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krahets
@@ -193,7 +193,7 @@ comments: true
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}
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if (root->val == 7) {
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// 记录解
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vectorPushback(res, root, sizeof(int));
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res[resSize++] = root;
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}
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preOrder(root->left);
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preOrder(root->right);
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@@ -214,7 +214,7 @@ comments: true
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**之所以称之为回溯算法，是因为该算法在搜索解空间时会采用“尝试”与“回退”的策略**。当算法在搜索过程中遇到某个状态无法继续前进或无法得到满足条件的解时，它会撤销上一步的选择，退回到之前的状态，并尝试其他可能的选择。
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对于例题一，访问每个节点都代表一次“尝试”，而越过叶结点或返回父节点的 `return` 则表示“回退”。
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对于例题一，访问每个节点都代表一次“尝试”，而越过叶节点或返回父节点的 `return` 则表示“回退”。
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值得说明的是，**回退并不仅仅包括函数返回**。为解释这一点，我们对例题一稍作拓展。
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@@ -446,26 +446,23 @@ comments: true
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```c title="preorder_traversal_ii_compact.c"
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/* 前序遍历：例题二 */
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void preOrder(TreeNode *root, vector *path, vector *res) {
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void preOrder(TreeNode *root) {
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if (root == NULL) {
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return;
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}
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// 尝试
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vectorPushback(path, root, sizeof(TreeNode));
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path[pathSize++] = root;
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if (root->val == 7) {
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// 记录解
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vector *newPath = newVector();
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for (int i = 0; i < path->size; i++) {
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vectorPushback(newPath, path->data[i], sizeof(int));
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for (int i = 0; i < pathSize; ++i) {
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res[resSize][i] = path[i];
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}
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vectorPushback(res, newPath, sizeof(vector));
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resSize++;
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}
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preOrder(root->left, path, res);
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preOrder(root->right, path, res);
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preOrder(root->left);
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preOrder(root->right);
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// 回退
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vectorPopback(path);
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pathSize--;
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}
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```
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@@ -755,28 +752,24 @@ comments: true
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```c title="preorder_traversal_iii_compact.c"
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/* 前序遍历：例题三 */
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void preOrder(TreeNode *root, vector *path, vector *res) {
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void preOrder(TreeNode *root) {
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// 剪枝
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if (root == NULL || root->val == 3) {
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return;
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}
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// 尝试
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vectorPushback(path, root, sizeof(TreeNode));
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path[pathSize++] = root;
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if (root->val == 7) {
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// 记录解
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vector *newPath = newVector();
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for (int i = 0; i < path->size; i++) {
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vectorPushback(newPath, path->data[i], sizeof(int));
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for (int i = 0; i < pathSize; i++) {
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res[resSize][i] = path[i];
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}
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vectorPushback(res, newPath, sizeof(vector));
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res->depth++;
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resSize++;
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}
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preOrder(root->left, path, res);
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preOrder(root->right, path, res);
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preOrder(root->left);
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preOrder(root->right);
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// 回退
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vectorPopback(path);
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pathSize--;
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}
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```
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@@ -1595,56 +1588,52 @@ comments: true
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```c title="preorder_traversal_iii_template.c"
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/* 判断当前状态是否为解 */
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bool isSolution(vector *state) {
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return state->size != 0 && ((TreeNode *)(state->data[state->size - 1]))->val == 7;
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bool isSolution(void) {
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return pathSize > 0 && path[pathSize - 1]->val == 7;
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}
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/* 记录解 */
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void recordSolution(vector *state, vector *res) {
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vector *newPath = newVector();
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for (int i = 0; i < state->size; i++) {
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vectorPushback(newPath, state->data[i], sizeof(int));
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void recordSolution(void) {
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for (int i = 0; i < pathSize; i++) {
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res[resSize][i] = path[i];
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}
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vectorPushback(res, newPath, sizeof(vector));
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resSize++;
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}
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/* 判断在当前状态下，该选择是否合法 */
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bool isValid(vector *state, TreeNode *choice) {
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bool isValid(TreeNode *choice) {
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return choice != NULL && choice->val != 3;
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}
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/* 更新状态 */
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void makeChoice(vector *state, TreeNode *choice) {
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vectorPushback(state, choice, sizeof(TreeNode));
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void makeChoice(TreeNode *choice) {
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path[pathSize++] = choice;
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}
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/* 恢复状态 */
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void undoChoice(vector *state, TreeNode *choice) {
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vectorPopback(state);
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void undoChoice(void) {
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pathSize--;
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}
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/* 回溯算法：例题三 */
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void backtrack(vector *state, vector *choices, vector *res) {
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void backtrack(TreeNode *choices[2]) {
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// 检查是否为解
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if (isSolution(state)) {
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if (isSolution()) {
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// 记录解
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recordSolution(state, res);
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return;
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recordSolution();
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}
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// 遍历所有选择
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for (int i = 0; i < choices->size; i++) {
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TreeNode *choice = choices->data[i];
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for (int i = 0; i < 2; i++) {
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TreeNode *choice = choices[i];
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// 剪枝：检查选择是否合法
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if (isValid(state, choice)) {
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if (isValid(choice)) {
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// 尝试：做出选择，更新状态
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makeChoice(state, choice);
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makeChoice(choice);
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// 进行下一轮选择
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vector *nextChoices = newVector();
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vectorPushback(nextChoices, choice->left, sizeof(TreeNode));
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vectorPushback(nextChoices, choice->right, sizeof(TreeNode));
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backtrack(state, nextChoices, res);
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TreeNode *nextChoices[2] = {choice->left, choice->right};
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backtrack(nextChoices);
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// 回退：撤销选择，恢复到之前的状态
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undoChoice(state, choice);
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undoChoice();
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}
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}
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}
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@@ -1688,7 +1677,7 @@ comments: true
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| 约束条件 Constraint | 约束条件是问题中限制解的可行性的条件，通常用于剪枝 | 路径中不包含节点 $3$ |
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| 状态 State | 状态表示问题在某一时刻的情况，包括已经做出的选择 | 当前已访问的节点路径，即 `path` 节点列表 |
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| 尝试 Attempt | 尝试是根据可用选择来探索解空间的过程，包括做出选择，更新状态，检查是否为解 | 递归访问左（右）子节点，将节点添加进 `path` ，判断节点的值是否为 $7$ |
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| 回退 Backtracking | 回退指遇到不满足约束条件的状态时，撤销前面做出的选择，回到上一个状态 | 当越过叶结点、结束结点访问、遇到值为 $3$ 的节点时终止搜索，函数返回 |
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| 回退 Backtracking | 回退指遇到不满足约束条件的状态时，撤销前面做出的选择，回到上一个状态 | 当越过叶节点、结束节点访问、遇到值为 $3$ 的节点时终止搜索，函数返回 |
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| 剪枝 Pruning | 剪枝是根据问题特性和约束条件避免无意义的搜索路径的方法，可提高搜索效率 | 当遇到值为 $3$ 的节点时，则终止继续搜索 |
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</div>
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