Problem:


Score : 400 points

Problem Statement

Consider a grid with H rows and W columns of squares. Let (r, c) denote the square at the r-th row from the top and the c-th column from the left.
Each square is painted black or white.

The grid is said to be good if and only if the following condition is satisfied:

From (1, 1), we can reach (H, W) by moving one square right or down repeatedly, while always being on a white square.

Note that (1, 1) and (H, W) must be white if the grid is good.

Your task is to make the grid good by repeating the operation below. Find the minimum number of operations needed to complete the task. It can be proved that you can always complete the task in a finite number of operations.

Choose four integers r_0, c_0, r_1, c_1(1 \leq r_0 \leq r_1 \leq H, 1 \leq c_0 \leq c_1 \leq W). For each pair r, c (r_0 \leq r \leq r_1, c_0 \leq c \leq c_1), invert the color of (r, c) - that is, from white to black and vice versa.

Constraints

2 \leq H, W \leq 100

Input

Input is given from Standard Input in the following format:

H W
s_{11} s_{12} \cdots s_{1W}
s_{21} s_{22} \cdots s_{2W}
 \vdots
s_{H1} s_{H2} \cdots s_{HW}

Here s_{rc} represents the color of (r, c) - # stands for black, and . stands for white.

Output

Print the minimum number of operations needed.

Sample Input 1

3 3
.##
.#.
##.

Sample Output 1

1

Do the operation with (r_0, c_0, r_1, c_1) = (2, 2, 2, 2) to change just the color of (2, 2), and we are done.

Sample Input 2

2 2
#.
.#

Sample Output 2

2

Sample Input 3

4 4
..##
#...
###.
###.

Sample Output 3

0

No operation may be needed.

Sample Input 4

5 5
.#.#.
#.#.#
.#.#.
#.#.#
.#.#.

Sample Output 4

4



Sample input:
3 3
.##
.#.
##.


Sample output:
1

Submission status: Accepted

Solution code:
import sys, re, os
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians
from itertools import permutations, combinations, product, accumulate
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from fractions import gcd
 
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def S_MAP(): return map(str, input().split())
def LIST(): return list(map(int, input().split()))
def S_LIST(): return list(map(str, input().split()))
 
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7

H, W = MAP()
S = [input() for i in range(H)]
# 1
dp = [[INF] * W for i in range(H)]
dp[0][0] = 0
# 
# if S[0][0] == ".":
#     dp[0][0] = 0
# else:
#     dp[0][0] = 1

# 異なるやつにできるだけ合わなければいい
for h in range(1, H):
    if S[h][0] == S[h-1][0]:
        dp[h][0] = dp[h-1][0]
    else:
        dp[h][0] = dp[h-1][0] + 1
# yoko
# print(dp)
for w in range(1, W):
    if S[0][w] == S[0][w-1]:
        dp[0][w] = dp[0][w-1]
    else:
        dp[0][w] = dp[0][w-1] + 1
# print(*dp, sep="\n")

for i in range(1, H):
    for j in range(1, W):
        # nokori
        if S[i][j] == S[i-1][j] and S[i][j] == S[i][j-1]:
            dp[i][j] = min(dp[i-1][j], dp[i][j-1])
        elif S[i][j] != S[i-1][j] and S[i][j] == S[i][j-1]:
            dp[i][j] = min(dp[i-1][j]+1, dp[i][j-1])
        elif S[i][j] == S[i-1][j] and S[i][j] != S[i][j-1]:
            dp[i][j] = min(dp[i-1][j], dp[i][j-1]+1)            
        else:   
            dp[i][j] = min(dp[i-1][j]+1, dp[i][j-1]+1)

# print(*dp, sep="\n")
last = dp[H-1][W-1]
if S[0][0] == S[H-1][W-1] == ".":
    # #.#.の繰り返しがdp[]
    ans = last // 2
elif S[0][0] == S[H-1][W-1] == "#":
    ans = 1 + last // 2

elif S[0][0] != S[H-1][W-1]:
    ans = (last + 1) // 2
print(ans)



        # if S[i][j] == ".":
        #     dp[i][j] = min(dp[i-1][j], dp[i][j-1])
        # else:
        #     dp[i][j] = min(dp[i-1][j], dp[i][j-1]) + 1




exit()
# print(dp)
# exit()
for i in range(1, H):
    for j in range(1, W):
        # nokori
        if S[i][j] == ".":
            dp[i][j] = min(dp[i-1][j], dp[i][j-1])
        else:
            dp[i][j] = min(dp[i-1][j], dp[i][j-1]) + 1

ans1 = dp[H-1][W-1]
print(dp)
# print(ans1)


# 一回前半+1, ##
S_r = []
for i in range(H):
    l = []
    for j in range(W):
        if S[i][j] == ".":
            l.append("#")
        else:
            l.append(".")
    S_r.append(l)
dp = [[INF] * W for i in range(H)]
S = deepcopy(S_r)
if S[0][0] == ".":
    dp[0][0] = 0
else:
    dp[0][0] = 1

# tate
for h in range(1, H):
    if S[h][0] == "#":
        dp[h][0] = dp[h-1][0] + 1
    else:
        dp[h][0] = dp[h-1][0]
# yoko
for w in range(1, W):
    if S[0][w] == "#":
        dp[0][w] = dp[0][w-1] + 1
    else:
        dp[0][w] = dp[0][w-1]
# exit()
for i in range(1, H):
    for j in range(1, W):
        # nokori
        if S[i][j] == ".":
            dp[i][j] = min(dp[i-1][j], dp[i][j-1])
        else:
            dp[i][j] = min(dp[i-1][j], dp[i][j-1]) + 1

ans2 = dp[H-1][W-1]

print(min(ans1, ans2+1))


exit()

# # 
# dp2 = deepcopy(dp)

# for i in range(1, W):
#     for j in range(1, H):
#         # nokori
#         if S[j][i] == ".":
#             dp2[j][i] = min(dp2[j-1][i], dp2[j][i-1])
#         else:
#             dp2[j][i] = min(dp2[j-1][i], dp2[j][i-1]) + 1
# print("h")
# print(*dp, sep="\n")





# print(dp2)
# print(ans1)


# exit()
# second



dp = [[0] * W for i in range(H)]

# 
if S[0][0] == "#":
    dp[0][0] = 0
else:
    dp[0][0] = 1

# tate
for h in range(1, H):
    if S[h][0] == ".":
        dp[h][0] += dp[h-1][0] + 1
    else:
        dp[h][0] = dp[h-1][0]
# yoko
for w in range(1, W):
    if S[0][w] == ".":
        dp[0][w] += dp[0][w-1] + 1
    else:
        dp[0][w] = dp[0][w-1]
# print(dp)
# exit()
for i in range(1, H):
    for j in range(1, W):
        # nokori
        if S[i][j] == "#":
            dp[i][j] = min(dp[i-1][j], dp[i][j-1])
        else:
            dp[i][j] = min(dp[i-1][j], dp[i][j-1]) + 1

ans2 = dp[H-1][W-1]

print(ans1, ans2)
print(min(ans1, ans2+1))

Submission status: Accepted

Solution code:
if __name__ == "__main__":
    H, W = list(map(int, input().split()))
    A = []
    for _ in range(H):
        s = input()
        A.append(s)

    cost = [[float("inf") for i in range(W)] for i in range(H)]

    cost[0][0] = 1 if A[0][0] == '#' else 0

    for i in range(H)[1:]:
        if A[i-1][0] == '.' and A[i][0] == '#':
            cost[i][0] = cost[i-1][0] + 1
        else:
            cost[i][0] = cost[i-1][0]

    for j in range(W)[1:]:
        if A[0][j-1] == '.' and A[0][j] == '#':
            cost[0][j] = cost[0][j-1] + 1
        else:
            cost[0][j] = cost[0][j-1]

    for i in range(H)[1:]:
        for j in range(W)[1:]:

            # right
            if A[i][j-1] == '.' and A[i][j] == '#':
                cost_right = cost[i][j-1] + 1
            else:
                cost_right = cost[i][j-1]

            # down
            if A[i-1][j] == '.' and A[i][j] == '#':
                cost_down = cost[i-1][j] + 1
            else:
                cost_down = cost[i-1][j]

            cost[i][j] = min(cost_down, cost_right)

    # print(cost)
    print(cost[H-1][W-1])

Submission status: Accepted

Solution code:
import heapq

H,W=map(int,input().split())

mat=[]
for i in range(H):
  array=[x=='.' for x in input()]
  mat.append(array)
#print(mat)

#convert mat to graph
#(i0,j0)->(i1,j1,dist)
graph={}
if mat[0][0]:
  graph[(0,0)]=[(1,1,0)]
else:
  graph[(0,0)]=[(1,1,1)]
  
for i in range(H):
  for j in range(W):
    graph[(i+1,j+1)]=[]
    if mat[i][j]:
      if i<H-1:
        if mat[i+1][j]:
          graph[(i+1,j+1)].append((i+2,j+1,0))
        else:
          graph[(i+1,j+1)].append((i+2,j+1,1))
      if j<W-1:
        if mat[i][j+1]:
          graph[(i+1,j+1)].append((i+1,j+2,0))
        else:
          graph[(i+1,j+1)].append((i+1,j+2,1))
    else:
      if i<H-1:
        graph[(i+1,j+1)].append((i+2,j+1,0))
      if j<W-1:
        graph[(i+1,j+1)].append((i+1,j+2,0))
#print(graph)

# init used,queue,dist
dist={}
hq=[]
dist[(0,0)]=0
heapq.heappush(hq,(0,0,0))
for i in range(1,H+1):
  for j in range(1,W+1):
    dist[(i,j)]=10**9
    heapq.heappush(hq,(i+j,i,j))
#print(queue)

#dkjstra
while(True):
  if len(hq)==0:
    break

  ij,ii,jj=heapq.heappop(hq)
  
  candlist=graph[(ii,jj)]
  for cand in candlist:
    xx,yy,dd=cand
    dist[(xx,yy)]=min(dist[(xx,yy)],dist[(ii,jj)]+dd)
  
print(dist[(H,W)])

Submission status: Accepted

Solution code:
#


def main():
    h, w = map(int, input().split(" "))
    m = []
    for i in range(h):
        line = ['']
        line.extend(input())
        line[0] = line[1]
        m.append(line)
        if i == 0:
            m.append(line)
    dp = [[float("inf")] * (w + 1) for _ in range(h + 1)]
    if m[0][0] == "#":
        dp[0][1] = 1
        dp[1][0] = 1
    else:
        dp[0][1] = 0
        dp[1][0] = 0
    for i in range(1, h + 1):
        for j in range(1, w + 1):
            c = m[i][j]
            sh, sw = i - 1, j
            if dp[sh][sw] == dp[i][j -1]:
                if m[sh][sw] != c:
                    sh, sw = i, j - 1
            elif dp[sh][sw] > dp[i][j - 1]:
                sh, sw = i, j -1
            dp[i][j] = dp[sh][sw]
            if m[sh][sw] != c and c != '.':
                dp[i][j] += 1
            # 上のマスのコスト(dp上の位置)
            # sh, sw = i - 1, j
            # # m上の位置へ変換
            # th, tw = sh - 1, sw - 1
            # if dp[sh][sw] > dp[i][j - 1]:
            #     sh, sw = i, j - 1
            #     th, tw = sh - 1, sw - 1
            #     # どちらのコストも同じなら色が同じ方を選ぶ
            # elif m[th][tw] != c:
            #     sh, sw = i, j - 1
            #     th, tw = sh - 1, sw - 1
            # dp[i][j] = dp[sh][sw]
            # ph, pw = i - 1, j - 1
            # if th < 0 or tw < 0:
            #     continue
            # if m[th][tw] != c:
            #     dp[i][j] += 1
    print(dp[h][w])


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
X = 10**4
H, W = map(int, input().split())

# 入力マップ(1,1~(H,W)を埋める)
map_data = [['.' for j in range(W+1)] for i in range(H+1)]
for i in range(H):
    dat = list(input())
    for j in range(W):
        map_data[i+1][j+1] = dat[j]

# 計算マップ
r_map_data = [[X for j in range(W+1)] for i in range(H+1)]
# 始めのマスが0となるように初期化
r_map_data[0][1] = 0
r_map_data[1][0] = 0

# (1,1)~(H-1,W-1)のマスを調べる
for i in range(H):
    for j in range(W):
        # 真上の値を取得
        t_val = r_map_data[i][j+1]
        # 白→黒ときは+1
        if(map_data[i][j+1] == '.' and map_data[i+1][j+1] == '#'):
            t_val += 1

        # 真左の値を取得
        l_val = r_map_data[i+1][j]
        if(map_data[i+1][j] == '.' and map_data[i+1][j+1] == '#'):
            l_val += 1

        val = min([t_val, l_val])
        # 取得した値をセット
        r_map_data[i+1][j+1] = val

print(r_map_data[H][W])

Submission status: Accepted

Solution code:
import math
import fractions

def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)

    # divisors.sort()
    return divisors

def ValueToBits(x,digit):
    res = [0 for i in range(digit)]
    now = x
    for i in range(digit):
        res[i]=now%2
        now = now >> 1
    return res

def BitsToValue(arr):
    n = len(arr)
    ans = 0
    for i in range(n):
        ans+= arr[i] * 2**i
    return ans

def ValueToArray10(x, digit):
    ans = [0 for i in range(digit)]
    now = x
    for i in range(digit):
        ans[digit-i-1] = now%10
        now = now //10
    return ans
'''
def cmb(n, r, p):
    if (r < 0) or (n < r):
        return 0
    r = min(r, n - r)
    return fact[n] * factinv[r] * factinv[n-r] % p

p = 10 ** 9 + 7
N = 10 ** 6 + 2
fact = [1, 1]  # fact[n] = (n! mod p)
factinv = [1, 1]  # factinv[n] = ((n!)^(-1) mod p)
inv = [0, 1]  # factinv 計算用

for i in range(2, N + 1):
    fact.append((fact[-1] * i) % p)
    inv.append((-inv[p % i] * (p // i)) % p)
    factinv.append((factinv[-1] * inv[-1]) % p)
'''


#a = list(map(int, input().split()))

h,w = list(map(int, input().split()))

s = []
for i in range(h):
    ss=[]
    a=input()
    for j in range(w):
        if(a[j]=='.'):
            ss.append(0)
        else:
            ss.append(1)
    s.append(ss)
        
dp = [[999 for j in range(w)]for i in range(h)]
dp[0][0] = s[0][0]

for i in range(h+w-2):
    for j in range(i+2):
        x = j
        y = i+1-j
        
        if(0<= x and x<=h-1 and 0<=y and y<=w-1):
            #print(x,y)
            if(s[x][y]==0):
                dp[x][y] = min(dp[max(0,x-1)][y], dp[x][max(0,y-1)])
            else:
                if(x!=0 and s[x-1][y]==1):
                    dp[x][y] = dp[x-1][y]
                elif(x!=0 and s[x-1][y]==0):
                    dp[x][y] = dp[x-1][y]+1
                if(y!=0 and s[x][y-1]==1):
                    dp[x][y] = min(dp[x][y],dp[x][y-1])
                elif(y!=0 and s[x][y-1]==0):
                    dp[x][y] = min(dp[x][y],dp[x][y-1]+1)
                   




print(dp[-1][-1])

Submission status: Accepted

Solution code:
import itertools

H,W=map(int, input().split())
garden=[]

for i in range(H):
    garden.append(list(input().replace(".","1").replace("#","0")))

#print(garden)
dct=[(1,0),(0,1),(-1,0),(0,-1)]
#garden=[[1,0,1,0,1],[0,1,0,1,0],[1,0,1,0,1],[0,1,0,1,0],[1,0,1,0,1]]
#H,W=5,5
start=(0,0)
goal=(H-1,W-1)
path=[start]
d=[ [i+j for i in range(W)] for j in range(H)]
#print(d)
done=[(0,0)]
for i, j in itertools.product(range(H),range(W)):
    color=garden[i][j]
    for each in dct:
        di,dj=each[0],each[1]
        if i+di<H and j+dj< W and i+di>=0 and j+dj>=0 and  garden[i+di][j+dj]==color:
            d[i+di][j+dj]=min(d[i+di][j+dj],d[i][j])
            done.append((i+di,j+dj))
            #print((i,j),(i+di,j+dj))
            #print("same")
        elif i+di<H and j+dj< W and i+di>=0 and j+dj>=0 :
            d[i+di][j+dj]=min(d[i+di][j+dj],d[i][j]+1)
            done.append((i+di,j+dj))
            #print((i,j),(i+di,j+dj))
            #print("not same")
    #print(d)
if int(garden[0][0])+int(garden[H-1][W-1])==0:
  print(int((d[H-1][W-1]+1)/2)+1)
else:
  print(int((d[H-1][W-1]+1)/2))

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-

import sys

def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
sys.setrecursionlimit(10 ** 9)
INF = 10 ** 18
MOD = 10 ** 9 + 7

def build_grid(H, W, intv, _type, space=True, padding=False):
    # 入力がスペース区切りかどうか
    if space:
        _input = lambda: input().split()
    else:
        _input = lambda: input()
    _list = lambda: list(map(_type, _input()))
    # 余白の有無
    if padding:
        offset = 1
    else:
        offset = 0
    grid = list2d(H+offset*2, W+offset*2, intv)
    for i in range(offset, H+offset):
        row = _list()
        for j in range(offset, W+offset):
            grid[i][j] = row[j-offset]
    return grid

H, W = MAP()
grid = build_grid(H, W, '*', str, space=0, padding=1)

dp = list2d(H+2, W+2, INF)
if grid[1][1] == '.':
    dp[1][1] = 0
else:
    dp[1][1] = 1
for i in range(H+1):
    for j in range(W+1):
        if grid[i][j] == grid[i][j+1]:
            dp[i][j+1] = min(dp[i][j+1], dp[i][j])
        else:
            dp[i][j+1] = min(dp[i][j+1], dp[i][j] + 1)  
        if grid[i][j] == grid[i+1][j]:  
            dp[i+1][j] = min(dp[i+1][j], dp[i][j])
        else:
            dp[i+1][j] = min(dp[i+1][j], dp[i][j] + 1)
ans = ceil(dp[H][W], 2)
print(ans)

Submission status: Accepted

Solution code:
H,W=map(int,input().split())

a=[[0]*W for i in range(H)]
b=[[0]*W for i in range(H)]

#print(b)

for i in range(H):
	a[i]=list(input())
#print(a)
    
for j in range(1,W):
	b[0][j]=b[0][j-1]+int(not(a[0][j]==a[0][j-1]))

for i in range(1,H):
	b[i][0]=b[i-1][0]+int(not(a[i-1][0]==a[i][0]))
	for j in range(1,W):
		b[i][j]=min(b[i-1][j]+int(not(a[i-1][j]==a[i][j])),b[i][j-1]+int(not(a[i][j-1]==a[i][j])))

if(a[0][0]=="." and a[H-1][W-1]=="."):
	print(int(b[H-1][W-1]/2))
elif(a[0][0]=="#" and a[H-1][W-1]=="#"):
  print(int(b[H-1][W-1]/2+1))
else:
  print(int((b[H-1][W-1]+1)/2))
#print(int(b[H-1][W-1]/2))

Submission status: Accepted

Solution code:
H, W = map(int, input().split())

S = [""] * H

for i in range(H):
    S[i] = input()

dist = [[1000000 for i in range(W)] for j in range(H)]

dist[0][0] = 0 if S[0][0] == "." else 1

for i in range(H):
    for j in range(W):
        if i > 0:
            if S[i][j] == "#":
                dist[i][j] = min(dist[i][j], dist[i - 1][j] +
                                 (1 if S[i - 1][j] == "." else 0))
            else:
                dist[i][j] = min(dist[i][j], dist[i - 1][j])
        if j > 0:
            if S[i][j] == "#":
                dist[i][j] = min(dist[i][j], dist[i][j - 1] +
                                 (1 if S[i][j - 1] == "." else 0))
            else:
                dist[i][j] = min(dist[i][j], dist[i][j - 1])

print(dist[H - 1][W - 1])

Submission status: Accepted

Solution code:
from collections import deque

H, W = map(int, input().split())
s = [list(input()) for _ in range(H)]

d = deque([[0,0,s[0][0]]])
distance = [[float("inf")]*W for _ in range(H)]
if s[0][0] == ".":
    distance[0][0] = 0
else:
    distance[0][0] = 1

while d:
    y, x, c = d.popleft()
    for new_y, new_x in ([int(y)+1, int(x)], [int(y), int(x)+1]):
        if 0 <= new_y <= H-1 and 0 <= new_x <= W-1:
            if c == "." and s[new_y][new_x] == "#":
                new_cost = distance[y][x] + 1
            else:
                new_cost = distance[y][x]
            if new_cost < distance[new_y][new_x]:
                distance[new_y][new_x] = new_cost
                d.append([new_y, new_x, s[new_y][new_x]])

print(distance[H-1][W-1])

Submission status: Accepted

Solution code:
h, w = map(int, input().split())
sw = [list(input()) for _ in range(h)]

result = [[10**5 for i in range(w)] for j in range(h)]
result[0][0] = 0
for i in range(h):
    for j in range(w):
        if j > 0:
            result[i][j] = result[i][j-1]+(sw[i][j-1]!=sw[i][j])
        if i > 0:
            result[i][j] = min(result[i][j], result[i-1][j]+(sw[i-1][j]!=sw[i][j]))


if sw[0][0]=="#":
    print(1+result[h-1][w-1]//2)
else:
    print(result[h-1][w-1]//2+(sw[0][0]!=sw[h-1][w-1]))

Submission status: Accepted

Solution code:
h,w = map(int,input().split())
s = [list(input()) for _ in range(h)]
dp = [[0 for _ in range(w)] for i in range(h)]
if s[0][0] == "#":
  dp[0][0] = 1
for i in range(1,w):
  if s[0][i] == "#" and s[0][i-1] == "#":
    dp[0][i] = dp[0][i-1]
  elif s[0][i] == "#":
    dp[0][i] = dp[0][i-1]+1
  else:
    dp[0][i] = dp[0][i-1]
for i in range(1,h):
  if s[i][0] == "#" and s[i-1][0] == "#":
    dp[i][0] = dp[i-1][0]
  elif s[i][0] == "#":
    dp[i][0] = dp[i-1][0]+1
  else:
    dp[i][0] = dp[i-1][0]
for i in range(1,h):
  for j in range(1,w):
    if s[i][j] == "#":
      if s[i-1][j] == "." and s[i][j-1] == ".":
        dp[i][j] = min(dp[i-1][j]+1,dp[i][j-1]+1)
      elif s[i-1][j] == ".":
        dp[i][j] = min(dp[i-1][j]+1,dp[i][j-1])
      elif s[i][j-1] == ".":
        dp[i][j] = min(dp[i-1][j],dp[i][j-1]+1)
      else:
        dp[i][j] = min(dp[i-1][j],dp[i][j-1])
    else:      
      dp[i][j] = min(dp[i-1][j],dp[i][j-1])
#print(dp)
print(dp[-1][-1])

Submission status: Accepted

Solution code:
H,W=map(int,input().split())
s=[input() for _  in range(H)]
G=[[0 for j in range (W)] for i in range(H)]

if s[0][0]==".":G[0][0]=0
else:G[0][0]=1

for i in range(1,H):
    if s[i][0]==".":
        if s[i-1][0]==".":G[i][0]=G[i-1][0]
        if s[i-1][0]=="#":G[i][0]=G[i-1][0]
    if s[i][0]=="#":
        if s[i-1][0]==".":G[i][0]=G[i-1][0]+1
        if s[i-1][0]=="#":G[i][0]=G[i-1][0]

for i in range(1,W):
    if s[0][i]==".":
        if s[0][i-1]==".":G[0][i]=G[0][i-1]
        if s[0][i-1]=="#":G[0][i]=G[0][i-1]
    if s[0][i]=="#":
        if s[0][i-1]==".":G[0][i]=G[0][i-1]+1
        if s[0][i-1]=="#":G[0][i]=G[0][i-1]

for i in range(1,H):
    for j in range(1,W):
        if s[i][j]==".":
            G[i][j]=min(G[i-1][j],G[i][j-1])
        if s[i][j]=="#":
            if s[i-1][j]=="#" and s[i][j-1]=="#":G[i][j]=min(G[i-1][j],G[i][j-1])
            if s[i-1][j]=="." and s[i][j-1]=="#":G[i][j]=min(G[i-1][j]+1,G[i][j-1])
            if s[i-1][j]=="#" and s[i][j-1]==".":G[i][j]=min(G[i-1][j],G[i][j-1]+1)
            if s[i-1][j]=="." and s[i][j-1]==".":G[i][j]=min(G[i-1][j]+1,G[i][j-1]+1)

print(G[H-1][W-1])

Submission status: Accepted

Solution code:
import sys
import numpy as np
from collections import deque
sys.setrecursionlimit(10 ** 6)
input = sys.stdin.readline
H, W = [int(x) for x in input().strip().split()]
G = np.zeros((H, W), dtype=int)
pre = np.ones(W, dtype=int) * -1
NH = H
for h in range(H):
    s = np.array([1 if s == '#' else 0 for s in input().strip()])
    if np.all(s == pre):
        NH -= 1
    else:
        G[h, :] = s
        pre = s

H = NH
C = [[float('inf') for _ in range(W)] for _ in range(H)]
pre = ''
def dfs(r, c, cost):
    # print(' -- dfs --')
    C[r][c] = cost
    ret = deque([])
    q = deque([(r, c)])
    while q:
        cr, cc = q.popleft()
        # print('    cr = {}, cc = {}'.format(cr, cc))
        for i, j in [(0, 1), (1, 0)]:
            if not(0 <= cr + i < H and 0 <= cc + j < W):
                continue
            if C[cr+i][cc+j] != float('inf'):
                continue
            if G[r][c] == G[cr+i][cc+j]:
                C[cr+i][cc+j] = cost
                q.append((cr+i, cc+j))
                if cr+i == H-1 and cc+j == W-1:
                    return ret
            else:
                ret.append((cr+i, cc+j))
    # print(ret)
    return ret
q = deque([(0, 0)])
cost = 0
while True:
    # print('q = {}'.format(q))
    nq = deque([])
    if G[q[0][0]][q[0][1]] == 1:
        cost += 1
    for r, c in q:
        # print('  r = {}, c = {}'.format(r, c))
        if C[r][c] != float('inf'):
            continue
        nq.extend(dfs(r, c, cost))
    q = nq
    # print(C)
    # print('nq = {}'.format(nq))
    if C[H-1][W-1] != float('inf'):
        print(C[H-1][W-1])
        exit()

Submission status: Accepted

Solution code:
import sys

grid = []
H, W = map(int, input().split(' '))
for i in range(H):
    grid.append(input())

dp = [[0 for i in range(W)] for j in range(H)]
if grid[0][0] == '#':
    dp[0][0] = 1

for i in range(1, H):
    dp[i][0] = dp[i-1][0] + (grid[i][0] == '#' and grid[i-1][0] == '.')

for j in range(1, W):
    dp[0][j] = dp[0][j-1] + (grid[0][j] == '#' and grid[0][j-1] == '.')

for i in range(1, H):
    for j in range(1, W):
        choice_1 = dp[i-1][j] + (grid[i][j] == '#' and grid[i-1][j] == '.')
        choice_2 = dp[i][j-1] + (grid[i][j] == '#' and grid[i][j-1] == '.')
        dp[i][j] = min(choice_1, choice_2)

print(dp[H-1][W-1])

Submission status: Accepted

Solution code:
H, W = map(int, input().split())
def change(x):
    if x == '#':
        return 1
    else:
        return 0
field = list()
for i in range(H):
    field.append(list(map(change,[i for i in input()])))

vector = [[1, 0], [0, 1]]
check_list = [[0 for _ in range(W)] for i in range(H)]
check_list[0][0] = 1
count_list = [[[0, [0, 0]] for _ in range(W)] for i in range(H)]
count_list[0][0][0] = field[0][0]
zahyo_check = [[(0, 0)]]
for i in range(H+W-2):
    zahyo = zahyo_check[i]
    zahyo_kari = list()
    for (y, x) in zahyo:
        for (dy, dx) in vector:
            v = count_list[y][x][0]
            y_k = y + dy
            x_k = x + dx
            try:
                if field[y_k][x_k] == 1 and field[y][x] == 0:
                    v += 1
                        
                if check_list[y_k][x_k] == 0:
                    count_list[y_k][x_k][0] = v
                    count_list[y_k][x_k][1] = [y, x]
                    check_list[y_k][x_k] = 1
                    zahyo_kari.append((y_k, x_k))
                    
                else:
                    if v < count_list[y_k][x_k][0]:
                        count_list[y_k][x_k][0] = v
                        count_list[y_k][x_k][1] = [y, x]
                        
            except:
                pass
    zahyo_check.append(zahyo_kari)

print(count_list[H-1][W-1][0])

Submission status: Accepted

Solution code:
from collections import deque

h,w = map(int,input().split())
F = [input() for _ in range(h)]
direct = [[0,1],[1,0]]
que = deque()
que.append([0,0])
INF = 10**5
dp = [[INF]*w for _ in range(h)]


dp[0][0] = 0

while len(que)>0:  
  y,x = que.popleft()    
  for dy,dx in direct:    
    ny = y+dy
    nx = x+dx
    if (0 <= nx < w) and (0 <= ny < h):
      if F[ny][nx] == F[y][x]:         
        if dp[ny][nx] > dp[y][x]:
          dp[ny][nx] = dp[y][x]
          que.append([ny,nx])
      else:                
        if dp[ny][nx] > dp[y][x] + 1 :        
          dp[ny][nx] = dp[y][x] + 1          
          que.append([ny,nx])   


ans = dp[-1][-1]//2
if F[0][0] == '#' or F[-1][-1] == '#':
  ans += 1

print(ans)

Submission status: Accepted

Solution code:
h, w = map(int, input().split())
dp = [[0]] * h
m = [''] * h
inf = h * w

for i in range(h):
  dp[i] = [0] * w 
  m[i] = input()
# print(h, w)
# print(m)

    
if m[0][0] == '#':
  dp[0][0] = 1

# print(dp)
for i in range(h):
  for j in range(w):
    if i == 0 and j == 0:
      continue
    
    current = m[i][j]
    ue = '' if i == 0 else m[i-1][j]
    ue_val = inf if i == 0 else dp[i-1][j]
    left = '' if j == 0 else m[i][j-1]
    left_val = inf if j == 0 else dp[i][j-1]
    
    if current == '#' and ue == '.':
      ue_val += 1
    if current == '#' and left == '.':
      left_val += 1
    
    dp[i][j] = min(ue_val, left_val)
        
        

# print(dp)
print(dp[h-1][w-1])

Submission status: Accepted

Solution code:
def inp(wide):
    a = input()
    ans = []
    for i in range(wide):
        if a[i] == '.':
            ans.append(['w',float('Inf')])
        else:
            ans.append(['b',float('Inf')])
    return ans
def chang(up,left,nex): 
    if nex[0] == 'w':
        return min(up[1],left[1])
    else:
        d = up[1]
        g = left[1]
        if up[0] == 'w':
            d = d+1
        if left[0] == 'w':
            g = g+1
        return min(d,g)
def main(board,high,wide,already):
    for i in range(wide):
        if 0 <= already-i and already -i < high:
            nex = board[already-i][i]
            if 0 <= already-i-1 and 0 <= i-1:
                board[already-i][i][1] = chang(board[already-i-1][i],board[already-i][i-1],nex)
            elif 0 <= already-i-1 and 0 > i-1:
                board[already-i][i][1] = chang(board[already-i-1][i],['w',float('inf')],nex)
            else:
                board[already-i][i][1] = chang(['w',float('inf')],board[already-i][i-1],nex)
    
    if already == high + wide -1:
        return board[high-1][wide-1][1]
    return main(board,high,wide,already+1)
    

a = input().split()
high = int(a[0])
wide = int(a[1])

board = []
for i in range(high):
    board.append([])
    board[i] = inp(wide)
if board[0][0][0] == 'w':
    board[0][0][1] = 0
else:
    board[0][0][1] = 1

if high < wide:
    bo = []
    for i in range(wide):
        bo.append([])
        for j in range(high):
            bo[i].append(board[j][i])   
else:
    bo = board
ans = main(bo,max(wide,high),min(wide,high),1)
print(ans)

Submission status: Accepted

Solution code:
from heapq import heappush,heappop,heapify
from collections import deque,defaultdict,Counter
from itertools import permutations,combinations,groupby
import sys,bisect,string,math,time,functools,random
def Golf():*a,=map(int,open(0))
def I():return int(input())
def S_():return input()
def IS():return input().split()
def LS():return [i for i in input().split()]
def LI():return [int(i) for i in input().split()]
def LI_():return [int(i)-1 for i in input().split()]
def NI(n):return [int(input()) for i in range(n)]
def NI_(n):return [int(input())-1 for i in range(n)]
def StoLI():return [ord(i)-97 for i in input()]
def ItoS(n):return chr(n+97)
def LtoS(ls):return ''.join([chr(i+97) for i in ls])
def GI(V,E,Directed=False,index=0):
    org_inp=[];g=[[] for i in range(n)]
    for i in range(E):
        inp=LI();org_inp.append(inp)
        if index==0:inp[0]-=1;inp[1]-=1
        if len(inp)==2:
            a,b=inp;g[a].append(b)
            if not Directed:g[b].append(a)
        elif len(inp)==3:
            a,b,c=inp;aa=(inp[0],inp[2]);bb=(inp[1],inp[2]);g[a].append(bb)
            if not Directed:g[b].append(aa)
    return g,org_inp
def GGI(h,w,search=None,replacement_of_found='.',mp_def={'#':1,'.':0}):
#h,w,g,sg=GGI(h,w,search=['S','G'],replacement_of_found='.',mp_def={'#':1,'.':0}) # sample usage
    mp=[1]*(w+2);found={}
    for i in range(h):
        s=input()
        for char in search:
            if char in s:
                found[char]=((i+1)*(w+2)+s.index(char)+1)
                mp_def[char]=mp_def[replacement_of_found]
        mp+=[1]+[mp_def[j] for j in s]+[1]
    mp+=[1]*(w+2)
    return h+2,w+2,mp,found
def TI(n):return GI(n,n-1)
def bit_combination(k,n=2):return [[tb//(n**bt)%n for bt in range(k)] for tb in range(n**k)]
def show(*inp,end='\n'):
    if show_flg:print(*inp,end=end)

YN=['YES','NO'];Yn=['Yes','No']
mo=10**9+7
inf=float('inf')
l_alp=string.ascii_lowercase
#sys.setrecursionlimit(10**7)
input=lambda: sys.stdin.readline().rstrip()

def ran_input():
    n=random.randint(4,16)
    rmin,rmax=1,10
    a=[random.randint(rmin,rmax) for _ in range(n)]
    return n,a

show_flg=False
show_flg=True

h,w=LI()
h,w,g,sg=GGI(h,w,search=['S','G'],replacement_of_found='.',mp_def={'#':1,'.':0})
dp=[10**6]*(h*w)
g[1],dp[1]=0,0

for j in range(h*w-h):
    r,c=j//w,j%w
    if (r in [0,h-1]) or (c in [0,w-1]):
      	if j!=1:
            continue

    dp[j+1]=min(dp[j]+1 if (g[j],g[j+1])==(0,1) else dp[j],dp[j+1])
    dp[j+w]=min(dp[j]+1 if (g[j],g[j+w])==(0,1) else dp[j],dp[j+w])

print(dp[(h-2)*w+w-2])

Submission status: Accepted

Solution code:
def inputs(): return [int(x) for x in input().split()]
h,w = inputs()
meiro=[list(input()) for _ in range(h)]
visit = [[-1]*w for _ in range(h)]
if meiro[0][0]=="#":
    visit[0][0]=1
else:
    visit[0][0]=0
for j in range(1,w):
    if meiro[0][j]=="#":
        if meiro[0][j-1]=="#":
            visit[0][j]=visit[0][j-1]
        else:
            visit[0][j]=visit[0][j-1]+1
    if meiro[0][j]==".":
        visit[0][j]=visit[0][j-1]
for i in range(1,h):
    if meiro[i][0]=="#":
        if meiro[i-1][0]=="#":
            visit[i][0]=visit[i-1][0]
        else:
            visit[i][0]=visit[i-1][0]+1
    if meiro[i][0]==".":
        visit[i][0]=visit[i-1][0]
#print(visit)
for i in range(1,h):
    for j in range(1,w):
        if meiro[i][j]=="#":
            if meiro[i-1][j]=="#" and meiro[i][j-1]=="#":
                visit[i][j]=min(visit[i-1][j],visit[i][j-1])
            elif meiro[i-1][j]=="#":
                visit[i][j]=min(visit[i-1][j],visit[i][j-1]+1)
            elif meiro[i][j-1]=="#":
                visit[i][j]=min(visit[i-1][j]+1,visit[i][j-1])
            else:
                visit[i][j]=min(visit[i-1][j]+1,visit[i][j-1]+1)
        else:
            visit[i][j]=min(visit[i-1][j],visit[i][j-1])
print(visit[h-1][w-1])