def isFeasible(node, currPath, definingBounds):
    task = taskList[node]
    routeIndex = int(currPath[0]) / dayLength

    noEndingTime = currPath[1:]
    
    if not definingBounds[0]:
        for r in range(len(task.dependencyTasks)):
            releaseTask = int(task.dependencyTasks[r])
            if releaseTask not in noEndingTime:
                return None
    
    #limit is the earliest we could reach node and begin proposed task
    limit = currPath[0]
    if len(currPath) > 2:
        dist = helperFunctions.getDistanceBetweenTasks(taskList[currPath[-1]], taskList[node])
        if int(limit + dist)/dayLength == int(limit)/dayLength:
            limit += dist
    
    #return a proposedEnd based on the earliest we can schedule the node, considering its time windows
    for d in range(routeIndex - 1, len(task.timeWindows)):
        for tw in range(len(task.timeWindows[d])):

            timeWindow = task.timeWindows[d][tw]
            proposedEnd = max(timeWindow[0], limit) + task.duration
            
            #if we could fit the task in its time window after the earliest possible starting time
            if timeWindow[1] - task.duration >= limit and proposedEnd <= timeLimit:
                return proposedEnd
    
    #if it's not possible to schedule the task (visit the node) then it's not feasible
    return None
def makeDijConstants(taskList):
    numTasks = len(taskList)
    dijConstants = [[None for j in range(numTasks)] for i in range(numTasks)]
    for i in range(numTasks):
        for j in range(numTasks):
            if i != j:
                dijConstants[i][j] = helperFunctions.getDistanceBetweenTasks(taskList[i], taskList[j])
    return dijConstants
def makeDijConstants(taskList):
    numTasks = len(taskList)
    dijConstants = [[None for j in range(numTasks)] for i in range(numTasks)]
    for i in range(numTasks):
        for j in range(numTasks):
            if i != j:
                dijConstants[i][j] = helperFunctions.getDistanceBetweenTasks(
                    taskList[i], taskList[j])
    return dijConstants
 def getDistanceTraveled(self):
     distanceTraveled = 0
     for route in self.routeList:
         for i in range(len(route.taskList)):
             if i == len(route.taskList) - 1:
                 pass
             else:
                 extraDistance = helperFunctions.getDistanceBetweenTasks(route.taskList[i], route.taskList[i + 1])
                 distanceTraveled += extraDistance
     return distanceTraveled
 def getDistanceTraveled(self):
     distanceTraveled = 0
     for route in self.routeList:
         for i in range(len(route.taskList)):
             if i == len(route.taskList) - 1:
                 pass
             else:
                 extraDistance = helperFunctions.getDistanceBetweenTasks(
                     route.taskList[i], route.taskList[i + 1])
                 distanceTraveled += extraDistance
     return distanceTraveled
def scheduleASAP(path, initTime = 0):
    '''
    returns a new path with the lowest possible ending time, as well as a duration
    
    @param path: a list of task ids in order that they're scheduled. the first 
    index is the ending time of the path
    '''
    currentTime = initTime
    dayIndex = 0
    if len(path) <= 1:
        return 0, 0
    
    task = taskList[path[1]]
    
    setTime = False
    #schedule the first task as early as possible
    t = 1
    for day in range(0, len(task.timeWindows)):
        for tw in range(len(task.timeWindows[day])):
            
            #if task can be scheduled in this time window..
            timeWindow = task.timeWindows[day][tw]
            if timeWindow[1] - task.duration >= currentTime:
                currentTime = max(timeWindow[0], currentTime) + task.duration
                schedStartTime = currentTime - task.duration
                setTime = True
                dayIndex = day
                break
        if setTime:
            break
    if not setTime:
        return None
    #schedule each task as early as possible and update currentTime
    for t in range(2, len(path)):
        task = taskList[path[t]]
        setTime = False
        # find the next possible time window to schedule node in in this day or any later days... 
        for day in range(dayIndex, len(task.timeWindows)):
            for tw in range(len(task.timeWindows[day])):
                
                #if task can be scheduled in this time window..
                timeWindow = task.timeWindows[day][tw]
                travelTime = helperFunctions.getDistanceBetweenTasks(taskList[path[t-1]], taskList[path[t]])
                if timeWindow[1] - task.duration >= currentTime + travelTime:
                    currentTime = max(timeWindow[0], currentTime + travelTime) + task.duration
                    setTime = True
                    dayIndex = day
                    break
            if setTime:
                break
        if not setTime:
            return None
    return currentTime, currentTime - schedStartTime
 def getWaitingTime(self):
     waitingTime = 0
     for route in self.routeList:
         for i in range(len(route.taskList)):
             if i == len(route.taskList)-1:
                 pass
             else:
                 extraWaitingTime = (route.endingTimes[i + 1] - route.endingTimes[i])
                 extraWaitingTime -= route.taskList[i + 1].duration
                 extraWaitingTime -= helperFunctions.getDistanceBetweenTasks(route.taskList[i], route.taskList[i + 1])
                 waitingTime += extraWaitingTime
     return waitingTime
 def getWaitingTime(self):
     waitingTime = 0
     for route in self.routeList:
         for i in range(len(route.taskList)):
             if i == len(route.taskList) - 1:
                 pass
             else:
                 extraWaitingTime = (route.endingTimes[i + 1] -
                                     route.endingTimes[i])
                 extraWaitingTime -= route.taskList[i + 1].duration
                 extraWaitingTime -= helperFunctions.getDistanceBetweenTasks(
                     route.taskList[i], route.taskList[i + 1])
                 waitingTime += extraWaitingTime
     return waitingTime
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def getExtraDistanceFromInsertion(route, position):
    if len(route) == 0:
        extraDist = 0
    elif position == 0:
        if len(route) > 1:
            extraDist = helperFunctions.getDistanceBetweenTasks(
                route[0], route[1])
        # takes care of case in which the route only has one task scheduled
        else:
            extraDist = 0
    elif position == len(route) - 1:
        # last task in the route
        extraDist = helperFunctions.getDistanceBetweenTasks(
            route[position - 1], route[position])
    else:
        # triangle inequality
        extraDist = helperFunctions.getDistanceBetweenTasks(
            route[position], route[position + 1])
        extraDist += helperFunctions.getDistanceBetweenTasks(
            route[position], route[position - 1])
        extraDist -= helperFunctions.getDistanceBetweenTasks(
            route[position - 1], route[position + 1])
    return extraDist
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def getWaitingTimeOfRoute(route):
    if len(route) == 0:
        return 0
    else:
        # accounts for time before first task starts
        totalWaitingTime = route.endingTimes[0] - route[0].duration
        for i in range(len(route) - 1):
            # add waiting time between task i and task i + 1
            firstTask = route[i]
            endingTimeOfFirstTask = route.endingTimes[i]
            secondTask = route[i + 1]
            startingTimeOfSecondTask = route.endingTimes[
                i + 1] - secondTask.duration
            distanceBetweenTasks = helperFunctions.getDistanceBetweenTasks(
                route[i], route[i + 1])
            taskWaitTime = startingTimeOfSecondTask - endingTimeOfFirstTask - distanceBetweenTasks
            totalWaitingTime += taskWaitTime
        return totalWaitingTime
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def findAvgDistance(taskList):
    distance = 0.0
    for task in taskList:
        for task2 in taskList:
            distance += helperFunctions.getDistanceBetweenTasks(task, task2)
    return distance / (len(taskList) * (len(taskList) - 1))