【问题标题】:Implementing Bellman-Ford in python在 python 中实现 Bellman-Ford
【发布时间】:2017-12-27 16:57:31
【问题描述】:

我正在尝试使 Python 中的 Bellman-Ford 图算法适应我的需要。

我已经从一个 json 文件中解决了解析部分。

这是我在 github 上找到的 Bellman Ford 代码: https://github.com/rosshochwert/arbitrage/blob/master/arbitrage.py

这是我改编而来的代码:

import math, urllib2, json, re


def download():
    graph = {}
    page = urllib2.urlopen("https://bittrex.com/api/v1.1/public/getmarketsummaries")
    jsrates = json.loads(page.read())

    result_list = jsrates["result"]
    for result_index, result in enumerate(result_list):
        ask = result["Ask"]
        market = result["MarketName"]
        pattern = re.compile("([A-Z0-9]*)-([A-Z0-9]*)")
        matches = pattern.match(market)
        if (float(ask != 0)):
            conversion_rate = -math.log(float(ask))
            if matches:
                from_rate = matches.group(1).encode('ascii','ignore')
                to_rate = matches.group(2).encode('ascii','ignore')
                if from_rate != to_rate:
                    if from_rate not in graph:
                        graph[from_rate] = {}
                    graph[from_rate][to_rate] = float(conversion_rate)
    return graph

# Step 1: For each node prepare the destination and predecessor
def initialize(graph, source):
    d = {} # Stands for destination
    p = {} # Stands for predecessor
    for node in graph:
        d[node] = float('Inf') # We start admiting that the rest of nodes are very very far
        p[node] = None
    d[source] = 0 # For the source we know how to reach
    return d, p

def relax(node, neighbour, graph, d, p):
    # If the distance between the node and the neighbour is lower than the one I have now
    if d[neighbour] > d[node] + graph[node][neighbour]:
        # Record this lower distance
        d[neighbour]  = d[node] + graph[node][neighbour]
        p[neighbour] = node

def retrace_negative_loop(p, start):
    arbitrageLoop = [start]
    next_node = start
    while True:
        next_node = p[next_node]
        if next_node not in arbitrageLoop:
            arbitrageLoop.append(next_node)
        else:
            arbitrageLoop.append(next_node)
            arbitrageLoop = arbitrageLoop[arbitrageLoop.index(next_node):]
            return arbitrageLoop


def bellman_ford(graph, source):
    d, p = initialize(graph, source)
    for i in range(len(graph)-1): #Run this until is converges
        for u in graph:
            for v in graph[u]: #For each neighbour of u
                relax(u, v, graph, d, p) #Lets relax it


    # Step 3: check for negative-weight cycles
    for u in graph:
        for v in graph[u]:
            if d[v] < d[u] + graph[u][v]:
                return(retrace_negative_loop(p, source))
    return None

paths = []

graph = download()

print graph

for ask in graph:
    path = bellman_ford(graph, ask)
    if path not in paths and not None:
        paths.append(path)

for path in paths:
    if path == None:
        print("No opportunity here :(")
    else:
        money = 100
        print "Starting with %(money)i in %(currency)s" % {"money":money,"currency":path[0]}

        for i,value in enumerate(path):
            if i+1 < len(path):
                start = path[i]
                end = path[i+1]
                rate = math.exp(-graph[start][end])
                money *= rate
                print "%(start)s to %(end)s at %(rate)f = %(money)f" % {"start":start,"end":end,"rate":rate,"money":money}
    print "\n"

错误:

Traceback (most recent call last):
  File "belltestbit.py", line 78, in <module>
    path = bellman_ford(graph, ask)
  File "belltestbit.py", line 61, in bellman_ford
    relax(u, v, graph, d, p) #Lets relax it
  File "belltestbit.py", line 38, in relax
    if d[neighbour] > d[node] + graph[node][neighbour]:
KeyError: 'LTC'

当我打印图表时,我得到了所需的一切。它是“LTC”,因为它是列表的第一个。我尝试执行和过滤 LTC,它给了我同样的错误,名字出现在图表上:

Traceback (most recent call last):
  File "belltestbit.py", line 78, in <module>
    path = bellman_ford(graph, ask)
  File "belltestbit.py", line 61, in bellman_ford
    relax(u, v, graph, d, p) #Lets relax it
  File "belltestbit.py", line 38, in relax
    if d[neighbour] > d[node] + graph[node][neighbour]:
KeyError: 'NEO'

我不知道我该如何解决这个问题。

谢谢大家。

PS:似乎一个答案被删除了,我是新来的,所以我不知道发生了什么。我编辑了帖子,因为答案帮助我前进:)

【问题讨论】:

  • 很遗憾,我没有时间帮助你,但我添加了一些标签,希望这个问题能引起关注。此外,“解释”一行对于 SO 来说有点边界,因此能够引用具体的预期输出会更安全。
  • 感谢@errantlinguist,请注意。

标签: python algorithm math graph-algorithm bellman-ford


【解决方案1】:

免责声明:请注意,虽然您可以通过这种方式发现“效率低下”,但您实际上可以利用它们来赚钱的机会非常低。很可能你实际上会损失一些钱。从我在测试期间看到的数据来看,这些“低效率”来自这样一个事实,即汇率在几分钟内的波动比买卖价差更大。所以你看到的低效率可能只是一个陈旧的数据,你实际上不能足够快地执行所有必需的订单,以使汇率足够稳定以赚钱。因此请注意,如果您尝试将此应用程序用于除您的好奇心之外的任何其他事情,您可能会损失金钱

现在开始做生意: 您的数据与原始代码的设计格式不同。典型的数据如下所示:

{
    "MarketName": "BTC-ETH",
    "High": 0.05076884,
    "Low": 0.04818392,
    "Volume": 77969.61816991,
    "Last": 0.04978511,
    "BaseVolume": 3875.47491925,
    "TimeStamp": "2017-12-29T05:45:10.18",
    "Bid": 0.04978511,
    "Ask": 0.04986673,
    "OpenBuyOrders": 4805,
    "OpenSellOrders": 8184,
    "PrevDay": 0.04955001,
    "Created": "2015-08-14T09:02:24.817"
}

您感兴趣的是MarketNameBidAsk。您需要了解那些Bid and Ask 的含义。粗略地说,Ask 值意味着如果您想以ETH 出售BTC,有(或者说是不久前)愿意使用汇率0.04986673 BTC 购买您的BTC 的买家为1 ETH。同样,Bid 值意味着如果您想以BTC 出售ETH,则(曾经)有买家愿意使用汇率0.04978511 BTC1 ETH 购买您的ETH。请注意,此结构意味着您将不会拥有带有 "MarketName": "ETH-BTC" 的记录,因为它不提供其他数据。

所以知道你可以用适当的距离填充你的graph,这是相应速率的对数。另外我相信您的代码中还有另一个错误:由于retrace_negative_loop 的参数p 实际上是前驱节点的字典,retrace_negative_loop 以相反的顺序返回负循环。而且由于您的图表是有向的,因此相同的循环在一个方向上可能是正的,而在另一个方向上可能是负的。

import math, urllib2, json, re


def download():
    graph = {}
    page = urllib2.urlopen("https://bittrex.com/api/v1.1/public/getmarketsummaries")
    data = page.read()
    jsrates = json.loads(data)

    result_list = jsrates["result"]
    for result_index, result in enumerate(result_list):
        ask = result["Ask"]
        bid = result["Bid"]
        market = result["MarketName"]
        pattern = re.compile("([A-Z0-9]*)-([A-Z0-9]*)")
        matches = pattern.match(market)
        if matches:
            from_rate = matches.group(1).encode('ascii', 'ignore')
            to_rate = matches.group(2).encode('ascii', 'ignore')

            # different sign of log is effectively 1/x
            if ask != 0:
                if from_rate not in graph:
                    graph[from_rate] = {}
                graph[from_rate][to_rate] = math.log(float(ask))
            if bid != 0:
                if to_rate not in graph:
                    graph[to_rate] = {}
                graph[to_rate][from_rate] = -math.log(float(bid))

    return graph  # Step 1: For each node prepare the destination and predecessor


def initialize(graph, source):
    d = {}  # Stands for destination
    p = {}  # Stands for predecessor
    for node in graph:
        d[node] = float('Inf')  # We start admiting that the rest of nodes are very very far
        p[node] = None
    d[source] = 0  # For the source we know how to reach
    return d, p


def relax(node, neighbour, graph, d, p):
    # If the distance between the node and the neighbour is lower than the one I have now
    dist = graph[node][neighbour]
    if d[neighbour] > d[node] + dist:
        # Record this lower distance
        d[neighbour] = d[node] + dist
        p[neighbour] = node


def retrace_negative_loop(p, start):
    arbitrageLoop = [start]
    prev_node = start
    while True:
        prev_node = p[prev_node]
        if prev_node not in arbitrageLoop:
            arbitrageLoop.append(prev_node)
        else:
            arbitrageLoop.append(prev_node)
            arbitrageLoop = arbitrageLoop[arbitrageLoop.index(prev_node):]
            # return arbitrageLoop
            return list(reversed(arbitrageLoop))


def bellman_ford(graph, source):
    d, p = initialize(graph, source)
    for i in range(len(graph) - 1):  # Run this until is converges
        for u in graph:
            for v in graph[u]:  # For each neighbour of u
                relax(u, v, graph, d, p)  # Lets relax it

    # Step 3: check for negative-weight cycles
    for u in graph:
        for v in graph[u]:
            if d[v] < d[u] + graph[u][v]:
                return retrace_negative_loop(p, v)
    return None




graph = download()

# print graph
for k, v in graph.iteritems():
    print "{0} => {1}".format(k, v)
print "-------------------------------"

paths = []
for currency in graph:
    path = bellman_ford(graph, currency)
    if path not in paths and not None:
        paths.append(path)

for path in paths:
    if path == None:
        print("No opportunity here :(")
    else:
        money = 100
        print "Starting with %(money)i in %(currency)s" % {"money": money, "currency": path[0]}

        for i, value in enumerate(path):
            if i + 1 < len(path):
                start = path[i]
                end = path[i + 1]
                rate = math.exp(-graph[start][end])
                money *= rate
                print "%(start)s to %(end)s at %(rate)f = %(money)f" % {"start": start, "end": end, "rate": rate,
                                                                        "money": money}

    print "\n"

此外,检查if path not in paths and not None: 可能还不够,因为它不会过滤我们的paths,这些paths 只是彼此的旋转,但我也没有费心去修复它。

【讨论】:

  • 哇,非常感谢。我想了一整夜,意识到我错过了我也需要所有带有投标价格的配对。我正要删除它,因为它不是代码错误,但根本不可能。我不打算从中赚钱,这只​​是为了一个班级项目,这不是必需的,但我想做更多的事情并提高我未来的编码技能。我会尝试找到路径的修复程序。此外,加密货币经纪人要从中赚钱的费用也很高。
  • 您认为可以将算法的计算限制为像 n 个节点吗?起初我最后用 len(path) 来做,但后来我意识到在计算发生时限制它会更快。当交易超过 3 或 4 次时,长路径无关紧要。谢谢
  • @mescu,我不明白你的问题。您想限制哪些计算以及用于什么目的?世界上没有那么多货币,所以不管怎样它都运行得很快。
  • 例如,它可以计算出一条路径是:BTC->LTC->XRP->USDT->ADA->BTC​​,所以在这种情况下不是很相关。因此,我认为我可以将图表限制为仅从起点获取最多 3 或 4 个节点,以使其运行得更快。
  • @mescu,我还是不明白。如果您不打算将其作为实际尝试赚钱的工具,那么循环BTC-&gt;LTC-&gt;XRP-&gt;USDT-&gt;ADA-&gt;BTC 在什么意义上比任何较短的路径都更不相关?通常,您可以尝试过滤掉更长的循环,但我不知道有什么算法可以有效地找到所有负循环。因此,您无法按任何指标过滤它们。当然,您可以只找到所有基本循环,然后只过滤它们的负数,但这可能效率不高。
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