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Problem solution · Python

Minimum Time to Transport All Individuals

Minimum Time to Transport All Individuals: a Python solution using heap or priority queue. Learn the idea, check the complexity, and read the full code, with credit to Kamyu LeetCode Solutions.

Technique
Heap or priority queue
Source
Kamyu LeetCode Solutions
Length
55 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

Heap or priority queue

For Minimum Time to Transport All Individuals, the implementation repeatedly takes the currently best candidate from a heap while inserting newly available choices.

  1. Define the priority key and whether the smallest or largest item should lead.
  2. Push each candidate when it becomes eligible.
  3. Discard stale entries when necessary and process the best live candidate.

Code notes

  • 55 lines of Python from the credited upstream file minimum-time-to-transport-all-individuals.py.
  • The implementation visibly relies on sequence storage, work queue.
  • No explicit loop blocks detected.

Complexity

Count heap pushes and pops; each normally contributes a logarithmic factor in the heap size.

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 codeMinimum Time to Transport All Individuals · PythonPython
Use this to learn the idea, then write your own version.
# Time:  O((n * m * 2^n + m * 3^n) * log(n * m * 2^n + m * 3^n)) = O(m * 3^n * log(m * 3^n))# Space: O(n * m * 2^n + m * 3^n) = O(m * 3^n) import heapq  # dijkstra's algorithm, submask enumerationclass Solution(object):    def minTime(self, n, k, m, time, mul):        """        :type n: int        :type k: int        :type m: int        :type time: List[int]        :type mul: List[float]        :rtype: float        """        def update(d, r, s, mask, submask):            t = lookup[submask]*mul[s]            nr = r^1            ns = (s+int(t))%m            new_mask = mask^submask            nd = d+t            if dist[nr][ns][new_mask] > nd:                dist[nr][ns][new_mask] = nd                heapq.heappush(min_heap, (nd, nr, ns, new_mask))            popcount = [0]*(1<<n)  # for better performance        for i in xrange(1, (1<<n)):            popcount[i] = popcount[i>>1]+(i&1)        lookup = [max(time[i] for i in xrange(n) if mask&(1<<i)) if mask else 0 for mask in xrange(1<<n)]  # Time: O(n * 2^n)        INF = float("inf")        dist = [[[INF]*(1<<n) for _ in xrange(m)] for _ in xrange(2)]        dist[0][0][(1<<n)-1] = 0.0        min_heap = [(0.0, 0, 0, (1<<n)-1)]        while min_heap:            d, r, s, mask = heapq.heappop(min_heap)  # Total Time: O((n * m * 2^n + m * 3^n) * log(n * m * 2^n + m * 3^n))            if d != dist[r][s][mask]:                continue            if mask == 0:                assert(r == 1)                return d            if r == 0:                submask = mask                while submask:  # Total Time: O(m * 3^n)                    if popcount[submask] <= k:                        update(d, r, s, mask, submask)                    submask = (submask-1)&mask            else:                for i in xrange(n):  # Total Time: O(n * m * 2^n)                    if mask&(1<<i):                        continue                    update(d, r, s, mask, 1<<i)        return -1.0

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