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[LeetCode] Sudoku Solver

时间:2015-05-01 21:19:09      阅读:209      评论:0      收藏:0      [点我收藏+]

标签:c++   leetcode   

Sudoku Solver

Write a program to solve a Sudoku puzzle by filling the empty cells.

Empty cells are indicated by the character ‘.‘.

You may assume that there will be only one unique solution.

技术分享

A sudoku puzzle...

技术分享

...and its solution numbers marked in red.

解题思路:

之前没有玩过数独,于是就上网恶补了一下。于是我就陷入了一个误区,数独的几种技巧想用程序完全实现出来。于是乎,纠结了很久。本来用程序员思维来做非常容易的,就是回溯而已。我实现了唯一余数法和行列摒除法,若不能继续求解,则用暴力法。代码如下。

class Solution {
public:
	void solveSudoku(vector<vector<char> > &board) {
		set<int> allCan({ 1, 2, 3, 4, 5, 6, 7, 8, 9 });
		map<int, set<int>> candidates;
		map<int, set<int>> rowLeft;		//某一行还剩下哪些数
		map<int, set<int>> colLeft;		//某一列还剩下哪些数

		for (int i = 0; i < 9; i++){
			rowLeft[i] = allCan;
			colLeft[i] = allCan;
		}

		for (int i = 0; i<9; i++){
			for (int j = 0; j<9; j++){
				if (board[i][j] == '.'){
					candidates[get1D(i, j)] = allCan;
					prunning(board, i, j, candidates);
				}
				else{
					rowLeft[i].erase(board[i][j]-'0');
					colLeft[j].erase(board[i][j] - '0');
				}
			}
		}
		while (candidates.size()>0){
			int unknowNumber = candidates.size();
			showBoard(board);

			//唯一余数法
			{
				for (map<int, set<int>>::iterator it = candidates.begin(); it != candidates.end();){
					if (it->second.size() == 1){
						int i = get2Di(it->first);
						int j = get2Dj(it->first);
						board[i][j] = *(it->second.begin()) + '0';
						rowLeft[i].erase(board[i][j] - '0');
						colLeft[j].erase(board[i][j] - '0');
						candidates.erase(it++);
					}
					else{
						it++;
					}
				}
				for (int i = 0; i<9; i++){
					for (int j = 0; j<9; j++){
						if (board[i][j] == '.'){
							prunning(board, i, j, candidates);
						}
					}
				}
			}


			//行摒除法
			{
				for (int i = 0; i < 9; i++){
					for (set<int>::iterator it = rowLeft[i].begin(); it != rowLeft[i].end();){
						int pos = -1;
						bool onlyOne = true;
						for (int j = 0; j < 9; j++){
							int index = get1D(i, j);
							if (candidates.find(index) != candidates.end() && candidates[index].find(*it) != candidates[index].end()){
								if (pos >= 0){
									onlyOne = false;
									break;
								}
								pos = j;
							}
						}
						if (onlyOne&&pos >= 0){
							board[i][pos] = *it + '0';
							colLeft[pos].erase(*it);
							rowLeft[i].erase(it++);
							candidates.erase(get1D(i, pos));
						}
						else{
							it++;
						}
					}
				}
				for (int i = 0; i < 9; i++){
					for (int j = 0; j < 9; j++){
						if (board[i][j] == '.'){
							prunning(board, i, j, candidates);
						}
					}
				}
			}


			//列摒除法
			{
				for (int j = 0; j < 9; j++){
					for (set<int>::iterator it = colLeft[j].begin(); it != colLeft[j].end();){
						int pos = -1;
						bool onlyOne = true;
						for (int i = 0; i < 9; i++){
							int index = get1D(i, j);
							if (candidates.find(index) != candidates.end() && candidates[index].find(*it) != candidates[index].end()){
								if (pos >= 0){
									onlyOne = false;
									break;
								}
								pos = i;
							}
						}
						if (onlyOne&&pos >= 0){
							board[pos][j] = *it + '0';
							rowLeft[pos].erase(*it);
							colLeft[j].erase(it++);
							candidates.erase(get1D(pos, j));
						}
						else{
							it++;
						}
					}
				}
				for (int i = 0; i<9; i++){
					for (int j = 0; j<9; j++){
						if (board[i][j] == '.'){
							prunning(board, i, j, candidates);
						}
					}
				}
			}
			if (unknowNumber == candidates.size()){
				break;
			}
		}

		//若仍未解答出来,则暴力枚举
		if (candidates.size() > 0){
			dfsCheck(board, candidates, candidates.begin());
		}
		showBoard(board);
	}

	bool dfsCheck(vector<vector<char> > &board, map<int, set<int>> &candidates, map<int, set<int>>::iterator it){
		if (it == candidates.end()){
			return true;
		}
		int i = get2Di(it->first);
		int j = get2Dj(it->first);
		for (set<int>::iterator setIt = it->second.begin(); setIt != it->second.end(); setIt++){
			board[i][j] = *setIt+'0';
			it++;
			if (isValidSudoku(board) && dfsCheck(board, candidates, it)){
				return true;
			}
			it--;
			board[i][j] = '.';
		}
	}
	
private:
	int get1D(int i, int j){
		return i * 9 + j;
	}
	int get2Di(int index){
		return index / 9;
	}
	int get2Dj(int index){
		return index % 9;
	}

	void showBoard(vector<vector<char> > &board){
		/*for (int i = 0; i < 9; i++){
			for (int j = 0; j < 9; j++){
				cout << board[i][j];
				if ((j + 1) % 3 == 0){
					cout << " ";
				}
			}
			cout << endl;
		}
		cout << endl;*/
	};

	void prunning(vector<vector<char> > &board, int i, int j, map<int, set<int>> &candidates){
		pruningGrid(board, i, j, candidates);
		pruningRow(board, i, j, candidates);
		pruningColumn(board, i, j, candidates);
	}

	void pruningGrid(vector<vector<char> > &board, int i, int j, map<int, set<int>> &candidates){
		int index = get1D(i, j);
		while (i % 3 != 0){
			i--;
		}
		while (j % 3 != 0){
			j--;
		}
		for (int m = i; m < i + 3; m++){
			for (int n = j; n < j + 3; n++){
				if (board[m][n] != '.'){
					candidates[index].erase(board[m][n] - '0');
				}
			}
		}
	}

	void pruningRow(vector<vector<char> > &board, int i, int j, map<int, set<int>> &candidates){
		int index = get1D(i, j);
		for (int m = 0; m < 9; m++){
			if (board[i][m] != '.'){
				candidates[index].erase(board[i][m] - '0');
			}
		}
	}

	void pruningColumn(vector<vector<char> > &board, int i, int j, map<int, set<int>> &candidates){
		int index = get1D(i, j);
		for (int m = 0; m < 9; m++){
			if (board[m][j] != '.'){
				candidates[index].erase(board[m][j] - '0');
			}
		}
	}

	bool isValidSudoku(vector<vector<char>>& board) {
		//验证每一行是否有效
		for (int i = 0; i<9; i++){
			if (!checkRowValid(board, i)){
				return false;
			}
		}
		//验证每一列是否有效
		for (int i = 0; i<9; i++){
			if (!checkColumnValid(board, i)){
				return false;
			}
		}
		//验证每一格是否有效
		for (int i = 0; i<9; i = i + 3){
			for (int j = 0; j<9; j = j + 3){
				if (!checkGridValid(board, i, j)){
					return false;
				}
			}
		}
		return true;
	}

	//验证每个格是否有效,传入的是左上角的下标
	bool checkGridValid(vector<vector<char>>& board, int m, int n){
		bool flag[9];
		memset(flag, 0, sizeof(bool)* 9);
		for (int i = m; i<m + 3; i++){
			for (int j = n; j<n + 3; j++){
				if (board[i][j] == '.'){
					continue;
				}
				if (flag[board[i][j] - '1']){
					return false;
				}
				flag[board[i][j] - '1'] = true;
			}
		}
		return true;
	}

	//验证每一行是否有效,传入的是行号
	bool checkRowValid(vector<vector<char>>& board, int m){
		bool flag[9];
		memset(flag, 0, sizeof(bool)* 9);
		for (int i = 0; i<9; i++){
			if (board[m][i] == '.'){
				continue;
			}
			if (flag[board[m][i] - '1']){
				return false;
			}
			flag[board[m][i] - '1'] = true;
		}
		return true;
	}

	//验证每一列是否有效,传入的是列号
	bool checkColumnValid(vector<vector<char>>& board, int n){
		bool flag[9];
		memset(flag, 0, sizeof(bool)* 9);
		for (int i = 0; i<9; i++){
			if (board[i][n] == '.'){
				continue;
			}
			if (flag[board[i][n] - '1']){
				return false;
			}
			flag[board[i][n] - '1'] = true;
		}
		return true;
	}
};


[LeetCode] Sudoku Solver

标签:c++   leetcode   

原文地址:http://blog.csdn.net/kangrydotnet/article/details/45421957

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