五大演算法程式碼模板（DFS 遞迴非遞迴都算上，是六個）

這幾種演算法不僅要理解，更要能背下來虛擬碼，讓這些演算法的回想變成O(1)的時間複雜度。

1. Recursion 遞迴

def recursion(level, param1, param2, ...):
    # recursion terminator
    if level > MAX_LEVEL:
        print_result
        return

    # process logic in current level
    process_data(level, data...)

    # drill down
    self.recursion(level+1, p1, p2, ...)

    # reverse the current level status if needed
    reverse_state(level)

2. DFS(遞迴寫法)

   visited = set()
   def dfs(node, visited)
    visited.add(node)
    # process current node here.
    ...
    for next_node in node.children():
        if not next_node in visited:
            dfs(node, visited)

3. –DFS(非遞迴寫法)

   def dfs(graph, start, end):
    stack = []
    visited = set()
    stack.append(start)
    while stack:
        node = stack.pop()
        visited.add(node)
        # process current node here
        ...
        for next_node in node.children():
            if not next_node in visited:
                stack.append(next_node)

4. BFS

   def bfs(graph, start, end):
    queue = Queue()
    visited = set()
    queue.enqueue(start)
    while queue:
        node = queue.dequeue()
        visited.add(node)
        # process current node here
        ...
        for next_node in node.children():
            if not next_node in visited:
                queue.enqueue(next_node)

5. binary search

   l, r = 0, len(array) - 1
   while l <= r:
    mid = l + (r - l) // 2
    if  array[mid] == target:
        # find the target!
        break or return result
    elif array[mid] < target:
        l = mid + 1
    else:
        r = mid - 1

   二分查詢還有幾種變形，想法類似。第一個大於、大於等於、小於、小於等於的數

6. DP

   // 狀態定義
   dp = new int[m+1][n+1]
   // 初始狀態
   dp[0][0] = x;
   dp[0][1] = y;
   ...
   // DP狀態推導
   for i  = 0; i <= n; ++i {
    for j = 0; j <=  m; ++j {
        ...
        dp[i][j] = min{dp[i-1][j], dp[i][j-1], etc.}
    }
   }
   return dp[m][n] // 最優解

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