Word Search解題報告

DFS(深度優先搜索)

首先介紹下什麼是DFS吧。

DFS個人理解其實就是一條路走到黑，發現沒路了，再回到上一個地方，看有沒有路。

1. 查看根節點是否知足條件

   知足條件， 加入棧

   不知足，pass，棧爲空，退出循環

2. 查看該節點下的直接子節點是否知足條件

   知足條件，重複步驟2

   不知足條件，將父節點加入棧

3. 不斷循環，直到棧爲空

你們也看到了，這種概念一理清楚，就知道，能夠用遞歸去實現DFS。

Word Search

Word Search

首先思路應該很明顯了，咱們先找到board中跟word的首字母相同的座標，而後把這個設置爲當前的位置進行深度優先搜索，也就是查找當前位置的上下左右的字母，看看是否符合條件，不符合條件的話，就返回。符合的話，就把該位置設置爲當前位置，重複上面的步驟，直到找到整個word爲止。

可是有幾個點須要主要:

1. 查找的位置，不能超過board的邊界
2. 已經查找過的位置，須要標記出來，避免重複查找。這裏我引入了一個visited數組，做爲標記。

代碼以下:

class Solution {
    func exist(_ board: [[Character]], _ word: String) -> Bool {
        guard board.count > 0 else { return false }

        var visited = Array(repeating: Array(repeating: false, count: board[0].count), count: board.count)
        let cs = Array(word)
        for i in 0..<board.count {
          for j in 0..<board[0].count {
            if cs[0] == board[i][j] && dfs(board, i, j, cs, 0, &visited) {
              return true
            }
          }
        }
        return false
      }

      func dfs(_ board: [[Character]], _ i: Int, _ j: Int, _ cs: [Character], _ pos: Int, _ visited: inout [[Bool]]) -> Bool {
        guard cs.count > pos else { return true }

        if (i < 0 || i >= board.count || j < 0 || j >= board[0].count || board[i][j] != cs[pos] || visited[i][j]) {
          return false
        }
        visited[i][j] = true
        if dfs(board, i - 1, j, cs, pos + 1, &visited) ||
          dfs(board, i + 1, j, cs, pos + 1, &visited) ||
          dfs(board, i, j - 1, cs, pos + 1, &visited) ||
          dfs(board, i, j + 1, cs, pos + 1, &visited) {
          return true
        }
        visited[i][j] = false
        return false
      }
}
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Word Search 2

212. Word Search II

看了題目後，首先的想法就是，把這個words遍歷一遍，根據上面的dfs將符合的word給過濾出來。固然理想很豐滿，首先就是，會出現重複的word，這個沒有過。而後把重複的給去除了:

Array(Set(results))
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提交後，毫無心外的，超時了。

其實你算下複雜度，若是按照上面的方法的話，複雜度應該就是:

O(k * m * n * l * x)

k: words數組的數量
m: board的長
n: board的寬
l: word的最長的長度
x: 首字母跟board中字符相同的數量
複製代碼

給大家感覺下，沒有過的測試數據:

[["a","a","a","a"],["a","a","a","a"],["a","a","a","a"],["a","a","a","a"],["b","c","d","e"],["f","g","h","i"],["j","k","l","m"],["n","o","p","q"],["r","s","t","u"],["v","w","x","y"],["z","z","z","z"]]

["aaaaaaaaaaaaaaaa","aaaaaaaaaaaaaaab","aaaaaaaaaaaaaaac","aaaaaaaaaaaaaaad","aaaaaaaaaaaaaaae","aaaaaaaaaaaaaaaf","aaaaaaaaaaaaaaag","aaaaaaaaaaaaaaah","aaaaaaaaaaaaaaai","aaaaaaaaaaaaaaaj","aaaaaaaaaaaaaaak","aaaaaaaaaaaaaaal","aaaaaaaaaaaaaaam","aaaaaaaaaaaaaaan","aaaaaaaaaaaaaaao","aaaaaaaaaaaaaaap","aaaaaaaaaaaaaaaq","aaaaaaaaaaaaaaar","aaaaaaaaaaaaaaas","aaaaaaaaaaaaaaat","aaaaaaaaaaaaaaau","aaaaaaaaaaaaaaav","aaaaaaaaaaaaaaaw","aaaaaaaaaaaaaaax","aaaaaaaaaaaaaaay","aaaaaaaaaaaaaaaz","aaaaaaaaaaaaaaaa","aaaaaaaaaaaaaaab","aaaaaaaaaaaaaaac","aaaaaaaaaaaaaaad","aaaaaaaaaaaaaaae","aaaaaaaaaaaaaaaf","aaaaaaaaaaaaaaag","aaaaaaaaaaaaaaah","aaaaaaaaaaaaaaai","aaaaaaaaaaaaaaaj","aaaaaaaaaaaaaaak","aaaaaaaaaaaaaaal","aaaaaaaaaaaaaaam","aaaaaaaaaaaaaaan","aaaaaaaaaaaaaaao","aaaaaaaaaaaaaaap","aaaaaaaaaaaaaaaq","aaaaaaaaaaaaaaar","aaaaaaaaaaaaaaas","aaaaaaaaaaaaaaat","aaaaaaaaaaaaaaau","aaaaaaaaaaaaaaav","aaaaaaaaaaaaaaaw","aaaaaaaaaaaaaaax","aaaaaaaaaaaaaaay","aaaaaaaaaaaaaaaz","aaaaaaaaaaaaaaba","aaaaaaaaaaaaaabb","aaaaaaaaaaaaaabc","aaaaaaaaaaaaaabd","aaaaaaaaaaaaaabe","aaaaaaaaaaaaaabf","aaaaaaaaaaaaaabg","aaaaaaaaaaaaaabh","aaaaaaaaaaaaaabi","aaaaaaaaaaaaaabj","aaaaaaaaaaaaaabk","aaaaaaaaaaaaaabl","aaaaaaaaaaaaaabm","aaaaaaaaaaaaaabn","aaaaaaaaaaaaaabo","aaaaaaaaaaaaaabp","aaaaaaaaaaaaaabq","aaaaaaaaaaaaaabr","aaaaaaaaaaaaaabs","aaaaaaaaaaaaaabt","aaaaaaaaaaaaaabu","aaaaaaaaaaaaaabv","aaaaaaaaaaaaaabw","aaaaaaaaaaaaaabx","aaaaaaaaaaaaaaby","aaaaaaaaaaaaaabz","aaaaaaaaaaaaaaca","aaaaaaaaaaaaaacb","aaaaaaaaaaaaaacc","aaaaaaaaaaaaaacd","aaaaaaaaaaaaaace","aaaaaaaaaaaaaacf","aaaaaaaaaaaaaacg","aaaaaaaaaaaaaach","aaaaaaaaaaaaaaci","aaaaaaaaaaaaaacj","aaaaaaaaaaaaaack","aaaaaaaaaaaaaacl","aaaaaaaaaaaaaacm","aaaaaaaaaaaaaacn","aaaaaaaaaaaaaaco","aaaaaaaaaaaaaacp","aaaaaaaaaaaaaacq","aaaaaaaaaaaaaacr","aaaaaaaaaaaaaacs","aaaaaaaaaaaaaact","aaaaaaaaaaaaaacu","aaaaaaaaaaaaaacv","aaaaaaaaaaaaaacw","aaaaaaaaaaaaaacx","aaaaaaaaaaaaaacy","aaaaaaaaaaaaaacz","aaaaaaaaaaaaaada","aaaaaaaaaaaaaadb","aaaaaaaaaaaaaadc","aaaaaaaaaaaaaadd","aaaaaaaaaaaaaade","aaaaaaaaaaaaaadf","aaaaaaaaaaaaaadg","aaaaaaaaaaaaaadh","aaaaaaaaaaaaaadi","aaaaaaaaaaaaaadj","aaaaaaaaaaaaaadk","aaaaaaaaaaaaaadl","aaaaaaaaaaaaaadm","aaaaaaaaaaaaaadn","aaaaaaaaaaaaaado","aaaaaaaaaaaaaadp","aaaaaaaaaaaaaadq","aaaaaaaaaaaaaadr","aaaaaaaaaaaaaads","aaaaaaaaaaaaaadt","aaaaaaaaaaaaaadu","aaaaaaaaaaaaaadv","aaaaaaaaaaaaaadw","aaaaaaaaaaaaaadx","aaaaaaaaaaaaaady","aaaaaaaaaaaaaadz","aaaaaaaaaaaaaaea","aaaaaaaaaaaaaaeb","aaaaaaaaaaaaaaec","aaaaaaaaaaaaaaed","aaaaaaaaaaaaaaee","aaaaaaaaaaaaaaef","aaaaaaaaaaaaaaeg","aaaaaaaaaaaaaaeh","aaaaaaaaaaaaaaei","aaaaaaaaaaaaaaej","aaaaaaaaaaaaaaek","aaaaaaaaaaaaaael","aaaaaaaaaaaaaaem","aaaaaaaaaaaaaaen","aaaaaaaaaaaaaaeo","aaaaaaaaaaaaaaep","aaaaaaaaaaaaaaeq","aaaaaaaaaaaaaaer","aaaaaaaaaaaaaaes","aaaaaaaaaaaaaaet","aaaaaaaaaaaaaaeu","aaaaaaaaaaaaaaev","aaaaaaaaaaaaaaew","aaaaaaaaaaaaaaex","aaaaaaaaaaaaaaey","aaaaaaaaaaaaaaez","aaaaaaaaaaaaaafa","aaaaaaaaaaaaaafb","aaaaaaaaaaaaaafc","aaaaaaaaaaaaaafd","aaaaaaaaaaaaaafe","aaaaaaaaaaaaaaff","aaaaaaaaaaaaaafg","aaaaaaaaaaaaaafh","aaaaaaaaaaaaaafi","aaaaaaaaaaaaaafj","aaaaaaaaaaaaaafk","aaaaaaaaaaaaaafl","aaaaaaaaaaaaaafm","aaaaaaaaaaaaaafn","aaaaaaaaaaaaaafo","aaaaaaaaaaaaaafp","aaaaaaaaaaaaaafq","aaaaaaaaaaaaaafr","aaaaaaaaaaaaaafs","aaaaaaaaaaaaaaft","aaaaaaaaaaaaaafu","aaaaaaaaaaaaaafv","aaaaaaaaaaaaaafw","aaaaaaaaaaaaaafx","aaaaaaaaaaaaaafy","aaaaaaaaaaaaaafz","aaaaaaaaaaaaaaga","aaaaaaaaaaaaaagb","aaaaaaaaaaaaaagc","aaaaaaaaaaaaaagd","aaaaaaaaaaaaaage","aaaaaaaaaaaaaagf","aaaaaaaaaaaaaagg","aaaaaaaaaaaaaagh","aaaaaaaaaaaaaagi","aaaaaaaaaaaaaagj","aaaaaaaaaaaaaagk","aaaaaaaaaaaaaagl","aaaaaaaaaaaaaagm","aaaaaaaaaaaaaagn","aaaaaaaaaaaaaago","aaaaaaaaaaaaaagp","aaaaaaaaaaaaaagq","aaaaaaaaaaaaaagr","aaaaaaaaaaaaaags","aaaaaaaaaaaaaagt","aaaaaaaaaaaaaagu","aaaaaaaaaaaaaagv","aaaaaaaaaaaaaagw","aaaaaaaaaaaaaagx","aaaaaaaaaaaaaagy","aaaaaaaaaaaaaagz","aaaaaaaaaaaaaaha","aaaaaaaaaaaaaahb","aaaaaaaaaaaaaahc","aaaaaaaaaaaaaahd","aaaaaaaaaaaaaahe","aaaaaaaaaaaaaahf","aaaaaaaaaaaaaahg","aaaaaaaaaaaaaahh","aaaaaaaaaaaaaahi","aaaaaaaaaaaaaahj","aaaaaaaaaaaaaahk","aaaaaaaaaaaaaahl","aaaaaaaaaaaaaahm","aaaaaaaaaaaaaahn","aaaaaaaaaaaaaaho","aaaaaaaaaaaaaahp","aaaaaaaaaaaaaahq","aaaaaaaaaaaaaahr","aaaaaaaaaaaaaahs","aaaaaaaaaaaaaaht","aaaaaaaaaaaaaahu","aaaaaaaaaaaaaahv","aaaaaaaaaaaaaahw","aaaaaaaaaaaaaahx","aaaaaaaaaaaaaahy","aaaaaaaaaaaaaahz","aaaaaaaaaaaaaaia","aaaaaaaaaaaaaaib","aaaaaaaaaaaaaaic","aaaaaaaaaaaaaaid","aaaaaaaaaaaaaaie","aaaaaaaaaaaaaaif","aaaaaaaaaaaaaaig","aaaaaaaaaaaaaaih","aaaaaaaaaaaaaaii","aaaaaaaaaaaaaaij","aaaaaaaaaaaaaaik","aaaaaaaaaaaaaail","aaaaaaaaaaaaaaim","aaaaaaaaaaaaaain","aaaaaaaaaaaaaaio","aaaaaaaaaaaaaaip","aaaaaaaaaaaaaaiq","aaaaaaaaaaaaaair","aaaaaaaaaaaaaais","aaaaaaaaaaaaaait","aaaaaaaaaaaaaaiu","aaaaaaaaaaaaaaiv","aaaaaaaaaaaaaaiw","aaaaaaaaaaaaaaix","aaaaaaaaaaaaaaiy","aaaaaaaaaaaaaaiz","aaaaaaaaaaaaaaja","aaaaaaaaaaaaaajb","aaaaaaaaaaaaaajc","a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複製代碼

這種狀況下，該算法的執行時間就會變的很是的長，固然這還不是最差的狀況，最差的狀況是，board中的全部字符都是'a'。

因此下面咱們引入了字典樹:

字典樹

如圖所示，字典樹就是將全部的word的字符，變成樹中的一個個節點，而後咱們遍歷完一顆樹後，就能找到完整的word。

有了這個思路以後，咱們把上面的dfs少加改造:

func dfs(_ board: [[Character]], _ i: Int, _ j: Int, _ trie: TrieNode, _ str: String, _ visited: inout [[Bool]], _ res: inout [String]) {
    guard i >= 0 && i < board.count && j >= 0 && j < board[0].count && !visited[i][j] else { return }
    
    let c = board[i][j]
    guard let node = trie.child[c] else { return }
    
    let str = str + String(board[i][j])
    if node.isEnd && !res.contains(str) {
      res.append(str)
    }
    
    visited[i][j] = true
    dfs(board, i - 1, j, node, str, &visited, &res)
    dfs(board, i + 1, j, node, str, &visited, &res)
    dfs(board, i, j - 1, node, str, &visited, &res)
    dfs(board, i, j + 1, node, str, &visited, &res)
    visited[i][j] = false
  }
複製代碼

咱們把當前遍歷到的node與board中的字符作一個對比，若是存在該字符的話，咱們就認爲是符合條件的，否者的話，直接返回結果。重複上述步驟，直到找到葉子節點。

構造字典樹:

class TrieNode {
    var isEnd: Bool
    var child: [Character: TrieNode]
    
    init() {
      self.isEnd = false
      self.child = [:]
    }
  }

func buildTrie(_ words: [String]) -> TrieNode {
    let root = TrieNode()
    for word in words {
     insert(root, word)
    }
    return root
  }
  
  func insert(_ root: TrieNode, _ word: String) {
    var node = root
    for c in word {
      if node.child[c] == nil {
        node.child[c] = TrieNode()
      }
      node = node.child[c]!
    }
    node.isEnd = true
  }
複製代碼

好了，謝謝你們。