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牛客网【面试必刷TOP101】~ 06 递归/回溯

news 2025/8/6 5:54:08

牛客网【面试必刷TOP101】~ 06 递归/回溯

文章目录

牛客网【面试必刷TOP101】~ 06 递归/回溯
@[toc]
BM55 没有重复项数字的全排列(★★)
BM56 有重复项数字的全排列(★★)
BM57 岛屿数量(★★)
BM58 字符串的排列(★★)
BM59 N皇后问题(★★★)
BM60 括号生成(★★)
BM61 矩阵最长递增路径(★★)

BM55 没有重复项数字的全排列(★★)

回溯，移动元素至前

public class Solution {ArrayList<ArrayList<Integer>> res;public ArrayList<ArrayList<Integer>> permute (int[] nums) {res = new ArrayList<>();if (nums == null || nums.length == 0) return res;ArrayList<Integer> lists = new ArrayList<>();// Arrays.sort(nums);for (int num : nums) lists.add(num);backtrack(lists, 0, lists.size());return res;}  private void backtrack(ArrayList<Integer> lists, int begin, int end) {if (begin == end) {res.add(new ArrayList<>(lists));return;}for (int i = begin; i < end; i++) {int val = lists.remove(i);lists.add(begin, val);backtrack(lists, begin + 1, end);val = lists.remove(begin);lists.add(i, val);}}
}

BM56 有重复项数字的全排列(★★)

排序+ 回溯+set去重

public class Solution {ArrayList<ArrayList<Integer>> res;public ArrayList<ArrayList<Integer>> permuteUnique (int[] nums) {res = new ArrayList<>();if (nums == null || nums.length == 0) return res;ArrayList<Integer> lists = new ArrayList<>();Arrays.sort(nums);for (int num : nums) lists.add(num);backtrack(lists, 0, lists.size());return res;}private void backtrack(ArrayList<Integer> lists, int begin, int end) {if (begin == end) {res.add(new ArrayList<>(lists));return;}Set<Integer> set = new HashSet<>();for (int i = begin; i < end; i++) {if (set.contains(lists.get(i))) continue;set.add(lists.get(i));int val = lists.remove(i);lists.add(begin, val);backtrack(lists, begin + 1, end);lists.remove(begin);lists.add(i, val);}}}

BM57 岛屿数量(★★)

方法一：回溯（120ms）

public class Solution {private static int[] dirs = {-1, 0, 1, 0, -1}; public int solve (char[][] grid) {if (grid == null || grid.length == 0 || grid[0].length == 0) return 0;int count = 0;int r = grid.length, c = grid[0].length;for (int i = 0; i < r; i++) {for (int j = 0; j < c; j++) {if (grid[i][j] == '0') continue;dfs(grid, i, j, r, c);count++;}}return count;}private void dfs(char[][] grid, int i, int j, int r, int c) {if (i < 0 || j < 0 || i >= r || j >= c || grid[i][j] == '0') {return;}grid[i][j] = '0';for (int d = 0; d < 4; d++) {int x = i + dirs[d], y = j + dirs[d + 1];dfs(grid, x, y, r, c);}}}

更直观的定义

public class Solution {public int solve (char[][] grid) {int count = 0;for (int i = 0; i < grid.length; i++) {for (int j = 0; j < grid[0].length; j++) {if (grid[i][j] == '0') continue;sinkLand(grid, i, j);count++;}}return count;}private void sinkLand(char[][] grid, int i, int j) {if (i < 0 || j < 0 || i >= grid.length || j >= grid[0].length || grid[i][j] == '0') {return;}grid[i][j] = '0';sinkLand(grid, i - 1, j);sinkLand(grid, i + 1, j);sinkLand(grid, i, j - 1);sinkLand(grid, i, j + 1);}}

BM58 字符串的排列(★★)

同BM56，有重复字符的全排列

public class Solution {ArrayList<String> res;public ArrayList<String> Permutation (String str) {res = new ArrayList<>();if (str == null || str.equals("")) return res;char[] cs = str.toCharArray();Arrays.sort(cs);backtrack(cs, 0, cs.length);return res;}private void backtrack(char[] cs, int begin, int end) {if (begin == end) {res.add(new String(cs));return;}Set<Character> set = new HashSet<>();for (int i = begin; i < end; i++) {if (set.contains(cs[i])) continue;set.add(cs[i]);swap(cs, begin, i);backtrack(cs, begin + 1, end);swap(cs, begin, i);}}private void swap(char[] cs, int i, int j) {char c = cs[i];cs[i] = cs[j];cs[j] = c;}
}

BM59 N皇后问题(★★★)

public class Solution {private int count;private int[] x;public int Nqueen (int n) {count = 0;x = new int[n];Arrays.fill(x, -1);backtrack(n);return count;}private void backtrack(int n) {int k = 0;while (k >= 0) {x[k]++;while (x[k] < n && isClash(k)) x[k]++;if (x[k] < n && k == n - 1) count++;if (x[k] < n && k < n - 1) {k++;} else {x[k--] = -1;}}}private boolean isClash(int k) {for (int i = 0; i < k; i++) {if (x[i] == x[k] || Math.abs(i - k) == Math.abs(x[i] - x[k])) {return true;}}return false;}}

BM60 括号生成(★★)

递归

public class Solution {public ArrayList<String> res;public ArrayList<String> generateParenthesis (int n) {res = new ArrayList<>();dfs(new String(), n, n);return res;}private void dfs(String s, int le, int ri) {if (le > ri || le < 0 || ri < 0) return;if (le == 0 && ri == 0) {res.add(s);return;}dfs(s + "(", le - 1, ri);dfs(s + ")", le, ri - 1);}
}

BM61 矩阵最长递增路径(★★)

dfs+记忆化搜索

public class Solution {private static final int[] dirs = {-1, 0, 1, 0, -1};private int[][] ms;private int R, C;public int solve (int[][] matrix) {if (matrix == null || matrix.length == 0 || matrix[0].length == 0) {return 0;}R = matrix.length;C = matrix[0].length;ms = new int[R][C];int res = 0;for (int i = 0; i < R; i++) {for (int j = 0; j < C; j++) {res = Math.max(res, dfs(matrix, i, j));} }return res;}private int dfs(int[][] matrix, int i, int j) {if (ms[i][j] != 0) return ms[i][j];ms[i][j]++;for (int k = 0; k < 4; k++) {int x = i + dirs[k], y = j + dirs[k + 1];if (x < 0 || y < 0 || x >= R || y >= C || matrix[i][j] >= matrix[x][y]) {continue;}ms[i][j] = Math.max(ms[i][j], dfs(matrix, x, y) + 1);}return ms[i][j];}}