#! /usr/bin/env python3 
# -*- coding: utf-8 -*- 
# fileName ： robot_path.py 
# author : zoujiameng@aliyun.com.cn 
 
# 地上有一個m行和n列的方格。一個機器人從坐標0,0的格子開始移動，每一次只能向左，右，上，下四個方向移動一格，但是不能進入行坐標和列坐標的數位之和大于k的格子。  
# 例如，當k為18時，機器人能夠進入方格（35,37），因為3+5+3+7 = 18。但是，它不能進入方格（35,38），因為3+5+3+8 = 19。請問該機器人能夠達到多少個格子？ 
class Robot: 
# 共用接口,判斷是否超過K 
  def getDigitSum(self, num): 
    sumD = 0 
    while(num>0): 
      sumD+=num%10 
      num/=10 
    return int(sumD) 
 
  def PD_K(self, rows, cols, K): 
    sumK = self.getDigitSum(rows) + self.getDigitSum(cols) 
    if sumK > K: 
      return False 
    else: 
      return True 
 
  def PD_K1(self, i, j, k): 
    "確定該位置是否可以走,將復雜約束條件設定" 
    index = map(str,[i,j]) 
    sum_ij = 0 
    for x in index: 
      for y in x: 
        sum_ij += int(y) 
    if sum_ij <= k: 
      return True 
    else: 
      return False 
 
# 共用接口,打印遍歷的visited二維list 
  def printMatrix(self, matrix, r, c): 
    print("cur location(", r, ",", c, ")") 
    for x in matrix: 
      for y in x:  
        print(y, end=' ') 
      print() 
 
 #回溯法 
  def hasPath(self, threshold, rows, cols): 
    visited = [ [0 for j in range(cols)] for i in range(rows) ] 
    count = 0 
    startx = 0 
    starty = 0 
    #print(threshold, rows, cols, visited) 
    visited = self.findPath(threshold, rows, cols, visited, startx, starty, -1, -1) 
    for x in visited: 
      for y in x: 
        if( y == 1): 
          count+=1 
    print(visited) 
    return count 
 
  def findPath(self, threshold, rows, cols, visited, curx, cury, prex, prey): 
    if 0 <= curx < rows and 0 <= cury < cols and self.PD_K1(curx, cury, threshold) and visited[curx][cury] != 1: # 判斷當前點是否滿足條件 
      visited[curx][cury] = 1 
    self.printMatrix(visited, curx, cury) 
    prex = curx 
    prey = cury 
    if cury+1 < cols and self.PD_K1(curx, cury+1, threshold) and visited[curx][cury+1] != 1: # east 
      visited[curx][cury+1] = 1 
      return self.findPath(threshold, rows, cols, visited, curx, cury+1, prex, prey) 
    elif cury-1 >= 0 and self.PD_K1(curx, cury-1, threshold) and visited[curx][cury-1] != 1: # west 
      visited[curx][cury-1] = 1 
      return self.findPath(threshold, rows, cols, visited, curx, cury-1, prex, prey) 
    elif curx+1 < rows and self.PD_K1(curx+1, cury, threshold) and visited[curx+1][cury] != 1: # sourth 
      visited[curx+1][cury] = 1 
      return self.findPath(threshold, rows, cols, visited, curx+1, cury, prex, prey) 
    elif 0 <= curx-1 and self.PD_K1(curx-1, cury, threshold) and visited[curx-1][cury] != 1: # north 
      visited[curx-1][cury] = 1 
      return self.findPath(threshold, rows, cols, visited, curx-1, cury, prex, prey) 
    else: # 返回上一層,此處有問題 
      return visited#self.findPath(threshold, rows, cols, visited, curx, cury, prex, prey) 
 #回溯法2 
  def movingCount(self, threshold, rows, cols): 
    visited = [ [0 for j in range(cols)] for i in range(rows) ] 
    print(visited) 
    count = self.movingCountCore(threshold, rows, cols, 0, 0, visited); 
    print(visited) 
    return count 
 
  def movingCountCore(self, threshold, rows, cols, row, col, visited): 
    cc = 0 
    if(self.check(threshold, rows, cols, row, col, visited)):  
      visited[row][col] = 1 
      cc = 1 + self.movingCountCore(threshold, rows, cols, row+1, col,visited) + self.movingCountCore(threshold, rows, cols, row, col+1, visited) + self.movingCountCore(threshold, rows, cols, row-1, col, visited) + self.movingCountCore(threshold, rows, cols, row, col-1, visited) 
    return cc 
 
  def check(self, threshold, rows, cols, row, col, visited): 
    if( 0 <= row < rows and 0 <= col < cols and (self.getDigitSum(row)+self.getDigitSum(col)) <= threshold and visited[row][col] != 1):  
      return True; 
    return False  
 
# 暴力法，直接用當前坐標和K比較 
  def force(self, rows, cols, k): 
    count = 0 
    for i in range(rows): 
      for j in range(cols): 
        if self.PD_K(i, j, k): 
          count+=1 
    return count 
# 暴力法2, 用遞歸法來做 
  def block(self, r, c, k):  
    s = sum(map(int, str(r)+str(c))) 
    return s>k 
  def con_visited(self, rows, cols): 
    visited = [ [0 for j in range(cols)] for i in range(rows) ] 
    return visited 
  def traval(self, r, c, rows, cols, k, visited): 
    if not (0<=r<rows and 0<=c<cols): 
      return 
    if visited[r][c] != 0 or self.block(r, c, k): 
      visited[r][c] = -1 
      return 
    visited[r][c] = 1 
    global acc 
    acc+=1 
    self.traval(r+1, c, rows, cols, k, visited) 
    self.traval(r, c+1, rows, cols, k, visited) 
    self.traval(r-1, c, rows, cols, k, visited) 
    self.traval(r, c-1, rows, cols, k, visited) 
    return acc 
 
if __name__ == "__main__": 
  # 調用測試 
  m = 3 
  n = 3 
  k = 1 
  o = Robot() 
  print(o.hasPath(k, m, n)) 
  print(o.force(m,n,k)) 
  global acc 
  acc = 0 
  print(o.traval(0, 0, m, n, k, o.con_visited(m,n))) 
  print(o.movingCount(k, m, n))