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notes/Leetcode 题解.md
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@ -1237,9 +1237,9 @@ private int getShortestPath(List<Integer>[] graphic, int start, int end) {
<div align="center"> <img src="../pics//f7f7e3e5-7dd4-4173-9999-576b9e2ac0a2.png"/> </div><br> <div align="center"> <img src="../pics//f7f7e3e5-7dd4-4173-9999-576b9e2ac0a2.png"/> </div><br>
广度优先搜索一层一层遍历，每一层得到的所有新节点，要用队列先存储起来以备下一层遍历的时候再遍历。 广度优先搜索一层一层遍历，每一层得到的所有新节点，要用队列存储起来以备下一层遍历的时候再遍历。
而深度优先搜索在得到到一个新节点时立马对新节点进行遍历：从节点 0 出发开始遍历，得到到新节点 6 时，立马对新节点 6 进行遍历，得到新节点 4；如此反复以这种方式遍历新节点，直到没有新节点了，此时返回。返回到根节点 0 的情况是，继续对根节点 0 进行遍历，得到新节点 2，然后继续以上步骤。 而深度优先搜索在得到一个新节点时立马对新节点进行遍历：从节点 0 出发开始遍历，得到到新节点 6 时，立马对新节点 6 进行遍历，得到新节点 4；如此反复以这种方式遍历新节点，直到没有新节点了，此时返回。返回到根节点 0 的情况是，继续对根节点 0 进行遍历，得到新节点 2，然后继续以上步骤。
从一个节点出发，使用 DFS 对一个图进行遍历时，能够遍历到的节点都是从初始节点可达的，DFS 常用来求解这种 **可达性** 问题。 从一个节点出发，使用 DFS 对一个图进行遍历时，能够遍历到的节点都是从初始节点可达的，DFS 常用来求解这种 **可达性** 问题。
@ -1268,29 +1268,29 @@ private int m, n;
private int[][] direction = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}}; private int[][] direction = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
public int maxAreaOfIsland(int[][] grid) { public int maxAreaOfIsland(int[][] grid) {
if (grid == null || grid.length == 0) { if (grid == null || grid.length == 0)
return 0; return 0;
}
m = grid.length; m = grid.length;
n = grid[0].length; n = grid[0].length;
int maxArea = 0; int maxArea = 0;
for (int i = 0; i < m; i++) { for (int i = 0; i < m; i++)
for (int j = 0; j < n; j++) { for (int j = 0; j < n; j++)
maxArea = Math.max(maxArea, dfs(grid, i, j)); maxArea = Math.max(maxArea, dfs(grid, i, j));
}
}
return maxArea; return maxArea;
} }
private int dfs(int[][] grid, int r, int c) { private int dfs(int[][] grid, int r, int c) {
if (r < 0 || r >= m || c < 0 || c >= n || grid[r][c] == 0) { if (r < 0 || r >= m || c < 0 || c >= n || grid[r][c] == 0)
return 0; return 0;
}
grid[r][c] = 0; grid[r][c] = 0;
int area = 1; int area = 1;
for (int[] d : direction) { for (int[] d : direction)
area += dfs(grid, r + d[0], c + d[1]); area += dfs(grid, r + d[0], c + d[1]);
}
return area; return area;
} }
``` ```
@ -1300,11 +1300,13 @@ private int dfs(int[][] grid, int r, int c) {
[200. Number of Islands (Medium)](https://leetcode.com/problems/number-of-islands/description/) [200. Number of Islands (Medium)](https://leetcode.com/problems/number-of-islands/description/)
```html ```html
11110 Input:
11010
11000 11000
00000 11000
Answer: 1 00100
00011
Output: 3
``` ```
可以将矩阵表示看成一张有向图。 可以将矩阵表示看成一张有向图。
@ -1314,31 +1316,29 @@ private int m, n;
private int[][] direction = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}}; private int[][] direction = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
public int numIslands(char[][] grid) { public int numIslands(char[][] grid) {
if (grid == null || grid.length == 0) { if (grid == null || grid.length == 0)
return 0; return 0;
}
m = grid.length; m = grid.length;
n = grid[0].length; n = grid[0].length;
int islandsNum = 0; int islandsNum = 0;
for (int i = 0; i < m; i++) { for (int i = 0; i < m; i++)
for (int j = 0; j < n; j++) { for (int j = 0; j < n; j++)
if (grid[i][j] != '0') { if (grid[i][j] != '0') {
dfs(grid, i, j); dfs(grid, i, j);
islandsNum++; islandsNum++;
} }
}
}
return islandsNum; return islandsNum;
} }
private void dfs(char[][] grid, int i, int j) { private void dfs(char[][] grid, int i, int j) {
if (i < 0 || i >= m || j < 0 || j >= n || grid[i][j] == '0') { if (i < 0 || i >= m || j < 0 || j >= n || grid[i][j] == '0')
return; return;
}
grid[i][j] = '0'; grid[i][j] = '0';
for (int[] d : direction) { for (int[] d : direction)
dfs(grid, i + d[0], j + d[1]); dfs(grid, i + d[0], j + d[1]);
}
} }
``` ```
@ -1365,23 +1365,20 @@ public int findCircleNum(int[][] M) {
n = M.length; n = M.length;
int circleNum = 0; int circleNum = 0;
boolean[] hasVisited = new boolean[n]; boolean[] hasVisited = new boolean[n];
for (int i = 0; i < n; i++) { for (int i = 0; i < n; i++)
if (!hasVisited[i]) { if (!hasVisited[i]) {
dfs(M, i, hasVisited); dfs(M, i, hasVisited);
circleNum++; circleNum++;
} }
}
return circleNum; return circleNum;
} }
private void dfs(int[][] M, int i, boolean[] hasVisited) { private void dfs(int[][] M, int i, boolean[] hasVisited) {
hasVisited[i] = true; hasVisited[i] = true;
for (int k = 0; k < n; k++) { for (int k = 0; k < n; k++)
if (M[i][k] == 1 && !hasVisited[k]) { if (M[i][k] == 1 && !hasVisited[k])
dfs(M, k, hasVisited); dfs(M, k, hasVisited);
}
}
} }
``` ```
@ -1403,7 +1400,7 @@ X X X X
X O X X X O X X
``` ```
题目描述：使得被 'X' 的 'O' 转换为 'X'。 题目描述：使得被 'X' 包围的 'O' 转换为 'X'。
先填充最外侧，剩下的就是里侧了。 先填充最外侧，剩下的就是里侧了。
@ -1412,9 +1409,12 @@ private int[][] direction = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
private int m, n; private int m, n;
public void solve(char[][] board) { public void solve(char[][] board) {
if (board == null || board.length == 0) return; if (board == null || board.length == 0)
return;
m = board.length; m = board.length;
n = board[0].length; n = board[0].length;
for (int i = 0; i < m; i++) { for (int i = 0; i < m; i++) {
dfs(board, i, 0); dfs(board, i, 0);
dfs(board, i, n - 1); dfs(board, i, n - 1);
@ -1423,24 +1423,27 @@ public void solve(char[][] board) {
dfs(board, 0, i); dfs(board, 0, i);
dfs(board, m - 1, i); dfs(board, m - 1, i);
} }
for (int i = 0; i < m; i++) {
for (int i = 0; i < m; i++)
for (int j = 0; j < n; j++) { for (int j = 0; j < n; j++) {
if (board[i][j] == 'T') board[i][j] = 'O'; if (board[i][j] == 'T')
else if (board[i][j] == 'O') board[i][j] = 'X'; board[i][j] = 'O';
} else if (board[i][j] == 'O')
board[i][j] = 'X';
} }
} }
private void dfs(char[][] board, int r, int c) { private void dfs(char[][] board, int r, int c) {
if (r < 0 || r >= m || c < 0 || c >= n || board[r][c] != 'O') return; if (r < 0 || r >= m || c < 0 || c >= n || board[r][c] != 'O')
return;
board[r][c] = 'T'; board[r][c] = 'T';
for (int[] d : direction) { for (int[] d : direction)
dfs(board, r + d[0], c + d[1]); dfs(board, r + d[0], c + d[1]);
}
} }
``` ```
**从两个方向都能到达的区域** **能到达的太平洋和大西洋的区域**
[417. Pacific Atlantic Water Flow (Medium)](https://leetcode.com/problems/pacific-atlantic-water-flow/description/) [417. Pacific Atlantic Water Flow (Medium)](https://leetcode.com/problems/pacific-atlantic-water-flow/description/)
@ -1468,12 +1471,15 @@ private int[][] direction = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
public List<int[]> pacificAtlantic(int[][] matrix) { public List<int[]> pacificAtlantic(int[][] matrix) {
List<int[]> ret = new ArrayList<>(); List<int[]> ret = new ArrayList<>();
if (matrix == null || matrix.length == 0) return ret; if (matrix == null || matrix.length == 0)
return ret;
m = matrix.length; m = matrix.length;
n = matrix[0].length; n = matrix[0].length;
this.matrix = matrix; this.matrix = matrix;
boolean[][] canReachP = new boolean[m][n]; boolean[][] canReachP = new boolean[m][n];
boolean[][] canReachA = new boolean[m][n]; boolean[][] canReachA = new boolean[m][n];
for (int i = 0; i < m; i++) { for (int i = 0; i < m; i++) {
dfs(i, 0, canReachP); dfs(i, 0, canReachP);
dfs(i, n - 1, canReachA); dfs(i, n - 1, canReachA);
@ -1482,24 +1488,25 @@ public List<int[]> pacificAtlantic(int[][] matrix) {
dfs(0, i, canReachP); dfs(0, i, canReachP);
dfs(m - 1, i, canReachA); dfs(m - 1, i, canReachA);
} }
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) { for (int i = 0; i < m; i++)
if (canReachP[i][j] && canReachA[i][j]) { for (int j = 0; j < n; j++)
if (canReachP[i][j] && canReachA[i][j])
ret.add(new int[]{i, j}); ret.add(new int[]{i, j});
}
}
}
return ret; return ret;
} }
private void dfs(int r, int c, boolean[][] canReach) { private void dfs(int r, int c, boolean[][] canReach) {
if (canReach[r][c]) return; if (canReach[r][c])
return;
canReach[r][c] = true; canReach[r][c] = true;
for (int[] d : direction) { for (int[] d : direction) {
int nextR = d[0] + r; int nextR = d[0] + r;
int nextC = d[1] + c; int nextC = d[1] + c;
if (nextR < 0 || nextR >= m || nextC < 0 || nextC >= n if (nextR < 0 || nextR >= m || nextC < 0 || nextC >= n || matrix[r][c] > matrix[nextR][nextC])
|| matrix[r][c] > matrix[nextR][nextC]) continue; continue;
dfs(nextR, nextC, canReach); dfs(nextR, nextC, canReach);
} }
} }
@ -1533,7 +1540,8 @@ private static final String[] KEYS = {"", "", "abc", "def", "ghi", "jkl", "mno",
public List<String> letterCombinations(String digits) { public List<String> letterCombinations(String digits) {
List<String> ret = new ArrayList<>(); List<String> ret = new ArrayList<>();
if (digits == null || digits.length() == 0) return ret; if (digits == null || digits.length() == 0)
return ret;
combination(new StringBuilder(), digits, ret); combination(new StringBuilder(), digits, ret);
return ret; return ret;
} }
@ -1571,16 +1579,17 @@ public List<String> restoreIpAddresses(String s) {
private void doRestore(int k, StringBuilder path, String s, List<String> addresses) { private void doRestore(int k, StringBuilder path, String s, List<String> addresses) {
if (k == 4 || s.length() == 0) { if (k == 4 || s.length() == 0) {
if (k == 4 && s.length() == 0) { if (k == 4 && s.length() == 0)
addresses.add(path.toString()); addresses.add(path.toString());
}
return; return;
} }
for (int i = 0; i < s.length() && i <= 2; i++) { for (int i = 0; i < s.length() && i <= 2; i++) {
if (i != 0 && s.charAt(0) == '0') break; if (i != 0 && s.charAt(0) == '0')
break;
String part = s.substring(0, i + 1); String part = s.substring(0, i + 1);
if (Integer.valueOf(part) <= 255) { if (Integer.valueOf(part) <= 255) {
if (path.length() != 0) part = "." + part; if (path.length() != 0)
part = "." + part;
path.append(part); path.append(part);
doRestore(k + 1, path, s.substring(i + 1), addresses); doRestore(k + 1, path, s.substring(i + 1), addresses);
path.delete(path.length() - part.length(), path.length()); path.delete(path.length() - part.length(), path.length());
@ -1612,33 +1621,36 @@ private int m;
private int n; private int n;
public boolean exist(char[][] board, String word) { public boolean exist(char[][] board, String word) {
if (word == null || word.length() == 0) return true; if (word == null || word.length() == 0)
if (board == null || board.length == 0 || board[0].length == 0) return false; return true;
if (board == null || board.length == 0 || board[0].length == 0)
return false;
m = board.length; m = board.length;
n = board[0].length; n = board[0].length;
boolean[][] visited = new boolean[m][n]; boolean[][] visited = new boolean[m][n];
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) { for (int i = 0; i < m; i++)
for (int j = 0; j < n; j++)
if (backtracking(board, visited, word, 0, i, j)) return true; if (backtracking(board, visited, word, 0, i, j)) return true;
}
}
return false; return false;
} }
private boolean backtracking(char[][] board, boolean[][] visited, String word, int start, int r, int c) { private boolean backtracking(char[][] board, boolean[][] visited, String word, int start, int r, int c) {
if (start == word.length()) { if (start == word.length())
return true; return true;
} if (r < 0 || r >= m || c < 0 || c >= n || board[r][c] != word.charAt(start) || visited[r][c])
if (r < 0 || r >= m || c < 0 || c >= n || board[r][c] != word.charAt(start) || visited[r][c]) {
return false; return false;
}
visited[r][c] = true; visited[r][c] = true;
for (int[] d : direction) {
if (backtracking(board, visited, word, start + 1, r + d[0], c + d[1])) { for (int[] d : direction)
if (backtracking(board, visited, word, start + 1, r + d[0], c + d[1]))
return true; return true;
}
}
visited[r][c] = false; visited[r][c] = false;
return false; return false;
} }
``` ```
@ -1662,18 +1674,20 @@ private boolean backtracking(char[][] board, boolean[][] visited, String word, i
```java ```java
public List<String> binaryTreePaths(TreeNode root) { public List<String> binaryTreePaths(TreeNode root) {
List<String> paths = new ArrayList(); List<String> paths = new ArrayList();
if (root == null) return paths; if (root == null)
return paths;
List<Integer> values = new ArrayList<>(); List<Integer> values = new ArrayList<>();
backtracking(root, values, paths); backtracking(root, values, paths);
return paths; return paths;
} }
private void backtracking(TreeNode node, List<Integer> values, List<String> paths) { private void backtracking(TreeNode node, List<Integer> values, List<String> paths) {
if (node == null) return; if (node == null)
return;
values.add(node.val); values.add(node.val);
if (isLeaf(node)) { if (isLeaf(node))
paths.add(buildPath(values)); paths.add(buildPath(values));
} else { else {
backtracking(node.left, values, paths); backtracking(node.left, values, paths);
backtracking(node.right, values, paths); backtracking(node.right, values, paths);
} }
@ -1688,10 +1702,9 @@ private String buildPath(List<Integer> values) {
StringBuilder str = new StringBuilder(); StringBuilder str = new StringBuilder();
for (int i = 0; i < values.size(); i++) { for (int i = 0; i < values.size(); i++) {
str.append(values.get(i)); str.append(values.get(i));
if (i != values.size() - 1) { if (i != values.size() - 1)
str.append("->"); str.append("->");
} }
}
return str.toString(); return str.toString();
} }
``` ```
@ -1727,7 +1740,8 @@ private void backtracking(List<Integer> permuteList, boolean[] visited, int[] nu
return; return;
} }
for (int i = 0; i < visited.length; i++) { for (int i = 0; i < visited.length; i++) {
if (visited[i]) continue; if (visited[i])
continue;
visited[i] = true; visited[i] = true;
permuteList.add(nums[i]); permuteList.add(nums[i]);
backtracking(permuteList, visited, nums, ret); backtracking(permuteList, visited, nums, ret);
@ -1767,8 +1781,10 @@ private void backtracking(List<Integer> permuteList, boolean[] visited, int[] nu
} }
for (int i = 0; i < visited.length; i++) { for (int i = 0; i < visited.length; i++) {
if (i != 0 && nums[i] == nums[i - 1] && !visited[i - 1]) continue; // 防止重复 if (i != 0 && nums[i] == nums[i - 1] && !visited[i - 1])
if (visited[i]) continue; continue; // 防止重复
if (visited[i])
continue;
visited[i] = true; visited[i] = true;
permuteList.add(nums[i]); permuteList.add(nums[i]);
backtracking(permuteList, visited, nums, ret); backtracking(permuteList, visited, nums, ret);
@ -1827,15 +1843,13 @@ A solution set is:
``` ```
```java ```java
private List<List<Integer>> ret; public List<List<Integer>> combinationSum(int[] candidates, int target) {
List<List<Integer>> ret = new ArrayList<>();
public List<List<Integer>> combinationSum(int[] candidates, int target) { doCombination(candidates, target, 0, new ArrayList<>(), ret);
ret = new ArrayList<>();
doCombination(candidates, target, 0, new ArrayList<>());
return ret; return ret;
} }
private void doCombination(int[] candidates, int target, int start, List<Integer> list) { private void doCombination(int[] candidates, int target, int start, List<Integer> list, List<List<Integer>> ret) {
if (target == 0) { if (target == 0) {
ret.add(new ArrayList<>(list)); ret.add(new ArrayList<>(list));
return; return;
@ -1843,11 +1857,11 @@ A solution set is:
for (int i = start; i < candidates.length; i++) { for (int i = start; i < candidates.length; i++) {
if (candidates[i] <= target) { if (candidates[i] <= target) {
list.add(candidates[i]); list.add(candidates[i]);
doCombination(candidates, target - candidates[i], i, list); doCombination(candidates, target - candidates[i], i, list, ret);
list.remove(list.size() - 1); list.remove(list.size() - 1);
} }
} }
} }
``` ```
**含有相同元素的求组合求和** **含有相同元素的求组合求和**
@ -1866,26 +1880,25 @@ A solution set is:
``` ```
```java ```java
private List<List<Integer>> ret;
public List<List<Integer>> combinationSum2(int[] candidates, int target) { public List<List<Integer>> combinationSum2(int[] candidates, int target) {
ret = new ArrayList<>(); List<List<Integer>> ret = new ArrayList<>();
Arrays.sort(candidates); Arrays.sort(candidates);
doCombination(candidates, target, 0, new ArrayList<>(), new boolean[candidates.length]); doCombination(candidates, target, 0, new ArrayList<>(), new boolean[candidates.length], ret);
return ret; return ret;
} }
private void doCombination(int[] candidates, int target, int start, List<Integer> list, boolean[] visited) { private void doCombination(int[] candidates, int target, int start, List<Integer> list, boolean[] visited, List<List<Integer>> ret) {
if (target == 0) { if (target == 0) {
ret.add(new ArrayList<>(list)); ret.add(new ArrayList<>(list));
return; return;
} }
for (int i = start; i < candidates.length; i++) { for (int i = start; i < candidates.length; i++) {
if (i != 0 && candidates[i] == candidates[i - 1] && !visited[i - 1]) continue; if (i != 0 && candidates[i] == candidates[i - 1] && !visited[i - 1])
continue;
if (candidates[i] <= target) { if (candidates[i] <= target) {
list.add(candidates[i]); list.add(candidates[i]);
visited[i] = true; visited[i] = true;
doCombination(candidates, target - candidates[i], i + 1, list, visited); doCombination(candidates, target - candidates[i], i + 1, list, visited, ret);
visited[i] = false; visited[i] = false;
list.remove(list.size() - 1); list.remove(list.size() - 1);
} }
@ -1905,17 +1918,13 @@ Output:
[[1,2,6], [1,3,5], [2,3,4]] [[1,2,6], [1,3,5], [2,3,4]]
``` ```
题目描述：从 1-9 数字中选出 k 个数，使得它们的和为 n。 题目描述：从 1-9 数字中选出 k 个数不重复的数，使得它们的和为 n。
```java ```java
public List<List<Integer>> combinationSum3(int k, int n) { public List<List<Integer>> combinationSum3(int k, int n) {
List<List<Integer>> ret = new ArrayList<>(); List<List<Integer>> ret = new ArrayList<>();
List<Integer> path = new ArrayList<>(); List<Integer> path = new ArrayList<>();
for (int i = 1; i <= 9; i++) { backtracking(k, n, path, 1, ret);
path.add(i);
backtracking(k - 1, n - i, path, i, ret);
path.remove(0);
}
return ret; return ret;
} }
@ -1924,10 +1933,11 @@ private void backtracking(int k, int n, List<Integer> path, int start, List<List
ret.add(new ArrayList<>(path)); ret.add(new ArrayList<>(path));
return; return;
} }
if (k == 0 || n == 0) return; if (k == 0 || n == 0)
for (int i = start + 1; i <= 9; i++) { // 只能访问下一个元素，防止遍历的结果重复 return;
for (int i = start; i <= 9; i++) {
path.add(i); path.add(i);
backtracking(k - 1, n - i, path, i, ret); backtracking(k - 1, n - i, path, i + 1, ret);
path.remove(path.size() - 1); path.remove(path.size() - 1);
} }
} }
@ -1946,9 +1956,8 @@ private List<Integer> subsetList;
public List<List<Integer>> subsets(int[] nums) { public List<List<Integer>> subsets(int[] nums) {
ret = new ArrayList<>(); ret = new ArrayList<>();
subsetList = new ArrayList<>(); subsetList = new ArrayList<>();
for (int i = 0; i <= nums.length; i++) { // 不同的子集大小 for (int i = 0; i <= nums.length; i++) // 不同的子集大小
backtracking(0, i, nums); backtracking(0, i, nums);
}
return ret; return ret;
} }
@ -1957,7 +1966,6 @@ private void backtracking(int startIdx, int size, int[] nums) {
ret.add(new ArrayList(subsetList)); ret.add(new ArrayList(subsetList));
return; return;
} }
for (int i = startIdx; i < nums.length; i++) { for (int i = startIdx; i < nums.length; i++) {
subsetList.add(nums[i]); subsetList.add(nums[i]);
backtracking(i + 1, size, nums); backtracking(i + 1, size, nums);
@ -1994,9 +2002,10 @@ public List<List<Integer>> subsetsWithDup(int[] nums) {
subsetList = new ArrayList<>(); subsetList = new ArrayList<>();
visited = new boolean[nums.length]; visited = new boolean[nums.length];
Arrays.sort(nums); Arrays.sort(nums);
for (int i = 0; i <= nums.length; i++) {
for (int i = 0; i <= nums.length; i++)
backtracking(0, i, nums); backtracking(0, i, nums);
}
return ret; return ret;
} }
@ -2005,9 +2014,9 @@ private void backtracking(int startIdx, int size, int[] nums) {
ret.add(new ArrayList(subsetList)); ret.add(new ArrayList(subsetList));
return; return;
} }
for (int i = startIdx; i < nums.length; i++) { for (int i = startIdx; i < nums.length; i++) {
if (i != 0 && nums[i] == nums[i - 1] && !visited[i - 1]) continue; if (i != 0 && nums[i] == nums[i - 1] && !visited[i - 1])
continue;
subsetList.add(nums[i]); subsetList.add(nums[i]);
visited[i] = true; visited[i] = true;
backtracking(i + 1, size, nums); backtracking(i + 1, size, nums);
@ -2036,11 +2045,11 @@ private List<List<String>> ret;
public List<List<String>> partition(String s) { public List<List<String>> partition(String s) {
ret = new ArrayList<>(); ret = new ArrayList<>();
doPartion(new ArrayList<>(), s); doPartition(new ArrayList<>(), s);
return ret; return ret;
} }
private void doPartion(List<String> list, String s) { private void doPartition(List<String> list, String s) {
if (s.length() == 0) { if (s.length() == 0) {
ret.add(new ArrayList<>(list)); ret.add(new ArrayList<>(list));
return; return;
@ -2048,16 +2057,16 @@ private void doPartion(List<String> list, String s) {
for (int i = 0; i < s.length(); i++) { for (int i = 0; i < s.length(); i++) {
if (isPalindrome(s, 0, i)) { if (isPalindrome(s, 0, i)) {
list.add(s.substring(0, i + 1)); list.add(s.substring(0, i + 1));
doPartion(list, s.substring(i + 1)); doPartition(list, s.substring(i + 1));
list.remove(list.size() - 1); list.remove(list.size() - 1);
} }
} }
} }
private boolean isPalindrome(String s, int begin, int end) { private boolean isPalindrome(String s, int begin, int end) {
while (begin < end) { while (begin < end)
if (s.charAt(begin++) != s.charAt(end--)) return false; if (s.charAt(begin++) != s.charAt(end--))
} return false;
return true; return true;
} }
``` ```
@ -2076,20 +2085,19 @@ private char[][] board;
public void solveSudoku(char[][] board) { public void solveSudoku(char[][] board) {
this.board = board; this.board = board;
for (int i = 0; i < 9; i++) { for (int i = 0; i < 9; i++)
for (int j = 0; j < 9; j++) { for (int j = 0; j < 9; j++) {
if (board[i][j] == '.') continue; if (board[i][j] == '.')
continue;
int num = board[i][j] - '0'; int num = board[i][j] - '0';
rowsUsed[i][num] = true; rowsUsed[i][num] = true;
colsUsed[j][num] = true; colsUsed[j][num] = true;
cubesUsed[cubeNum(i, j)][num] = true; cubesUsed[cubeNum(i, j)][num] = true;
} }
}
for (int i = 0; i < 9; i++) { for (int i = 0; i < 9; i++)
for (int j = 0; j < 9; j++) { for (int j = 0; j < 9; j++)
backtracking(i, j); backtracking(i, j);
}
}
} }
private boolean backtracking(int row, int col) { private boolean backtracking(int row, int col) {
@ -2097,14 +2105,17 @@ private boolean backtracking(int row, int col) {
row = col == 8 ? row + 1 : row; row = col == 8 ? row + 1 : row;
col = col == 8 ? 0 : col + 1; col = col == 8 ? 0 : col + 1;
} }
if (row == 9) {
if (row == 9)
return true; return true;
}
for (int num = 1; num <= 9; num++) { for (int num = 1; num <= 9; num++) {
if (rowsUsed[row][num] || colsUsed[col][num] || cubesUsed[cubeNum(row, col)][num]) continue; if (rowsUsed[row][num] || colsUsed[col][num] || cubesUsed[cubeNum(row, col)][num])
continue;
rowsUsed[row][num] = colsUsed[col][num] = cubesUsed[cubeNum(row, col)][num] = true; rowsUsed[row][num] = colsUsed[col][num] = cubesUsed[cubeNum(row, col)][num] = true;
board[row][col] = (char) (num + '0'); board[row][col] = (char) (num + '0');
if (backtracking(row, col)) return true; if (backtracking(row, col))
return true;
board[row][col] = '.'; board[row][col] = '.';
rowsUsed[row][num] = colsUsed[col][num] = cubesUsed[cubeNum(row, col)][num] = false; rowsUsed[row][num] = colsUsed[col][num] = cubesUsed[cubeNum(row, col)][num] = false;
} }
@ -2124,15 +2135,15 @@ private int cubeNum(int i, int j) {
<div align="center"> <img src="../pics//1f080e53-4758-406c-bb5f-dbedf89b63ce.jpg"/> </div><br> <div align="center"> <img src="../pics//1f080e53-4758-406c-bb5f-dbedf89b63ce.jpg"/> </div><br>
题目描述：在 n\*n 的矩阵中摆放 n 个皇后，并且每个皇后不能在同一行，同一列，同一对角线上，要求解所有的 n 皇后解。 题目描述：在 n\*n 的矩阵中摆放 n 个皇后，并且每个皇后不能在同一行，同一列，同一对角线上，求所有的 n 皇后的解。
一行一行地摆放，在确定一行中的那个皇后应该摆在哪一列时，需要用三个标记数组来确定某一列是否合法，这三个标记数组分别为：列标记数组、45 度对角线标记数组和 135 度对角线标记数组。 一行一行地摆放，在确定一行中的那个皇后应该摆在哪一列时，需要用三个标记数组来确定某一列是否合法，这三个标记数组分别为：列标记数组、45 度对角线标记数组和 135 度对角线标记数组。
45 度对角线标记数组的维度为 2\*n - 1，通过下图可以明确 (r,c) 的位置所在的数组下标为 r + c。 45 度对角线标记数组的维度为 2 \* n - 1，通过下图可以明确 (r, c) 的位置所在的数组下标为 r + c。
<div align="center"> <img src="../pics//85583359-1b45-45f2-9811-4f7bb9a64db7.jpg"/> </div><br> <div align="center"> <img src="../pics//85583359-1b45-45f2-9811-4f7bb9a64db7.jpg"/> </div><br>
135 度对角线标记数组的维度也是 2\*n - 1，(r,c) 的位置所在的数组下标为 n - 1 - (r - c)。 135 度对角线标记数组的维度也是 2 \* n - 1，(r, c) 的位置所在的数组下标为 n - 1 - (r - c)。
<div align="center"> <img src="../pics//9e80f75a-b12b-4344-80c8-1f9ccc2d5246.jpg"/> </div><br> <div align="center"> <img src="../pics//9e80f75a-b12b-4344-80c8-1f9ccc2d5246.jpg"/> </div><br>
@ -2147,21 +2158,21 @@ private int n;
public List<List<String>> solveNQueens(int n) { public List<List<String>> solveNQueens(int n) {
ret = new ArrayList<>(); ret = new ArrayList<>();
nQueens = new char[n][n]; nQueens = new char[n][n];
Arrays.fill(nQueens, '.'); for(int i = 0; i < n; i++)
Arrays.fill(nQueens[i], '.');
colUsed = new boolean[n]; colUsed = new boolean[n];
diagonals45Used = new boolean[2 * n - 1]; diagonals45Used = new boolean[2 * n - 1];
diagonals135Used = new boolean[2 * n - 1]; diagonals135Used = new boolean[2 * n - 1];
this.n = n; this.n = n;
backstracking(0); backtracking(0);
return ret; return ret;
} }
private void backstracking(int row) { private void backtracking(int row) {
if (row == n) { if (row == n) {
List<String> list = new ArrayList<>(); List<String> list = new ArrayList<>();
for (char[] chars : nQueens) { for (char[] chars : nQueens)
list.add(new String(chars)); list.add(new String(chars));
}
ret.add(list); ret.add(list);
return; return;
} }
@ -2169,12 +2180,11 @@ private void backstracking(int row) {
for (int col = 0; col < n; col++) { for (int col = 0; col < n; col++) {
int diagonals45Idx = row + col; int diagonals45Idx = row + col;
int diagonals135Idx = n - 1 - (row - col); int diagonals135Idx = n - 1 - (row - col);
if (colUsed[col] || diagonals45Used[diagonals45Idx] || diagonals135Used[diagonals135Idx]) { if (colUsed[col] || diagonals45Used[diagonals45Idx] || diagonals135Used[diagonals135Idx])
continue; continue;
}
nQueens[row][col] = 'Q'; nQueens[row][col] = 'Q';
colUsed[col] = diagonals45Used[diagonals45Idx] = diagonals135Used[diagonals135Idx] = true; colUsed[col] = diagonals45Used[diagonals45Idx] = diagonals135Used[diagonals135Idx] = true;
backstracking(row + 1); backtracking(row + 1);
colUsed[col] = diagonals45Used[diagonals45Idx] = diagonals135Used[diagonals135Idx] = false; colUsed[col] = diagonals45Used[diagonals45Idx] = diagonals135Used[diagonals135Idx] = false;
nQueens[row][col] = '.'; nQueens[row][col] = '.';
} }

2
notes/设计模式.md
View File

@ -233,7 +233,7 @@ public class Client {
```java ```java
public abstract class Factory { public abstract class Factory {
abstract public Product factoryMethod(); abstract public Product factoryMethod();
public void doSomethind() { public void doSomething() {
Product product = factoryMethod(); Product product = factoryMethod();
// do something with the product // do something with the product
} }