三星机试也考了类似的题目,只不过是要针对给出的数独修改其中三个错误数字,总过10个测试用例只过了3个与世界500强无缘了
36. Valid Sudoku
Determine if a Sudoku is valid, according to: Sudoku Puzzles - The Rules.
The Sudoku board could be partially filled, where empty cells are filled with the character '.'
.
A partially filled sudoku which is valid.
Note:
A valid Sudoku board (partially filled) is not necessarily solvable. Only the filled cells need to be validated.
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Idea
Just go through all you see (like "7 in row 3") and check for duplicates.
Solution 1
Using Counter
. One logical line, seven physical lines.
def isValidSudoku(self, board):
return 1 == max(collections.Counter(
x
for i, row in enumerate(board)
for j, c in enumerate(row)
if c != '.'
for x in ((c, i), (j, c), (i/3, j/3, c))
).values() + [1])
The + [1]
is only for the empty board, where max
would get an empty list and complain. It's not necessary to get it accepted here, as the empty board isn't among the test cases, but it's good to have.
Solution 2
Using len(set)
.
def isValidSudoku(self, board):
seen = sum(([(c, i), (j, c), (i/3, j/3, c)]
for i, row in enumerate(board)
for j, c in enumerate(row)
if c != '.'), [])
return len(seen) == len(set(seen))
Solution 3
Using any
.
def isValidSudoku(self, board):
seen = set()
return not any(x in seen or seen.add(x)
for i, row in enumerate(board)
for j, c in enumerate(row)
if c != '.'
for x in ((c, i), (j, c), (i/3, j/3, c)))
Solution 4
Iterating a different way.
def isValidSudoku(self, board):
seen = sum(([(c, i), (j, c), (i/3, j/3, c)]
for i in range(9) for j in range(9)
for c in [board[i][j]] if c != '.'), [])
return len(seen) == len(set(seen))
Clean and Easy82ms Python
402 views
class Solution(object):
def isValidSudoku(self, board):
"""
:type board: List[List[str]]
:rtype: bool
"""
big = set()
for i in xrange(0,9):
for j in xrange(0,9):
if board[i][j]!='.':
cur = board[i][j]
if (i,cur) in big or (cur,j) in big or (i/3,j/3,cur) in big:
return False
big.add((i,cur))
big.add((cur,j))
big.add((i/3,j/3,cur))
37. 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.
A sudoku puzzle...
...and its solution numbers marked in red.
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最快的解决方案:
Sharing my 2ms C++ solution with comments and explanations.
3,937 views
Update: there's a follow-up 0ms solution which is even more optimized
This is one of the fastest Sudoku solvers I've ever written. It is compact enough - just 150 lines of C++ code with comments. I thought it'd be interesting to share it, since it combines several techniques like reactive network update propagation and backtracking with very aggressive pruning.
The algorithm is online - it starts with an empty board and as you add numbers to it, it starts solving the Sudoku.
Unlike in other solutions where you have bitmasks of allowed/disallowed values per row/column/square, this solution track bitmask for every(!) cell, forming a set of constraints for the allowed values for each particular cell. Once a value is written into a cell, new constraints are immediately propagated to row, column and 3x3 square of the cell. If during this process a value of other cell can be unambiguously deduced - then the value is set, new constraints are propagated, so on.... You can think about this as an implicit reactive network of cells.
If we're lucky (and we'll be lucky for 19 of 20 of Sudokus published in magazines) then Sudoku is solved at the end (or even before!) processing of the input.
Otherwise, there will be empty cells which have to be resolved. Algorithm uses backtracking for this purpose. To optimize it, algorithm starts with the cell with the smallest ambiguity. This could be improved even further by using priority queue (but it's not implemented here). Backtracking is more or less standard, however, at each step we guess the number, the reactive update propagation comes back into play and it either quickly proves that the guess is unfeasible or significantly prunes the remaining search space.
It's interesting to note, that in this case taking and restoring snapshots of the compact representation of the state is faster than doing backtracking rollback by "undoing the moves".
class Solution {
struct cell
{
uint8_t value;
uint8_t numPossibilities;
bitset<10> constraints;
cell() : value(0), numPossibilities(9),constraints() {};
};
array<array | ,9> cells;
bool set(int i, int j, int v)
{
cell& c = cells[i][j];
if (c.value == v)
return true;
if (c.constraints[v])
return false;
c.constraints = bitset<10>(0x3FE);
c.constraints.reset(v);
c.numPossibilities = 1;
c.value = v;
for (int k = 0; k<9; k++) {
if (i != k && !updateConstraints(k, j, v))
return false;
if (j != k && !updateConstraints(i, k, v))
return false;
int ix = (i / 3) * 3 + k / 3;
int jx = (j / 3) * 3 + k % 3;
if (ix != i && jx != j && !updateConstraints(ix, jx, v))
return false;
}
return true;
}
bool updateConstraints(int i, int j, int excludedValue)
{
cell& c = cells[i][j];
if (c.constraints[excludedValue]) {
return true;
}
if (c.value == excludedValue) {
return false;
}
c.constraints.set(excludedValue);
if (--c.numPossibilities > 1)
return true;
for (int v = 1; v <= 9; v++) {
if (!c.constraints[v]) {
return set(i, j, v);
}
}
assert(false);
}
vectorint, int>> bt;
bool findValuesForEmptyCells()
{
bt.clear();
for (int i = 0; i < 9; i++) {
for (int j = 0; j < 9; j++) {
if (!cells[i][j].value)
bt.push_back(make_pair(i, j));
}
}
sort(bt.begin(), bt.end(), [this](const pair<int, int>&a, const pair<int, int>&b) {
return cells[a.first][a.second].numPossibilities < cells[b.first][b.second].numPossibilities; });
return backtrack(0);
}
bool backtrack(int k)
{
if (k >= bt.size())
return true;
int i = bt[k].first;
int j = bt[k].second;
if (cells[i][j].value)
return backtrack(k + 1);
auto constraints = cells[i][j].constraints;
array<array | ,9> snapshot(cells);
for (int v = 1; v <= 9; v++) {
if (!constraints[v]) {
if (set(i, j, v)) {
if (backtrack(k + 1))
return true;
}
cells = snapshot;
}
}
return false;
}
public:
void solveSudoku(vector<vector<char>> &board) {
cells = array<array | ,9>();
for (int i = 0; i < 9; i++)
{
for (int j = 0; j < 9; j++) {
if (board[i][j] != '.' && !set(i, j, board[i][j] - '0'))
return;
}
}
if (!findValuesForEmptyCells())
return;
for (int i = 0; i < 9; i++)
{
for (int j = 0; j < 9; j++) {
if (cells[i][j].value)
board[i][j] = cells[i][j].value + '0';
}
}
}
};
Simple and Clean Solution / C++
871 views
bool check(vector<vector<char>> &board, int i, int j, char val)
{
int row = i - i%3, column = j - j%3;
for(int x=0; x<9; x++) if(board[x][j] == val) return false;
for(int y=0; y<9; y++) if(board[i][y] == val) return false;
for(int x=0; x<3; x++)
for(int y=0; y<3; y++)
if(board[row+x][column+y] == val) return false;
return true;
}
bool solveSudoku(vector<vector<char>> &board, int i, int j)
{
if(i==9) return true;
if(j==9) return solveSudoku(board, i+1, 0);
if(board[i][j] != '.') return solveSudoku(board, i, j+1);
for(char c='1'; c<='9'; c++)
{
if(check(board, i, j, c))
{
board[i][j] = c;
if(solveSudoku(board, i, j+1)) return true;
board[i][j] = '.';
}
}
return false;
}
public: void solveSudoku(vector& board) { solveSudoku(board, 0, 0); }
c++ clear solution using dfs, beating 90% c++ coder.
690 views
class Solution {
public:
bool col[10][10],row[10][10],f[10][10];
bool flag = false;
void solveSudoku(vector<vector<char>>& board) {
memset(col,false,sizeof(col));
memset(row,false,sizeof(row));
memset(f,false,sizeof(f));
for(int i = 0; i < 9;i++){
for(int j = 0; j < 9;j++){
if(board[i][j] == '.') continue;
int temp = 3*(i/3)+j/3;
int num = board[i][j]-'0';
col[j][num] = row[i][num] = f[temp][num] = true;
}
}
dfs(board,0,0);
}
void dfs(vector<vector<char>>& board,int i,int j){
if(flag == true) return ;
if(i >= 9){
flag = true;
return ;
}
if(board[i][j] != '.'){
if(j < 8) dfs(board,i,j+1);
else dfs(board,i+1,0);
if(flag) return;
}
else{
int temp = 3*(i/3)+j/3;
for(int n = 1; n <= 9; n++){
if(!col[j][n] && !row[i][n] && !f[temp][n]){
board[i][j] = n + '0';
col[j][n] = row[i][n] = f[temp][n] = true;
if(j < 8) dfs(board,i,j+1);
else dfs(board,i+1,0);
col[j][n] = row[i][n] = f[temp][n] = false;
if(flag) return;
}
}
board[i][j] = '.';
}
}
};
13-line Python solution, dfs, beats 47.79%
77 views
def solveSudoku(self, board):
def dfs():
for i, row in enumerate(board):
for j, char in enumerate(row):
if char == '.':
for x in s9 - {row[k] for k in r9} - {board[k][j] for k in r9} - \
{board[i / 3 * 3 + m][j / 3 * 3 + n] for m in r3 for n in r3}:
board[i][j] = x
if dfs(): return True
board[i][j] = '.'
return False
return True
r3, r9, s9 = range(3), range(9), {'1', '2', '3', '4', '5', '6', '7', '8', '9'}
dfs()
参考文献:
http://www.cnblogs.com/felixfang/p/3705754.html