代码随想录算法训练营Day26 | 491.递增子序列 | 46.全排列 | 47.全排列 II | 332.重新安排行程 | 51.N皇后 | 37.解数独

2024-07-18 07:24:01
开发
18

今日任务

491.递增子序列

题目链接： https://leetcode.cn/problems/non-decreasing-subsequences/description/
题目描述：

Code

class Solution {
public:
    vector<vector<int>> findSubsequences(vector<int>& nums) {
        vector<vector<int>> ans;
        vector<int> path;
        int n = nums.size();
        // function<void(int)> dfs = [&](int i)->void{
        //     if(path.size() > 1){
        //         ans.emplace_back(path);
        //     }
        //     if(i == n){
        //         return;
        //     }
        //     vector<bool> visited(201);
        //     for(int j = i; j < n; j++){
        //         if(!path.empty() && nums[j] < path.back() || j > i && nums[j - 1] == nums[j]
        //             || visited[nums[j] + 100]){
        //             continue;
        //         }
        //         visited[nums[j] + 100] = true;
        //         path.push_back(nums[j]);
        //         dfs(j + 1);
        //         path.pop_back();
        //     }
        // };


        // 选或不选
        function<void(int)> dfs = [&](int i)->void{
            if(i == n){
                if(path.size() > 1){
                    ans.emplace_back(path);
                }
                return;
            }

            // 不选
            if(path.empty() || nums[i] != path.back()){
                dfs(i + 1);
            }

            // 选
            if(path.empty() || nums[i] >= path.back()){
                path.push_back(nums[i]);
                dfs(i + 1);
                path.pop_back();
            }
        };
        dfs(0);
        return ans;
    }
};

46.全排列

题目链接： https://leetcode.cn/problems/permutations/description/
题目描述：

Code

class Solution {
public:
    vector<vector<int>> permute(vector<int>& nums) {
        vector<vector<int>> ans;
        int n = nums.size();
        vector<int> path(n);
        // vector<bool> visit(n);
        // function<void(int)> dfs = [&](int i)->void{
        //     if(i == n){
        //         ans.emplace_back(path);
        //         return;
        //     }
        //     for(int j = 0; j < n; j++){     
        //         if(!visit[j]){
        //             path[i] = nums[j]; //
        //             visit[j] = true;
        //             dfs(i + 1); // 
        //             visit[j] = false;
        //         }
        //     }
        // };

        function<void(int)> dfs = [&](int i)->void{
            if(i == n){
                ans.emplace_back(path);
                return;
            }
            for(int j = 0; j < n; j++){     
                if(nums[j] <= 10){
                    path[i] = nums[j]; //
                    nums[j] += 21;
                    dfs(i + 1); // 
                    nums[j] -= 21;
                }
            }
        };
        dfs(0);
        return ans;
    }
};

47.全排列 II

题目链接： https://leetcode.cn/problems/permutations-ii/description/
题目描述：

Code

class Solution {
public:
    vector<vector<int>> permuteUnique(vector<int>& nums) {
        vector<vector<int>> ans;
        int n = nums.size();
        vector<int> path;
        ranges::sort(nums);
        vector<int> visited(n);
        function<void(int)> dfs = [&](int i)->void{
            if(i == n){
                ans.emplace_back(path);
                return;
            }

            for(int j = 0; j < n; j++){
                if(visited[j] || j > 0 && nums[j] == nums[j - 1] && !visited[j - 1]){
                    continue;
                }

                path.push_back(nums[j]);
                visited[j] = true;
                dfs(i + 1);
                visited[j] = false;
                path.pop_back();

            }
        };
        dfs(0);
        return ans;
    }
};

332.重新安排行程

题目链接： https://leetcode.cn/problems/reconstruct-itinerary/description/
题目描述：

Code

class Solution {
public:
    vector<string> findItinerary(vector<vector<string>>& tickets) {
        vector<string> ans = {"JFK"};
        unordered_map<string, map<string, int>> targets;
        for(auto &ticket : tickets){
            targets[ticket[0]][ticket[1]]++;
        }
        function<bool(int)> dfs = [&](int i)->bool{
            if(ans.size() == i + 1){
                return true;
            }
            for(auto &[destination, cnt] : targets[ans.back()]){
                if(cnt > 0){
                    ans.push_back(destination);
                    cnt--;
                    if(dfs(i)){
                        return true;
                    }
                    ans.pop_back();
                    cnt++;
                }
            }
            return false;
        };
        dfs(tickets.size());
        return ans;
    }
};

51.N皇后

题目链接： https://leetcode.cn/problems/n-queens/
题目描述：

Code

class Solution {
public:
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>> ans;
        vector<int> columns(n);
        vector<bool> on_path(n), diag1(2 * n - 1), diag2(2 * n - 1);
        function<void(int)> dfs = [&](int r)->void {
            if(r == n){
                vector<string> board(n);
                for(int i = 0; i < n; i++){
                    board[i] = string(columns[i], '.') + 'Q' + string(n - 1 - columns[i], '.');
                }
                ans.emplace_back(board);
                return;
            }
            for(int c = 0; c < n; c++){
                int rc = r - c + n - 1;
                if(!on_path[c] && !diag1[r + c] && !diag2[rc]){
                    columns[r] = c;
                    on_path[c] = diag1[r + c] = diag2[rc] = true;
                    dfs(r + 1);
                    on_path[c] = diag1[r + c] = diag2[rc] = false;
                }
            }
        };
        dfs(0);
        return ans;
    }
};

37.解数独

题目链接： https://leetcode.cn/problems/sudoku-solver/
题目描述：

Code

class Solution {
public:
    void solveSudoku(vector<vector<char>>& board) {
        
        // function<bool(int, int, char)> isValid = [&](int row, int column, char val)->bool{
        //     for(int i = 0; i < 9; i++){
        //         if(board[row][i] == val || board[i][column] == val){
        //             return false;
        //         }
        //     }
        //     int startRow = (row / 3) * 3;
        //     int startCol = (column / 3) * 3;
        //     for(int i = startRow; i < startRow + 3; i++){
        //         for(int j = startCol; j < startCol + 3; j++){
        //             if(board[i][j] == val){
        //                 return false;
        //             }
        //         }
        //     }
        //     return true;
        // };

        // function<bool()> dfs = [&]()->bool{
        //     for(int i = 0; i < 9; i++){
        //         for(int j = 0; j < 9; j++){
        //             if(board[i][j] == '.'){
        //                 for(char c = '1'; c <= '9'; c++){
        //                     if(isValid(i, j, c)){
        //                         board[i][j] = c;
        //                         if(dfs()){
        //                             return true;
        //                         }
        //                         board[i][j] = '.';
        //                     }
        //                 }
        //                 return false;
        //             }
        //         }
        //     }
        //     return true;
        // };
        // dfs();

        // bitset
        vector<bitset<9>> rows(9, bitset<9>());
        vector<bitset<9>> columns(9, bitset<9>());
        vector<vector<bitset<9>>> cells(3, vector<bitset<9>>(3, bitset<9>()));

        function<bitset<9>(int, int)> getPossibleStatus = [&](int x, int y)->bitset<9>{
            return ~(rows[x] | columns[y] | cells[x / 3][y / 3]);
        };

        function<vector<int>()> getNext = [&]()->vector<int>{
            vector<int> ret;
            int minCnt = 10;
            for(int i = 0; i < 9; i++){
                for(int j = 0; j < 9; j++){
                    if(board[i][j] != '.'){
                        continue;
                    }
                    auto cur = getPossibleStatus(i, j);
                    if(cur.count() >= minCnt){
                        continue;
                    }
                    ret = {i, j};
                    minCnt = cur.count();
                }
            }
            return ret;
        };

        function<void(int ,int ,int , bool)> fillNum = [&](int x, int y, int n, bool fillFlag)->void{
            rows[x][n] = (fillFlag) ? 1 :0;
            columns[y][n] = (fillFlag) ? 1 : 0;
            cells[x / 3][y / 3][n] = (fillFlag) ? 1 : 0;
        };

        function<bool(int)> dfs = [&](int i)->bool{
            if(i == 0){
                return true;
            }
            auto next = getNext();
            auto bits = getPossibleStatus(next[0], next[1]);
            for(int n = 0; n < bits.size(); n++){
                if(!bits.test(n)){
                    continue;
                }
                fillNum(next[0], next[1], n, true);
                board[next[0]][next[1]] = n + '1';
                if(dfs(i - 1)){
                    return true;
                }
                board[next[0]][next[1]] = '.';
                fillNum(next[0], next[1], n, false);
            }
            return false;
        };
        int cnt = 0;
        for(int i = 0; i < 9; i++){
            for(int j = 0; j < 9; j++){
                cnt += (board[i][j] == '.');
                if(board[i][j] == '.'){
                    continue;
                }
                int n = board[i][j] - '1';
                rows[i] |= (1 << n);
                columns[j] |= (1 << n);
                cells[i / 3][j / 3] |= (1 << n);
            }
        }
        dfs(cnt);
    }
};

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