3148. 矩阵中的最大得分

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• [3148. 矩阵中的最大得分](#3148. 矩阵中的最大得分)
• • 题意
  • 思路
  • 代码

3148. 矩阵中的最大得分

题意

给你一个由 正整数 组成、大小为 m x n 的矩阵 grid。你可以从矩阵中的任一单元格移动到另一个位于正下方或正右侧的任意单元格（不必相邻）。从值为 c1 的单元格移动到值为 c2 的单元格的得分为 c2 - c1 。

你可以从 任一 单元格开始，并且必须至少移动一次。

返回你能得到的 最大 总得分。

思路

https://leetcode.cn/problems/maximum-difference-score-in-a-grid/solutions/2774823/nao-jin-ji-zhuan-wan-dppythonjavacgo-by-swux7/

1. dfs
   因为1->2->3和1->3是相同的，那么在dfs的时候只需要dfs下右两个点即可，代码略
2. 二维前缀
   思路就是只和终点起点有关，与路径无关，那对于每个终点，找到并维护二维前缀的最小值即可

代码

# 3.8.19 import
import random
from collections import Counter, defaultdict, deque
from datetime import datetime, timedelta
from functools import lru_cache, reduce
from heapq import heapify, heappop, heappush, nlargest, nsmallest
from itertools import combinations, compress, permutations, starmap, tee
from math import ceil, comb, fabs, floor, gcd, hypot, log, perm, sqrt
from string import ascii_lowercase, ascii_uppercase
from sys import exit, setrecursionlimit, stdin
from typing import Any, Callable, Dict, List, Optional, Tuple, TypeVar, Union

# Constants
TYPE = TypeVar('TYPE')
N = int(2e5 + 10)
M = int(20)
INF = int(1e12)
OFFSET = int(100)
MOD = int(1e9 + 7)

# Set recursion limit
setrecursionlimit(int(2e9))


class Arr:
    array = staticmethod(lambda x=0, size=N: [x() if callable(x) else x for _ in range(size)])
    array2d = staticmethod(lambda x=0, rows=N, cols=M: [Arr.array(x, cols) for _ in range(rows)])
    graph = staticmethod(lambda size=N: [[] for _ in range(size)])


class Math:
    max = staticmethod(lambda a, b: a if a > b else b)
    min = staticmethod(lambda a, b: a if a < b else b)


class IO:
    input = staticmethod(lambda: stdin.readline().rstrip("\r\n"))
    read = staticmethod(lambda: map(int, IO.input().split()))
    read_list = staticmethod(lambda: list(IO.read()))


class Std:
    class Graph:
        def __init__(self, n: int):
            self.n = n
            self.g = Arr.graph(n)

        def add_edge(self, u: int, v: int, w: int):
            """Add an edge to the graph."""
            self.g[u].append((v, w))

# --------------------------------------------------------------- Division line ------------------------------------------------------------------


class Solution:
    def maxScore(self, grid: List[List[int]]) -> int:
        m, n = len(grid), len(grid[0])
        dp = Arr.array2d(INF, m + 1, n + 1)
        ans = -INF

        for i, row in enumerate(grid):
            for j, x in enumerate(row):
                mn = Math.min(dp[i + 1][j], dp[i][j + 1])
                ans = Math.max(ans, x - mn)
                dp[i + 1][j + 1] = Math.min(mn, x)
        return ans


Solution().maxScore([[9, 5, 7, 3], [8, 9, 6, 1], [6, 7, 14, 3], [2, 5, 3, 1]])