3996. 涂色

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3996. 涂色

• 题意

  首开始的时候 从连通块中，选择一个作为起点，此后做的扩展操作，都是从这个连通块往边上扩展(就是改起点连通块的颜色)。

• 思路

  

  更清晰的情况：

  • 最终扩展到i
  • 最终扩展到j
  • 最终i,j被同时扩展到

  最终的dp递推式
  $f[i][j]=\{\begin{array}{ll}& \text{f[i][j] = min(f[i+1][j], f[i][j-1])+1}\\ c[i]==c[j]& \text{f[i][j] = min(f[i][j],f[i+1][j-1]+ 1)}\end{array}$

• 代码

  '''
  Author: NEFU AB-IN
  Date: 2023-03-24 17:07:53
  FilePath: \Acwing\3996\3996.py
  LastEditTime: 2023-03-24 19:48:13
  '''
  read = lambda: map(int, input().split())
  from collections import Counter, deque
  from heapq import heappop, heappush
  from itertools import permutations
  
  N = int(5e3 + 10)
  INF = int(2e9)
  
  n = int(input())
  c1 = list(read())
  c = [0]
  dp = [[0] * N for _ in range(N)]
  
  for i in range(n):
      if i == 0 or c1[i] != c1[i - 1]:
          c.append(c1[i])
  
  n = len(c) - 1
  for len in range(2, n + 1):
      l, r = 1, len
      while r <= n:
          dp[l][r] = min(dp[l + 1][r], dp[l][r - 1]) + 1
          if c[l] == c[r]:
              dp[l][r] = min(dp[l][r], dp[l + 1][r - 1] + 1)
          l += 1
          r += 1
  
  print(dp[1][n])