Problem:


Score : 500 points

Problem Statement

We have a grid with H horizontal rows and W vertical columns. Let (i,j) denote the square at the i-th row from the top and the j-th column from the left.

The square (i, j) has two numbers A_{ij} and B_{ij} written on it.

First, for each square, Takahashi paints one of the written numbers red and the other blue.

Then, he travels from the square (1, 1) to the square (H, W). In one move, he can move from a square (i, j) to the square (i+1, j) or the square (i, j+1). He must not leave the grid.

Let the unbalancedness be the absolute difference of the sum of red numbers and the sum of blue numbers written on the squares along Takahashi's path, including the squares (1, 1) and (H, W).

Takahashi wants to make the unbalancedness as small as possible by appropriately painting the grid and traveling on it.

Find the minimum unbalancedness possible.

Constraints

2 \leq H \leq 80

2 \leq W \leq 80

0 \leq A_{ij} \leq 80

0 \leq B_{ij} \leq 80

All values in input are integers.

Input

Input is given from Standard Input in the following format:

H W
A_{11} A_{12} \ldots A_{1W}
:
A_{H1} A_{H2} \ldots A_{HW}
B_{11} B_{12} \ldots B_{1W}
:
B_{H1} B_{H2} \ldots B_{HW}

Output

Print the minimum unbalancedness possible.

Sample Input 1

2 2
1 2
3 4
3 4
2 1

Sample Output 1

0

By painting the grid and traveling on it as shown in the figure below, the sum of red numbers and the sum of blue numbers are 3+3+1=7 and 1+2+4=7, respectively, for the unbalancedness of 0.

Sample Input 2

2 3
1 10 80
80 10 1
1 2 3
4 5 6

Sample Output 2

2



Sample input:
2 2
1 2
3 4
3 4
2 1


Sample output:
0

Submission status: Wrong Answer

Solution code:
import numpy as np
i8 = np.int64
i4 = np.int32

def calc(dp1, dp2, k):
    dp2[k:] += dp1[:dp1.shape[0]-k]
    dp2[:dp2.shape[0]-k] += dp1[k:]

def solve(z, dp):
    zero = dp.shape[2] // 2
    dp[0, 0, zero + z[0, 0]] = 1
    dp[0, 0, zero - z[0, 0]] = 1
    for x in range(1, z.shape[1]):
        calc(dp[0, x - 1], dp[0, x], z[0, x])
    for y in range(1, z.shape[0]):
        calc(dp[y - 1, 0], dp[y, 0], z[y, 0])
        for x in range(1, z.shape[1]):
            calc(dp[y, x - 1], dp[y, x], z[y, x])
            calc(dp[y - 1, x], dp[y, x], z[y, x])
            if (x + y) % 50 == 0:
                dp[y, x] = dp[y, x] > 0
    for i in range(zero, dp.shape[2]):
        if dp[dp.shape[0] - 1, dp.shape[1] - 1, i] > 0:
            return i - zero
    return -1

def main2():
    stdin = open('/dev/stdin')
    H, W = map(int, stdin.readline().split())
    a = np.empty((H, W), i8)
    b = np.empty((H, W), i8)
    for i in range(H):
        for j, c in enumerate(map(int, stdin.readline().split())):
            a[i, j] = c
    for i in range(H):
        for j, c in enumerate(map(int, stdin.readline().split())):
            b[i, j] = c
    z = np.abs(a - b)
    dp = np.zeros((H, W, 80 * 80 *2 + 1), i8)
    ans = solve(z, dp)
    print(ans)

Submission status: Wrong Answer

Solution code:
import numpy as np
i8 = np.int64
i4 = np.int32

def calc(dp1, dp2, k):
    dp2[k:] += dp1[:dp1.shape[0]-k]
    dp2[:dp2.shape[0]-k] += dp1[k:]

def solve(z, dp):
    zero = dp.shape[2] // 2
    dp[0, 0, zero + z[0, 0]] = 1
    dp[0, 0, zero - z[0, 0]] = 1
    for x in range(1, z.shape[1]):
        calc(dp[0, x - 1], dp[0, x], z[0, x])
    for y in range(1, z.shape[0]):
        calc(dp[y - 1, 0], dp[y, 0], z[y, 0])
        for x in range(1, z.shape[1]):
            calc(dp[y, x - 1], dp[y, x], z[y, x])
            calc(dp[y - 1, x], dp[y, x], z[y, x])
            if (x + y) % 10 == 0:
                dp[y, x] = dp[y, x] > 0
    for i in range(zero, dp.shape[2]):
        if dp[dp.shape[0] - 1, dp.shape[1] - 1, i] > 0:
            return i - zero
    return -1

def main2():
    stdin = open('/dev/stdin')
    H, W = map(int, stdin.readline().split())
    a = np.empty((H, W), i8)
    b = np.empty((H, W), i8)
    for i in range(H):
        for j, c in enumerate(map(int, stdin.readline().split())):
            a[i, j] = c
    for i in range(H):
        for j, c in enumerate(map(int, stdin.readline().split())):
            b[i, j] = c
    z = np.abs(a - b)
    dp = np.zeros((H, W, 80 * 80 *2 + 1), i8)
    ans = solve(z, dp)
    print(ans)

Submission status: Wrong Answer

Solution code:
import numpy as np
i8 = np.int64
i4 = np.int32

def calc(dp1, dp2, k):
    dp2[k:] += dp1[:dp1.shape[0]-k]
    dp2[:dp2.shape[0]-k] += dp1[k:]

def solve(z, dp):
    zero = dp.shape[2] // 2
    dp[0, 0, zero + z[0, 0]] = 1
    dp[0, 0, zero - z[0, 0]] = 1
    for x in range(1, z.shape[1]):
        calc(dp[0, x - 1], dp[0, x], z[0, x])
    for y in range(1, z.shape[0]):
        calc(dp[y - 1, 0], dp[y, 0], z[y, 0])
        for x in range(1, z.shape[1]):
            calc(dp[y, x - 1], dp[y, x], z[y, x])
            calc(dp[y - 1, x], dp[y, x], z[y, x])
    for i in range(zero, dp.shape[2]):
        if dp[dp.shape[0] - 1, dp.shape[1] - 1, i] > 0:
            return i - zero
    return -1

def main2():
    stdin = open('/dev/stdin')
    H, W = map(int, stdin.readline().split())
    a = np.empty((H, W), i8)
    b = np.empty((H, W), i8)
    for i in range(H):
        for j, c in enumerate(map(int, stdin.readline().split())):
            a[i, j] = c
    for i in range(H):
        for j, c in enumerate(map(int, stdin.readline().split())):
            b[i, j] = c
    z = np.abs(a - b)
    dp = np.zeros((H, W, 80 * 80 *2 + 1), i8)
    ans = solve(z, dp)
    print(ans)


main2()

Submission status: Wrong Answer

Solution code:
M = 6400*4
mid = M//2
INF = 10**18

H,W = map(int, input().split())
As = []
for i in range(H):
    As.append(list(map(int, input().split())))
diffs = []
for i in range(H):
    bs = list(map(int, input().split()))
    diffs.append([abs(a-b) for a,b in zip(As[i],bs)])

# bitset高速化
# 初期値
dp = [[0]*W for j in range(H)]
dp[0][0] = (diffs[0][0]+1) << mid #プラスマイナス考慮して、下駄をはかせる
for i in range(H):
    for j in range(W):
        # 行方向
        if i+1 < H:
            d = diffs[i+1][j]
            dp[i+1][j] |= dp[i][j] >> d  
            dp[i+1][j] |= dp[i][j] << d  
        # 列方向
        if j+1 < W:
            d = diffs[i][j+1]
            dp[i][j+1] |= dp[i][j] >> d
            dp[i][j+1] |= dp[i][j] << d

ans = INF
for i in range(M):
    if dp[H-1][W-1] >> i & 1:
        # print(i-mid)
        ans = min(ans, abs(i-mid))
print(ans)

Submission status: Wrong Answer

Solution code:
H,W = map(int, input().split())
As = []
for i in range(H):
    As.append(list(map(int, input().split())))
diffs = []
for i in range(H):
    bs = list(map(int, input().split()))
    diffs.append([abs(a-b) for a,b in zip(As[i],bs)])
 
M = 20000
mid = M//2
# bitset高速化
# (i,j)において、偏りがkになることがあるか(愚直)
# 初期値
dp = [[0]*W for j in range(H)]
dp[0][0] = (diffs[0][0]+1) << mid #プラスマイナス考慮して、下駄をはかせる
for i in range(H):
    for j in range(W):
        # 行方向
        if i+1 < H:
            d = diffs[i+1][j]
            dp[i+1][j] |= dp[i][j] >> d  
            dp[i+1][j] |= dp[i][j] << d  
        # 列方向
        if j+1 < W:
            d = diffs[i][j+1]
            dp[i][j+1] |= dp[i][j] >> d
            dp[i][j+1] |= dp[i][j] << d

INF = 10**18
ans = INF
# print("ans",dp[H-1][W-1])
for i in range(M):
    if dp[H-1][W-1] >> i & 1:
        ans = min(ans, abs(i-mid))
print(ans)

Submission status: Wrong Answer

Solution code:
H,W = map(int, input().split())
As = []
for i in range(H):
    As.append(list(map(int, input().split())))
diffs = []
for i in range(H):
    bs = list(map(int, input().split()))
    diffs.append([abs(a-b) for a,b in zip(As[i],bs)])
 
M = 12800
mid = 6400
# bitset高速化
# (i,j)において、偏りがkになることがあるか(愚直)
# 初期値
dp = [[0]*W for j in range(H)]
dp[0][0] = (diffs[0][0]+1) << mid #プラスマイナス考慮して、下駄をはかせる
for i in range(H):
    for j in range(W):
        # 行方向
        if i+1 < H:
            d = diffs[i+1][j]
            dp[i+1][j] |= dp[i][j] >> d  
            dp[i+1][j] |= dp[i][j] << d  
        # 列方向
        if j+1 < W:
            d = diffs[i][j+1]
            dp[i][j+1] |= dp[i][j] >> d
            dp[i][j+1] |= dp[i][j] << d

INF = 10**18
ans = INF
# print("ans",dp[H-1][W-1])
for i in range(M):
    if dp[H-1][W-1] >> i & 1:
        ans = min(ans, abs(i-mid))
print(ans)

Submission status: Wrong Answer

Solution code:
import sys
reader = (s.rstrip() for s in sys.stdin)
input = reader.__next__

h,w = map(int, input().split())
a = [list(map(int, input().split())) for i in range(h)]
b = [list(map(int, input().split())) for i in range(h)]

ma = 90
DP = [[[0]*(2*90) for j in range(w+1)] for i in range(h+1)]
mid = ma
DP[0][0][mid] = 1

for i in range(h):
    for j in range(w):
        k = abs(a[i][j]-b[i][j])
        for l in range(2*ma):
            if not DP[i][j][l]:
                continue
            if 0<=l-k:
                DP[i+1][j][l-k] = 1
                DP[i][j+1][l-k] = 1
            if l+k<2*ma:
                DP[i+1][j][l+k] = 1
                DP[i][j+1][l+k] = 1

ans = float("Inf")
for i, j in [(h,w-1),(h-1,w)]:
    for k in range(2*ma):
        if DP[i][j][k]:
            ans = min(ans, abs(mid-k))

print(ans)