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Problem solution · Python

Finish Time of Tasks II

Finish Time of Tasks II: a Python solution using depth-first search. Learn the idea, check the complexity, and read the full code, with credit to Kamyu LeetCode Solutions.

Technique
Depth-first search
Source
Kamyu LeetCode Solutions
Length
119 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Depth-first search

For Finish Time of Tasks II, the implementation follows one branch at a time, making it suitable for components, trees, backtracking, or dependency exploration.

  1. Define the state carried into one recursive or stack frame.
  2. Mark or choose the current state before exploring children.
  3. Combine child results or undo the choice when the branch finishes.

Code notes

  • 119 lines of Python from the credited upstream file finish-time-of-tasks-ii.py.
  • The implementation visibly relies on sequence storage, cached states.
  • No explicit loop blocks detected, together with recursive traversal.

Complexity

Count unique states for graph traversal; for backtracking, count the branching factor and maximum depth.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from Kamyu LeetCode Solutions by kamyu104 and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeFinish Time of Tasks II · PythonPython
Use this to learn the idea, then write your own version.
# Time:  O(n)# Space: O(n) # iterative dfs, tree dpclass Solution(object):    def finishTime(self, n, edges, baseTime):        """        :type n: int        :type edges: List[List[int]]        :type baseTime: List[int]        :rtype: int        """        POS_INF, NEG_INF = float("inf"), float("-inf")        def iter_dfs():            dp = [0]*n            stk = [(1, 0, -1)]            while stk:                step, u, p = stk.pop()                if step == 1:                    stk.append((2, u, p))                    for v in reversed(adj[u]):                        if v == p:                            continue                        stk.append((1, v, u))                elif step == 2:                    mx, mn = NEG_INF, POS_INF                    for v in adj[u]:                        if v == p:                            continue                        mx, mn = max(mx, dp[v]), min(mn, dp[v])                    dp[u] = ((2*mx-mn) if mx is not NEG_INF else 0)+baseTime[u]            return dp                def iter_dfs2():            def top2(a, b, x, cmp):                if cmp(x, a):                    a, b = x, a                elif cmp(x, b):                    b = x                return a, b                result = POS_INF            stk = [(0, -1, NEG_INF)]            while stk:                u, p, t = stk.pop()                mx1, mx2, mn1, mn2 = NEG_INF, NEG_INF, POS_INF, POS_INF                for v in adj[u]:                    x = dp[v] if v != p else t                    mx1, mx2 = top2(mx1, mx2, x, lambda x, y: x > y)                    mn1, mn2 = top2(mn1, mn2, x, lambda x, y: x < y)                result = min(result, ((2*mx1-mn1) if mx1 is not NEG_INF else 0)+baseTime[u])                for v in reversed(adj[u]):                    if v == p:                        continue                    mx = mx1 if dp[v] != mx1 else mx2                    mn = mn1 if dp[v] != mn1 else mn2                    stk.append((v, u, ((2*mx-mn) if mx is not NEG_INF else 0)+baseTime[u]))            return result            adj = [[] for _ in xrange(n)]        for u, v in edges:            adj[u].append(v)            adj[v].append(u)        dp = iter_dfs()        return iter_dfs2()  # Time:  O(n)# Space: O(n)# dfs, tree dpclass Solution2(object):    def finishTime(self, n, edges, baseTime):        """        :type n: int        :type edges: List[List[int]]        :type baseTime: List[int]        :rtype: int        """        POS_INF, NEG_INF = float("inf"), float("-inf")        def dfs(u, p):            mx, mn = NEG_INF, POS_INF            for v in adj[u]:                if v == p:                    continue                dfs(v, u)                mx, mn = max(mx, dp[v]), min(mn, dp[v])            dp[u] = ((2*mx-mn) if mx is not NEG_INF else 0)+baseTime[u]                def dfs2(u, p, t):            def top2(a, b, x, cmp):                if cmp(x, a):                    a, b = x, a                elif cmp(x, b):                    b = x                return a, b             mx1, mx2, mn1, mn2 = NEG_INF, NEG_INF, POS_INF, POS_INF            for v in adj[u]:                x = dp[v] if v != p else t                mx1, mx2 = top2(mx1, mx2, x, lambda x, y: x > y)                mn1, mn2 = top2(mn1, mn2, x, lambda x, y: x < y)            result[0] = min(result[0], ((2*mx1-mn1) if mx1 is not NEG_INF else 0)+baseTime[u])            for v in adj[u]:                if v == p:                    continue                mx = mx1 if dp[v] != mx1 else mx2                mn = mn1 if dp[v] != mn1 else mn2                dfs2(v, u, ((2*mx-mn) if mx is not NEG_INF else 0)+baseTime[u])            adj = [[] for _ in xrange(n)]        for u, v in edges:            adj[u].append(v)            adj[v].append(u)        dp = [0]*n        dfs(0, -1)        result = [POS_INF]        dfs2(0, -1, NEG_INF)        return result[0]

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