22.回溯算法4

递增子序列

这里不能排序，因为数组的顺序是对结果有影响的，所以只能通过used数组来去重

class Solution {
public:
    vector<int> path;
    vector<vector<int>> res;
    void backtracking(vector<int>& nums,int start){
        if(path.size()>1)
        res.push_back(path);
        int used[201]={0};
        for(int i=start;i<nums.size();i++){
           
            if(path.empty()||nums[i]>=path[path.size()-1]){
                if(used[nums[i]+100])continue;;
                path.push_back(nums[i]);
                used[nums[i]+100]=1;
                backtracking(nums,i+1);
                path.pop_back();
                
            }
        }
    }
    vector<vector<int>> findSubsequences(vector<int>& nums) {
        backtracking(nums,0);
        return res;
    }
};

全排列

class Solution {
public:
    vector<int> path;
    vector<vector<int>> res;
    int* used;
    int level=0;
    void backtracking(vector<int>& nums){
        if(level==nums.size()){
            res.push_back(path);
            return;
        }
        for(int i=0;i<nums.size();i++){
            if(used[i])continue;
            path.push_back(nums[i]);
            level++;
            used[i]=1;
            backtracking(nums);
            path.pop_back();
            used[i]=0;
            level--;
            
        }
        
    }
    vector<vector<int>> permute(vector<int>& nums) {
        used= new int[nums.size()]{0};
        backtracking(nums);
        return res;
    }
};

全排列2

class Solution {
public:
    vector<int> path;
    vector<vector<int>> res;
    int* used;
    int level=0;
    void backtracking(vector<int>& nums){
        if(level==nums.size()){
            res.push_back(path);
            return;
        }
        int pre=20040503;
        for(int i=0;i<nums.size();i++){
            if(used[i])continue;
            if(nums[i]==pre)continue;
            path.push_back(nums[i]);
            level++;
            used[i]=1;
            pre=nums[i];
            backtracking(nums);
            path.pop_back();
            used[i]=0;
            level--;
            
        }
        
    }
    vector<vector<int>> permuteUnique(vector<int>& nums) {
        used= new int[nums.size()]{0};
        sort(nums.begin(),nums.end());
        backtracking(nums);
        
        return res;
    }
};

重新安排行程

class Solution {
    public:
    unordered_map<string,map<string,int>> targets;
    vector<string> res; 
    int tiknum;
    vector<string> backtracking(int stop,string start){
        if(stop==tiknum)return res;
        vector<string> tmp;
        for(auto it:targets[start]){
            if(it.second){
                res.push_back(it.first);
                targets[start][it.first]--;
            }
            else continue;
            tmp=backtracking(stop+1,it.first);
            if(!tmp.empty())return tmp;
            res.pop_back();
            targets[start][it.first]++;
        }
        return tmp;
    }
    vector<string> findItinerary(vector<vector<string>>& tickets) {
        for(auto tick:tickets){
            targets[tick[0]][tick[1]]++;
        }
        tiknum=tickets.size();
        res.push_back("JFK");
        return backtracking(0,"JFK");
    }
};

N皇后

class Solution {
public:
    vector<string> tmp;
    vector<vector<string>> res;
    int n;
    bool isConf(int y,int x){
        for(int i=1;i<=y;i++){
            if(tmp[y-i][x]=='Q')return 1;
            if(x+i<n&&tmp[y-i][x+i]=='Q')return 1;
            if(x-i>=0&&tmp[y-i][x-i]=='Q')return 1;
        }
        return 0;
    }
    void backtracking(int k){
        if(k==n){
            res.push_back(tmp);
        }
        for(int i=0;i<n;i++){
            if(isConf(k,i))continue;
            tmp[k][i]='Q';
            backtracking(k+1);
            tmp[k][i]='.';
        }
    }
    vector<vector<string>> solveNQueens(int n0) {
        n=n0;
        tmp.resize(n);
        for(int i=0;i<n;i++){
            tmp[i].resize(n);
            for(int j=0;j<n;j++){
                tmp[i][j]='.';
            }
        }
        backtracking(0);
        return res;    
    }
};

• 时间复杂度: O(n!)
• 空间复杂度: O(n)

解数独

class Solution {
public:
    
    bool isValid(int row, int col, char val,vector<vector<char>>& board) {
    for (int i = 0; i < 9; i++) { // 判断行里是否重复
        if (board[row][i] == val) {
            return false;
        }
    }
    for (int j = 0; j < 9; j++) { // 判断列里是否重复
        if (board[j][col] == val) {
            return false;
        }
    }
    int startRow = (row / 3) * 3;
    int startCol = (col / 3) * 3;
    for (int i = startRow; i < startRow + 3; i++) { // 判断9方格里是否重复
        for (int j = startCol; j < startCol + 3; j++) {
            if (board[i][j] == val ) {
                return false;
            }
        }
    }
    return true;
}
    bool backtracking(int x,int y,vector<vector<char>>& board){
        int n=board.size();
        if(x>=n){
            x=x%n;
            y++;
            
        }
        while(x<n&&y<n){
            if(board[y][x]!='.'){
                x++;
                if(x>=n){
                    x=x%n;
                    y++;
                    
                }
                continue;
            }
            for(int i=1;i<10;i++){
                if(!isValid(y,x,i+'0',board))continue;
                board[y][x]=i+'0';           
                if(backtracking(x+1,y,board))return 1;
                board[y][x]='.';
            }
            return 0;
        }
        return 1;
    }
    void solveSudoku(vector<vector<char>>& board) {
        backtracking(0,0,board);
    }
};