury = cur.second;
        for (int i = 0; i < 4; i++) {
            int nx = curx + dirt[i][0];
            int ny = cury + dirt[i][1];
            if (nx >= grid.size() || nx < 0 || ny >= grid[0].size() || ny < 0) {
                continue;
            }
            if (grid[nx][ny] == 1) {
                    que.push({nx, ny});
                    grid[nx][ny] = 0;
            }
        }
    }


}

int main() {
    int result = 0;
    int n, m;
    cin >> n >> m;
    vector<vector<int>> grid(n, vector<int>(m));
  
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            cin >> grid[i][j];
        }
    }
    for (int i = 0; i < n; i++) {
        if (grid[i][0] == 1)
            bfs(grid, i, 0);
        if (grid[i][m - 1] == 1)
            bfs(grid, i, m - 1);
    }
    for (int i = 0; i < m; i++) {
        if (grid[0][i] == 1)
            bfs(grid, 0, i);
        if (grid[n - 1][i] == 1)
            bfs(grid, n - 1, i);
    }
    for (int i = 1; i < n - 1; i++) {
        for (int j = 1; j < m - 1; j++) {
            if (grid[i][j] == 1) result++;
            }
        }
    
    cout << result;
    return 0;
}

102. 沉没孤岛

#include <iostream>
#include <vector>
#include <queue>

using namespace std;
int dirt[4][2] = {0, 1, 1, 0, -1, 0, 0, -1};

void bfs(vector<vector<int>> &grid, vector<vector<int>> &visited, int x, int y, int flag) {
    queue<pair<int, int>> que;
    que.push({x, y});
    if (flag == 0) visited[x][y] = 1;
    else grid[x][y] = 0;
    while (!que.empty()) {
        pair<int, int> cur = que.front();
        que.pop();
        int curx = cur.first, cury = cur.second;
        for (int i = 0; i < 4; i++) {
            int nx = curx + dirt[i][0];
            int ny = cury + dirt[i][1];
            if (nx >= grid.size() || nx < 0 || ny >= grid[0].size() || ny < 0) {
                continue;
            }
            if (grid[nx][ny] == 1 && !visited[nx][ny]) {
                que.push({nx, ny});
                    if (flag == 0) {
                        visited[nx][ny] = 1;
                    }
                    else {
                         grid[nx][ny] = 0;
                    }
                    
            }
        }
    }


}

int main() {
    int result = 0;
    int n, m;
    cin >> n >> m;
    vector<vector<int>> grid(n, vector<int>(m));
    vector<vector<int>> visited(n, vector<int>(m, 0));
  
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            cin >> grid[i][j];
        }
    }
    for (int i = 0; i < n; i++) {
        if (grid[i][0] == 1)
            bfs(grid, visited, i, 0, 0);
        if (grid[i][m - 1] == 1)
            bfs(grid, visited, i, m - 1, 0);
    }
    for (int i = 0; i < m; i++) {
        if (grid[0][i] == 1)
            bfs(grid, visited, 0, i, 0);
        if (grid[n - 1][i] == 1)
            bfs(grid, visited, n - 1, i, 0);
    }
    for (int i = 1; i < n - 1; i++) {
        for (int j = 1; j < m - 1; j++) {
            if(grid[i][j] == 1 && !visited[i][j]) {
                bfs(grid, visited, i, j, 1);

            }
        }
    }
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            cout << grid[i][j] << " ";
        }
        cout << '\n';
    }
    return 0;
}

103. 水流问题

#include <iostream>
#include <vector>

using namespace std;
int dir[4][2] = {1, 0, 0, 1, -1, 0, 0, -1};

void dfs(vector<vector<int>> &grid, vector<vector<int>> &visit, int x, int y) {
    visit[x][y] = 1;
    for (int i = 0; i < 4; i++) {
        int nx = x + dir[i][0];
        int ny = y + dir[i][1];
        if (nx < 0 || ny < 0 || nx >= grid.size() || ny >= grid[0].size()) {
            continue;
        }
        if (grid[nx][ny] >= grid[x][y] && !visit[nx][ny])
            dfs(grid, visit, nx, ny);
    }
}

int main() {
    int n, m;
    cin >> n >> m;
    vector<vector<int>> grid(n, vector<int>(m, 0));
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            cin >> grid[i][j];
        }
    }
    vector<vector<int>> firstVisit(n, vector<int>(m, 0));
    vector<vector<int>> secondVisit(n, vector<int>(m, 0));
    for (int i = 0; i < n; i++) {
        dfs(grid, firstVisit, i, 0);
        dfs(grid, secondVisit, i , m - 1);
    }
    for (int j = 0; j < m; j++) {
        dfs(grid, firstVisit, 0, j);
        dfs(grid, secondVisit, n - 1, j);
    }
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
           if (firstVisit[i][j] == 1 && secondVisit[i][j] == 1) 
                cout << i << " " << j  << "\n";
        }

    }

    return 0;
}

104. 建造最大岛屿

#include <iostream>
#include <vector>
#include <unordered_map>
#include <unordered_set>

using namespace std;

int dir[4][2] = {1, 0, 0, 1, -1, 0, 0, -1};
int result = 0;
int count = 0;
void dfs(vector<vector<int>> &grid, vector<vector<int>> &visit, int x, int y, int mark) {
    for (int i = 0; i < 4; i++) {
        int nx = x + dir[i][0];
        int ny = y + dir[i][1];
        if (nx < 0 || ny < 0 || nx >= grid.size() || ny >= grid[0].size()) {
            continue;
        }
        if (grid[nx][ny] == 1 && !visit[nx][ny]) {
            count++;
            visit[nx][ny] = 1;
            grid[nx][ny] = mark;
            dfs(grid, visit, nx, ny, mark);
        }
    }
}

int main() {
    int n, m;
    cin >> n >> m;
    vector<vector<int>> grid(n, vector<int>(m, 0));
    vector<vector<int>> visit(n, vector<int>(m, 0));
    unordered_map<int, int> map;
    int mark = 2;
    bool isAllGrid = true;
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            cin >> grid[i][j];
        }
    }
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            if (grid[i][j] == 0) isAllGrid = false;
            if (grid[i][j] == 1 && !visit[i][j]) {
                count++;
                visit[i][j] = 1;
                grid[i][j] = mark;
                dfs(grid, visit, i, j,   mark);
                map[mark] = count;

                mark++;
                count = 0;
            }
             
        }
    }
    if (isAllGrid) {
        cout << n * m << endl; // 如果都是陆地，返回全面积
        return 0; // 结束程序
    }
    unordered_set<int> visitedGrid;
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            int scount = 1; // 记录连接之后的岛屿数量
            visitedGrid.clear(); // 每次使用时，清空
            if (grid[i][j] == 0) {
                for (int k = 0; k < 4; k++) {
                    int kx = i + dir[k][0];
                    int ky = j + dir[k][1];
                    if (kx < 0 || ky < 0 || kx >= grid.size() || ky >= grid[0].size()) {
                        continue;
                    }
                    if (visitedGrid.count(grid[kx][ky]))            continue; // 添加过的岛屿不要重复添加
                    scount += map[grid[kx][ky]];
                    // cout << grid[kx][ky] << " " << i << " " << j << " " << scount << ' ';
                    visitedGrid.insert(grid[kx][ky]); // 标记该岛屿已经添加过             
                }
            }
            result = max(result, scount);
        }
    }
    cout << result;
    return 0;
}