AtCoder Regular Contest 067 - Yakiniku Restaurants

There are N barbecue restaurants along a street.
The restaurants are numbered 1 through N from west to east, and the distance between restaurant i and restaurant i+1 is A_i.
Joisino has M tickets, numbered 1 through M.
Every barbecue restaurant offers barbecue meals in exchange for these tickets.
Restaurant i offers a meal of deliciousness B_{i,j} in exchange for ticket j.
Each ticket can only be used once, but any number of tickets can be used at a restaurant.
Joisino wants to have M barbecue meals by starting from a restaurant of her choice, then repeatedly traveling to another barbecue restaurant and using unused tickets at the restaurant at her current location.
Her eventual happiness is calculated by the following formula: "(The total deliciousness of the meals eaten) - (The total distance traveled)".
Find her maximum possible eventual happiness.

-----Constraints-----
 - All input values are integers.
 - 2≤N≤5×10^3
 - 1≤M≤200
 - 1≤A_i≤10^9
 - 1≤B_{i,j}≤10^9

-----Input-----
The input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_{N-1}
B_{1,1} B_{1,2} ... B_{1,M}
B_{2,1} B_{2,2} ... B_{2,M}
:
B_{N,1} B_{N,2} ... B_{N,M}

-----Output-----
Print Joisino's maximum possible eventual happiness.

-----Sample Input-----
3 4
1 4
2 2 5 1
1 3 3 2
2 2 5 1

-----Sample Output-----
11

The eventual happiness can be maximized by the following strategy: start from restaurant 1 and use tickets 1 and 3, then move to restaurant 2 and use tickets 2 and 4.

Source: atcoder | Difficulty: VERY_HARD


Solutions:
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
import itertools
INF = 10 ** 10
(N, M) = map(int, readline().split())
A = [0, 0] + list(map(int, readline().split()))
B = [[INF] * M] + [list(map(int, line.split())) for line in readlines()]
for i in range(1, N + 1):
	A[i] += A[i - 1]
answer = 0
INF = 10 ** 12
diff = [INF] + [0] * N
left = [list(range(-1, N)) for m in range(M)]
arr = [INF, 2, 1, 2]
for i in range(1, N + 1):
	for m in range(M):
		p = i
		prev_val = 0
		q = left[m][p]
		x = B[i][m]
		while prev_val <= x:
			diff[p] += x - prev_val
			diff[q] -= x - prev_val
			p = q
			q = left[m][p]
			prev_val = B[p][m]
		left[m][i] = p
	ticket_sum = list(itertools.accumulate(diff[::-1]))[::-1]
	for start in range(1, i + 1):
		happy = ticket_sum[start] + A[start] - A[i]
		if answer < happy:
			answer = happy
print(answer)


import sys
readline = sys.stdin.readline
(N, M) = map(int, readline().split())
A = [0] + list(map(int, readline().split()))
for i in range(1, N):
	A[i] += A[i - 1]
INF = 10 ** 9 + 7
B = [list(map(int, readline().split())) for _ in range(N)] + [[INF] * M] + [[0] * M]
right = [[0] * M for _ in range(N)]
for m in range(M):
	L = list(range(N))
	L.sort(key=lambda x: B[x][m])
	RR = list(range(1, N + 3))
	LL = list(range(-1, N + 1))
	for vn in L:
		vn += 1
		right[vn - 1][m] = RR[vn] - 1
		RR[LL[vn]] = RR[vn]
		LL[RR[vn]] = LL[vn]
diff = [0] * (N + 1)
for m in range(M):
	diff[0] += B[0][m]
	pre = B[0][m]
	for i in range(1, N):
		if B[i][m] > pre:
			diff[i] += B[i][m] - pre
			pre = B[i][m]
offset = 0
ans = 0
for l in range(N):
	offset += diff[l]
	for m in range(M):
		if B[l][m] < B[l - 1][m]:
			oldr = right[l - 1][m]
			diff[oldr] -= B[oldr][m] - B[l - 1][m]
			offset += B[l][m] - B[l - 1][m]
			cnt = l
			while cnt < N and right[cnt][m] <= oldr:
				rcm = right[cnt][m]
				diff[rcm] += B[rcm][m] - B[cnt][m]
				cnt = rcm
	ans = max(ans, offset)
	roff = offset
	for r in range(l + 1, N):
		roff += diff[r]
		ans = max(ans, roff - (A[r] - A[l]))
print(ans)


def main():
	import sys
	from array import array
	input = sys.stdin.readline

	class Bit:

		def __init__(self, n):
			self.size = n
			self.size_bit_length = n.bit_length()
			self.tree = array('h', [0] * (n + 1))

		def reset(self):
			self.tree = array('h', [0] * (self.size + 1))

		def sum(self, i):
			s = 0
			while i > 0:
				s += self.tree[i]
				i -= i & -i
			return s

		def add(self, i, x):
			while i <= self.size:
				self.tree[i] += x
				i += i & -i

		def lower_bound(self, w):
			if w <= 0:
				return 0
			x = 0
			k = 1 << self.size_bit_length - 1
			while k:
				if x + k <= self.size and self.tree[x + k] < w:
					w -= self.tree[x + k]
					x += k
				k >>= 1
			return x + 1
	(N, M) = list(map(int, input().split()))
	dist = [0] + list(map(int, input().split()))
	for i in range(N - 1):
		dist[i + 1] += dist[i]
	B = [0] * (M * N)
	for i in range(N):
		BB = list(map(int, input().split()))
		for j in range(M):
			B[j * N + i] = BB[j] * (N + 1) + i + 1
	imos = []
	for i in range(N + 1):
		imos.append([0] * (N + 1 - i))
	bit = Bit(N)
	for m in range(M):
		bit.reset()
		for bi in sorted(B[m * N:(m + 1) * N], reverse=True):
			(b, i) = divmod(bi, N + 1)
			k = bit.sum(i)
			l = bit.lower_bound(k)
			r = bit.lower_bound(k + 1)
			imos[l + 1][i - (l + 1)] += b
			if i != N:
				imos[i + 1][0] -= b
			if r != N + 1:
				imos[l + 1][r - (l + 1)] -= b
			if i != N and r != N + 1:
				imos[i + 1][r - (i + 1)] += b
			bit.add(i, 1)
	for i in range(1, N + 1):
		for j in range(i + 1, N + 1):
			imos[i][j - i] += imos[i][j - 1 - i]
	for i in range(2, N + 1):
		for j in range(i, N + 1):
			imos[i][j - i] += imos[i - 1][j - (i - 1)]
	ans = 0
	for i in range(1, N + 1):
		for j in range(i, N + 1):
			ans = max(ans, imos[i][j - i] - (dist[j - 1] - dist[i - 1]))
	print(ans)

def __starting_point():
	main()
__starting_point()