sicily 1317. Sudoku

1317. Sudoku

Constraints

Time Limit: 10 secs, Memory Limit: 32 MB

Description

Sudoku is a placement puzzle. The goal is to enter a symbol in each cell of a grid, most frequently a9 x 9 grid made up of 3 x 3 subgrids. Each row, column and subgrid must contain only one instance of each symbol. Sudoku initially became popular in Japan in 1986 and attained international popularity in 2005.

 

The word Sudoku means ``single number" in Japanese. The symbols in Sudoku puzzles are often numerals, but arithmetic relationships between numerals are irrelevant.

According to wikipedia:

The number of valid Sudoku solution grids for the standard 9 x 9 grid was calculated by Bertram Felgenhauer in 2005 to be 6,670,903,752,021,072,936,960, which is roughly the number of micrometers to the nearest star. This number is equal to9! * 722* 27* 27, 704, 267, 971 , the last factor of which is prime. The result was derived through logic and brute force computation. The number of valid Sudoku solution grids for the16 x 16 derivation is not known.

Write a program to find a solution to a 9 x 9 Sudoku puzzle given a starting configuration.

Input

The first line will contain an integer specifying the number of puzzles to be solved. The remaining lines will specify the starting configuration for each of the puzzles. Each line in a starting configuration will have nine characters selected from the numerals 1-9 and the underscore which indicates an empty cell.

Output

For each puzzle, the output should specify the puzzle number (starting at one) and describe the solution characteristics. If there is a single solution, it should be printed. Otherwise, a message indicating whether there are no solutions or multiple solutions should be printed. The output should be similar to that shown below. All input cases have less than 10,000 solutions.

Sample Input

3________41____9_7___37_28______7_26_4_______8_91_6______42_36___3_14___99________7_9__2___3_____891___39___448__6______5___6______4__232___57___568_____7___8__4_282__________5__2____6_4_7___5___1_7_9_2_5_4_1_3_8_6_9___3_6_1____5__2__________34

Sample Output

Puzzle 1 has 6 solutionsPuzzle 2 solution is719482365324675891856391274482563719135729648697148523243957186568214937971836452Puzzle 3 has no solution

题目分析

与1162不同的是要求找到共有几种解法,所以蛮力深搜10s也会超时
优化内容有
一,开三个标记数组,确定在某行,某列,某小宫格是否已经有了某个数字

int inRow[10][10];int inCol[10][10];int inBlock[10][10];

二,标记为零的区域,而不是整个盘扫一遍去判断某个位置是否需要填数

struct Test {
  int row, col, poss;
  bool valid[10];
} nodes[81];
poss记录其可填的数值个数
valid标记那些数字可以填

三,将nodes按照poss值排序在深搜,这样可以减少搜索的分支和回溯的时间

然后格式要求每个样例后面加空行

#include <iostream>#include <algorithm>#include <memory.h>int sudoku[10][10];int inRow[10][10];int inCol[10][10];int inBlock[10][10];struct Test {  int row, col, poss;  bool valid[10];} nodes[81];int count;int ans;std::string solution;int getBlockId(int row, int col) {  return (row-1)/3*3 + (col-1)/3 + 1;}void getPoss() {  for (int i = 0; i < count; ++i) {    int rr = nodes[i].row;    int cc = nodes[i].col;    for (int j = 1; j <= 9; ++j) {      if (inRow[rr][j] || inCol[cc][j] || inBlock[getBlockId(rr,cc)][j]) {        nodes[i].valid[j] = false;      } else {        nodes[i].valid[j] = true;        ++nodes[i].poss;      }    }  }/*std::cout << count << std::endl;for (int i = 0; i < count; ++i) {  std::cout << nodes[i].poss << "===";  for (int j = 1; j <= 9; ++j)    if (nodes[i].valid[j])      std::cout << j << "   ";  std::cout << std::endl;}*/}bool com(Test a, Test b) {  return a.poss < b.poss;}void storeSol() {  for (int i = 1; i <= 9; ++i) {    for (int j = 1; j <= 9; ++j)      solution = solution + (char)('0' + sudoku[i][j]);    solution = solution + '\n';  }}void dfs(int index) {  if (index == count) {    if (!ans) storeSol();    ans++;    return;  }  int rr = nodes[index].row;  int cc = nodes[index].col;  for (int i = 1; i <= 9; ++i) {    if (inRow[rr][i] || inCol[cc][i] || inBlock[getBlockId(rr,cc)][i])      continue;    sudoku[rr][cc] = i;    inRow[rr][i] = inCol[cc][i] = inBlock[getBlockId(rr,cc)][i] = true;    ++index;    dfs(index);    sudoku[rr][cc] = 0;    inRow[rr][i] = inCol[cc][i] = inBlock[getBlockId(rr,cc)][i] = false;    --index;  }}int main(){  int num;  std::cin >> num;  for (int id = 1; id <= num; ++id) {    if (id != 1)      std::cout << "\n";    memset(inRow, 0, sizeof(inRow));    memset(inCol, 0, sizeof(inCol));    memset(inBlock, 0, sizeof(inBlock));    count = 0;    ans = 0;    solution = "";    std::string str;    for (int i = 1; i <= 9; ++i) {      std::cin >> str;      for (int j = 1; j <= 9; ++j) {        if (str[j-1] == '_')          sudoku[i][j] = 0;        else          sudoku[i][j] = str[j-1] - '0';        if (sudoku[i][j]) {          inRow[i][sudoku[i][j]] = true;          inCol[j][sudoku[i][j]] = true;          inBlock[getBlockId(i,j)][sudoku[i][j]] = true;        } else {          nodes[count].row = i;          nodes[count].col = j;          nodes[count].poss = 0;          count++;        }      }    }    getPoss();    std::sort(nodes, nodes+count, com);    dfs(0);    if (ans == 0) {      std::cout << "Puzzle " << id << " has no solution" << std::endl;    } else if (ans == 1) {      std::cout << "Puzzle " << id << " solution is" << std::endl;      std::cout << solution;    } else {      std::cout << "Puzzle " << id << " has " << ans << " solutions" << std::endl;    }  }}