数独自动求解

Posted 2021-12-01 pluslius

数独

游戏规则

1.所有小方格填入数字1-9
2.每个数字在每行只能出现1次
3.每个数字在每列只能出现1次
4.每个数字在每宫只能出现1次

检查算法

//按行，按列，按宫
第6宫，序号 n = 5
坐标 x = n % 3 = 2
     y = n / 3 = 1

每宫的起始格坐标 x0 = x * 3 = 6
                 y0 = y * 3 = 3
                 
宫内小格坐标 x1 = x0 + i % 3
             y1 = y0 + i / 3
             
坐标从宫内(0,0)开始
             row = row - (row % 3)
             col = col - (col % 3)

数独自动求解

const NOTASIGN = 0

function usedInCol(map,row,num){
  for(let col = 0; col < map[0].length; col++){
    if(map[row][col] === num){
      return true
    }
 }
 return false
}

function usedInRow(map,col,num){
  for(let row = 0; row < map.length; row++){
     if(map[row][col] === num){
       return true
     }
  }
  return false
}

function usedInBox(map,startRow,startCol,num){
  for(let row = 0; row < 3; row++){
    for(let col = 0; col < 3; col++){
      if(map[startRow + row][startCol + col] === num){
        return true
      }
    }
  }
  return false
}

function isSafe(map,row,col,num){
  return (
    !usedInRow(map,col,num)&&
    !usedInCol(map,row,num)&&
    !usedInBox(map,row - (row % 3),col - (col % 3),num)
  )
}

function sudokuSolution(map){
  let row = 0,
      col = 0,
      rowLen = map.length,
      colLen = map[0].length,
      checkBlankSpaces = false;

      for(row = 0; row < rowLen; row++){
        for(col = 0; col < colLen; col++){
          if(map[row][col] === NOTASIGN){
            checkBlankSpaces = true
            break
          }
        }
        if(checkBlankSpaces){
          break
        }
      }

      if(!checkBlankSpaces){
        return true
      }

      for(let num =1; num<=9; num++){
        if(isSafe(map,row,col,num)){
          map[row][col] = num
          if(sudokuSolution(map,row,col)){
            return true
          }
        }
        map[row][col] = NOTASIGN
      }

      return false
}

function sudokuSolver(map){
  if(sudokuSolution(map)){
    return map
  }
  return 'not result solution'
}


const sudokuGrid = [
    [5, 3, 0, 0, 7, 0, 0, 0, 0],
    [6, 0, 0, 1, 9, 5, 0, 0, 0],
    [0, 9, 8, 0, 0, 0, 0, 6, 0],
    [8, 0, 0, 0, 6, 0, 0, 0, 3],
    [4, 0, 0, 8, 0, 3, 0, 0, 1],
    [7, 0, 0, 0, 2, 0, 0, 0, 6],
    [0, 6, 0, 0, 0, 0, 2, 8, 0],
    [0, 0, 0, 4, 1, 9, 0, 0, 5],
    [0, 0, 0, 0, 8, 0, 0, 7, 9]
];

console.log(sudokuSolver(sudokuGrid));