【牛客刷题】bfs和dfs （二叉树层序遍历、矩阵最长递增路径、被围绕的区域）
二叉树层序遍历
vector<vector<int> > levelOrder(TreeNode* root) {
// write code here
vector<int> res;
vector<vector<int>> result;
if (root == nullptr) return result;
queue<TreeNode*> que;
que.push(root);
while (!que.empty()) {
int size = que.size();
for (int i = 0; i < size; i++) {
TreeNode* temp = que.front();
que.pop();
res.push_back(temp->val);
if (temp->left) que.push(temp->left);
if (temp->right) que.push(temp->right);
}
result.push_back(res);
res.clear();
}
return result;
}
矩阵最长递增路径
https://www.nowcoder.com/share/jump/9321389651694076681305
BFS 通常是为了找到最短路径，求最长路径最好用DFS！
拓扑排序（增加inDegrees矩阵）+ BFS
int dir[4][2] = {0, 1, 0, -1, 1, 0, -1, 0};
vector<vector<int>> getInDegrees(vector<vector<int> >& grid) {
int m = grid.size();
int n = grid[0].size();
vector<vector<int>> inDegrees(m, vector<int> (n, 0));
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
for (int k = 0; k < 4; k++) {
int newX = i + dir[k][0];
int newY = j + dir[k][1];
if (newX < 0 || newX >= m || newY < 0 || newY >= n) continue;
if (grid[i][j] > grid[newX][newY]) {
inDegrees[i][j]++;
}
}
}
}
return inDegrees;
}
int solve(vector<vector<int> >& matrix) {
// write code here
vector<vector<int>> inDegrees = getInDegrees(matrix);
int maxLen = 0;
queue<pair<int, int>> que;
for (int i = 0; i < matrix.size(); i++) {
for (int j = 0; j < matrix[0].size(); j++) {
if (inDegrees[i][j] == 0) {
que.push({i, j});
}
}
}
while (!que.empty()) {
maxLen++;
int size = que.size();
for (int i = 0; i < size; i++) {//需要处理每层信息时这样写，类似于二叉树的层序遍历
int x = que.front().first;
int y = que.front().second;
que.pop();
for (int k = 0; k < 4; k++) {//遍历方向
int newX = x + dir[k][0];
int newY = y + dir[k][1];
if (newX < 0 || newX >= matrix.size() || newY < 0 ||
newY >= matrix[0].size()) continue;
if (matrix[x][y] < matrix[newX][newY]) {//保证是递增序列
inDegrees[newX][newY]--;//因为已经确保递增了，所以减少newX和newY的一个入度
if (inDegrees[newX][newY] == 0) {//当入度全为0，表示条件全满足，所以可以入队
que.push({newX, newY});
}
}
}
}
}
return maxLen;
}
};
单纯的bfs：
int dir[4][2] = {0, 1, 0, -1, 1, 0, -1, 0};
int bfs(vector<vector<int>>& matrix, vector<vector<bool>>& visited, int x,
int y) {
queue<pair<int, int>> que;
que.push({x, y});
visited[x][y] = true;
int maxLen = 0;
while (!que.empty()) {
maxLen++;
int size = que.size();
for (int i = 0; i < size; i++) {//层处理
int curX = que.front().first;
int curY = que.front().second;
que.pop();
for (int k = 0; k < 4; k++) {//方向处理
int newX = curX + dir[k][0];
int newY = curY + dir[k][1];
if (newX < 0 || newX >= matrix.size() || newY < 0 ||
newY >= matrix[0].size()) continue;
if (!visited[newX][newY] && matrix[curX][curY] < matrix[newX][newY]) {
que.push({newX, newY});
visited[newX][newY] = true;
}
}
}
}
return maxLen;
}
int solve(vector<vector<int> >& matrix) {
// write code here
vector<vector<bool>> visited(matrix.size(), vector<bool>(matrix[0].size(),
false));
int maxLen = 0;
for (int i = 0; i < matrix.size(); i++) {
for (int j = 0; j < matrix[0].size(); j++) {
maxLen = max(maxLen, bfs(matrix, visited, i, j));
}
}
return maxLen;
}
};
dfs+记忆化搜索（memo）：
int dir[4][2] = {0, 1, 1, 0, 0, -1, -1, 0};
int dfs(vector<vector<int>>& matrix, vector<vector<int>>& memo, int x, int y) {
if (memo[x][y] != -1) return memo[x][y];//递归终止条件
int maxLen = 1;
for (int i = 0; i < 4; i++) {//遍历方向
int newX = x + dir[i][0];
int newY = y + dir[i][1];
if (newX < 0 || newX >= matrix.size() || newY < 0 || newY >= matrix[0].size() ||
matrix[newX][newY] <= matrix[x][y]) continue;//满足条件才递归
maxLen = max(maxLen, 1 + dfs(matrix, memo, newX, newY));//表示从(x, y)到(newX, newY)这一步
}
memo[x][y] = maxLen;
return memo[x][y];
}
int solve(vector<vector<int> >& matrix) {
vector<vector<int>> memo(matrix.size(), vector<int>(matrix[0].size(), -1));
int maxLen = 0;
for (int i = 0; i < matrix.size(); i++) {
for (int j = 0; j < matrix[0].size(); j++) {
maxLen = max(maxLen, dfs(matrix, memo, i, j));
}
}
return maxLen;
}
};
被围绕的区域
https://www.nowcoder.com/share/jump/9321389651694087623428
dfs:
int dir[4][2] = {0, 1, 0, -1, 1, 0, -1, 0};
void dfs(vector<vector<char>>& matrix, int x,
int y) {
int m = matrix.size(), n = matrix[0].size();
matrix[x][y] = 'E';
for (int i = 0; i < 4; i++) {
int newX = x + dir[i][0];
int newY = y + dir[i][1];
if (newX < 0 || newX >= m || newY < 0 || newY >= n ||
matrix[newX][newY] != 'O')
continue;//(newX,newY)中超出边界的、不是O的不用管
dfs(matrix, newX, newY);
}
}
vector<vector<char> > surroundedArea(vector<vector<char> >& board) {
// write code here
int m = board.size(), n = board[0].size();
//将连接边界的O全部替换
for (int i = 0; i < m; i++) {
if (board[i][0] == 'O') dfs(board, i, 0);
if (board[i][n - 1] == 'O') dfs(board, i, n - 1);
}
for (int j = 0; j < n; j++) {
if (board[0][j] == 'O') dfs(board, 0, j);
if (board[m - 1][j] == 'O') dfs(board, m - 1, j);
}
//又替换回来
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (board[i][j] == 'E') board[i][j] = 'O';
else board[i][j] = 'X';
}
}
return board;
}
};
bfs:
int dir[4][2] = {0, 1, 0, -1, 1, 0, -1, 0};
void bfs(vector<vector<char>>& matrix, int x, int y) {
int m = matrix.size(), n = matrix[0].size();
queue<pair<int, int>> que;
que.push({x, y});
while (!que.empty()) {
int curX = que.front().first;
int curY = que.front().second;
que.pop();
matrix[curX][curY] = 'E';
for (int i = 0; i < 4; i++) {
int newX = curX + dir[i][0];
int newY = curY + dir[i][1];
if (newX < 0 || newX >= m || newY < 0 || newY >= n ||
matrix[newX][newY] != 'O')
continue;//(newX,newY)中超出边界的、不是O的不用管
que.push({newX, newY});
}
}
}
vector<vector<char> > surroundedArea(vector<vector<char> >& board) {
// write code here
int m = board.size(), n = board[0].size();
for (int i = 0; i < m; i++) {
if (board[i][0] == 'O') bfs(board, i, 0);
if (board[i][n - 1] == 'O') bfs(board, i, n - 1);
}
for (int j = 0; j < n; j++) {
if (board[0][j] == 'O') bfs(board, 0, j);
if (board[m - 1][j] == 'O') bfs(board, m - 1, j);
}
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (board[i][j] == 'E') board[i][j] = 'O';
else board[i][j] = 'X';
}
}
return board;
}
};