Program to count number of words we can generate from matrix of letters in Python

Suppose we have a 4 x 4 board of letters and a list of words, we have to find the largest number of words that can be generated in the board by a sequence of adjacent letters, using one cell at most once per word (but we can reuse cells for other words). We can go up, down, left, right, or diagonal direction.

So, if the input is like

words = ["bat", "far", "mat"], then the output will be 3, as we can generate mat [0,1] → [1,1] → [2,0], bat [0,2] → [1,1] → [2,2], and far [0,2] → [1,3] → [2,3].

To solve this, we will follow these steps −

• N := row count of A, M := column count of size of A

• trie := a new map

• for each word in words, do

  • current := trie

  • for each c in word, do

    • if c is in current, then

      • current := current[c]

    • otherwise,

      • current[c] := a new map

      • current := current[c]

  • current["*"] := True

• ans := 0

• Define a function dfs() . This will take x, y, d

• if "*" is in d, then

  • remove d["*"]

  • ans := ans + 1

• temp := A[x, y]

• A[x, y] := "#"

• for each item i in [x - 1, x, x + 1], do

  • for each item j in [y - 1, y, y + 1], do

    • if i and j in range of matrix and A[i, j] is in d, then

      • dfs(i, j, d[A[i, j]])

• A[x, y] := temp

• From the main method do the following −

• for i in range 0 to N, do

  • for j in range 0 to M, do

    • if A[i][j] is in trie, then

      • dfs(i, j, trie[A[i, j]])

• return ans

Example (Python)

Let us see the following implementation to get better understanding −

 Live Demo

class Solution:
   def solve(self, A, words):
      N = len(A)
      M = len(A[0])
      trie = dict()
      for word in words:
         current = trie
         for c in word:
            if c in current:
               current = current[c]
            else:
               current[c] = dict()
               current = current[c]
         current["*"] = True
      ans = 0
      def dfs(x, y, d):
         nonlocal ans
         if "*" in d:
            del d["*"]
            ans += 1
         temp = A[x][y]
         A[x][y] = "#"
         for i in [x - 1, x, x + 1]:
            for j in [y - 1, y, y + 1]:
               if 0 <= i < N and 0 <= j < M and A[i][j] in d: dfs(i, j, d[A[i][j]])
         A[x][y] = temp
      for i in range(N):
         for j in range(M):
            if A[i][j] in trie:
               dfs(i, j, trie[A[i][j]])
      return ans
ob = Solution()
matrix = [
   ["m", "b", "f", "d"],
   ["x", "a", "y", "a"],
   ["t", "z", "t", "r"],
   ["s", "q", "q", "q"]
]
words = ["bat", "far", "mat"]
print(ob.solve(matrix, words))

Input

[
["m", "b", "f", "d"],
["x", "a", "y", "a"],
["t", "z", "t", "r"],
["s", "q", "q", "q"] ],
["bat", "far", "mat"]

Output

3