CISC 365 Lecture Notes - Lecture 1: The Algorithm

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25 Sep 2016

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Dijkstra"s algorithm works by building a set r (for reached) of vertices for which the shortest route from a has been found. On each iteration one more vertex is added to r until no more can be added (either because all vertices have been added or because some vertices cannot be reached from a). The algorithm also maintains a set c (for candidates) of vertices for which some path from a has been found (but not necessarily the best path). The algorithm maintains a vector b with one element for each vertex. On each iteration, the algorithm chooses the vertex in c that has the lowest b() value. (on the rst iteration this will be a. On the second iteration, it will be one of a"s neighbours, etc. ) Call this vertex x. vertex x is moved from c to r (so x can never be chosen again).

Related Questions

Periodic inventory system. Each of the following four horizontal lines represents data taken from a separate multiple-step income statement. Insert the missing amounts in the space (empty box) provided. Indicate any net loss by placing brackets around the amount.

Hint: Not all parts of the income statement are shown, so be careful with your arithmetic.

	Beginning Inventory	Purchases	Cost of Goods Available for Sale	Ending Inventory	Cost of Goods Sold
a.	$180,000		$325,000	$80,000

	Sales (Revenue)	Cost of Goods Sold	Gross Profit	Operating Expenses	Net Income
b.	$240,000	$145,000			$32,000

	Revenue (Sales)	Cost of Goods Available for Sale	Ending Inventory	Cost of Goods Sold	Gross Profit	Operating Expenses	Net Income
c.	$515,000	$240,000		$145,000		$225,000	$145,000

. For each question below, circle the best answer from the choices given. (

1 : Under the periodic inventory system the purchases of merchandise are recorded at their selling prices.
a. True b. False

2 : Inventory shrinkage does not include the loss of merchandise through shoplifting.
a. True b. False

3 : Only under the periodic inventory system is a physical count of the inventory necessary.
a. True b. False

4 : It is not possible to have more inventory at the end of a period then at the beginning of a period.
a. True b. False

5) True and false. Indicate whether each of the following is True (T) or False (F). (5 POINTS)

T F 1. US Treasury bills that mature within 120 days are cash equivalents.

T F 2. Financial assets describe not just cash, but all assets that are easily and directly convertible into known amounts of cash.

T F 3. Good cash mgmt. dictates that any cash and checks received each day should be deposited the same day.

T F 4. The income statement approach to estimating Bad debts Expense emphasizes the aging of accounts receivable and the adjustment of the Allowance for Doubtful Accounts account to the level of the estimated uncollectible amount.

T F 5. When I use the allowance method for accounts receivable, I will recognize a Bad Debt Expense at the same time the account is taken off the Accounts Receivable Subsidiary Ledger.

. For each question below, circle the best answer from the choices given.

1. Which of the following items would cause the ending balance on the bank statement to be larger than the ending balance of cash shown in the accounting records (checkbook)?

A) Bank service charges.

B) Deposits in transit.

C) Outstanding checks.

D) NSF check from one of the depositor's customers.

2. When a bank reconciliation has been satisfactorily completed, the only related entries to be made in the companyâs records are:

A) To correct errors made by the bank in recording the dollar amounts of cash transactions during the period.

B) To reconcile items explaining the difference between the balance per books and the balance per bank stmt.

C) To record outstanding checks and bank service charges.

D) To record items explaining the difference between the balance per accounting records and the adj. cash bal.

3. The Allowance for Doubtful Accounts represents:

A) Cash set aside to make up for bad debt losses.

B) The amount of uncollectible accounts written off to date.

C) The difference between total credit sales and collections on credit sales.

D) The difference between the face value of A/R and the net realizable value of A/R.

4. In preparing a bank reconciliation, a service charge shown on the bank statement should be:

A) Added to the balance per the bank statement.

B) Deducted from the balance per the bank statement.

C) Added to the balance per the depositor's records.

D) Deducted from the balance per the depositor's records.

5. During preparation of a bank reconciliation, outstanding checks should be:

A) Added to the balance per the bank statement.

B) Deducted from the balance per the bank statement.

C) Added to the balance per the depositor's records.

D) Deducted from the balance per the depositor's records.

Bank reconciliation. Indicate what effect each situation will have on the bank reconciliation process (Match the situation with the bank reconciliation process below by placing the number of the process next to the situation). Note that there are more situations than processes, so some processes may be used more than once, but not all processes have to be used. Only one process is required for each situation. Hint: Determine if Cash is increasing or decreasing

Process

Deduct from bank balance 2. Add to bank balance

3. Deduct from checkbook balance 4. Add to checkbook balance

Situation

_______ Bank received $2,750 from one of your customers (Terms: Cash in advance)

_______ Bank collection (wire) fee was $15

_______ Check number 111 was outstanding for $55

_______ A $400 check was written, but recorded on the books as $40

_______ Interest received from your bank for the month was $16.55

ceriseraccoon894

Medical History:
Ms. PW, a 58 yr old Caucasian woman, is referred by her physician for the development of an exercise prescription. She is 6 yr postmenopausal and has never been on hormone replacement therapy. In 1987, she was diagnosed with hyperthyroidism (overactive thyroid gland), which was treated with radioactive iodine. Since the treatment, Ms. PW has been on synthroid, a drug used when the thyroid gland does not produce enough thyroid hormones. She has mild hypertension, which is regulated by blood pressureâaltering medications. Ms. PW is 5 ft 5 in. (165 cm) tall with a weight of 128 lb (58 kg), and her body mass index is in the normal range. She does not follow a regular exercise regimen but reports that she enjoys biking.

Diagnosis:
A few months ago, Ms. PW was diagnosed with osteopenia. Considering her medical history, she is likely to become osteoporotic. Her risk factors are age, sedentary lifestyle, being Caucasian, being petite in stature, loss of menstrual function, and lack of thyroid hormone production.

Exercise Test Results:
She recently underwent an exercise stress test that was normal, but no physiological testing was done other than regular blood chemistries.

Exercise Prescription:
A walking program is surely the best choice because it has the potential of improving not only her cardiorespiratory fitness, but also her bone density. However, Ms. PW is particularly fond of bicycling, and therefore the exercise prescription will incorporate some biking activities, as that is likely to increase her adherence to exercise. These cardiorespiratory activities will start slow and gradually progress over time. Ultimately, her goal would be to walk (3.5 mph [5.6 kph] or faster) or bike 30 to 45 min five times a week. In order to reach this goal, Ms. PW may need to start walking or biking at a slower pace and for a shorter distance, but she should strive to exercise five times a week. After it is determined that she can comfortably handle the speed and distance used for the first 2 wk, these two components should be gradually increased. The best choice is to increase the speed a couple of days a week and increase the distance covered on the other days of the week.
A resistance training program should also be implemented, and may be more beneficial with respect to bone than the cardiorespiratory program. Resistance training should also start slowly, with the frequency beginning at 2 d/wk and moving up to 3 or 4 d/wk. Initially, resistance should be low enough that she can easily complete 12 repetitions of an exercise without undue strain. Exercises that target all the major muscle groups should be incorporated, especially for the legs and back. However, exercises that involve spinal flexion should be avoided. In order to strengthen abdominal muscles, Ms. PW can do leg lifts or modified sit-ups, in which only the head is being lifted off the floor. Upon completion of the first 2 wk, during which the patient does one set of 12 repetitions of each exercise, she can add a second set. This same progression can be used after Ms. PW completes another 2 wk. At this point, the patient should start increasing the intensity by slowly increasing the resistance. An adequate resistance at this point would allow the patient to complete no more than 10 repetitions on the second set. All exercises should be performed with slow, controlled movements. Based on Ms. PWâs medical history, this exercise prescription should be well tolerated and should provide optimal health benefits. Individual cases vary, however, and for a woman who has suffered fragility fractures as a result of osteoporosis, even the minimal exercise described here may not be tolerated initially. Such a patient will need a more gradual, less intense program.

Questions:
1. What other information should be obtained from Ms. PW?

2. What other physiological tests might be recommended?

3. Explain the difference in benefits achieved through cardiorespiratory training versus resistance training for this patient. Why is it always important to incorporate both?

1. A sludge containing 4% solid (by weight) needs to be thickened by centrifugation to â¥15% solid for disposal. The centrifuge has a high constant speed and produces a dewatered sludge containing 20% solid. To increase the processing capacity while still meeting the disposal requirement, you decide to bypass (i.e., not dewater) some of the feed sludge and blend the untreated sludge with the dewatered (20% solid) sludge, so as to produce a final sludge with a 15% solid content. Assume all sludge streams have the density of water.

(a) Give the centrate production rate (in L/min) and the percent solid (of the total coming in) discharged via the centrate?

(b) What % of the feed sludge is bypassed (i.e., not centrifuged)?

2. Eutrophication is a natural aging process all lakes undergo as nutrients and organic matter accumulate from their drainage basins. Over time the accumulated nutrients enable increased aquatic growth and stimulate biological activities. The increase in phytoplankton causes the lake to become murky, while decaying organic matter depletes the available dissolved O2. Further accumulation of silt, nutrients, and organic matter causes the eutrophic ("well-fed") lake to become shallower and warmer with more plants growing in the shallow edges. This process transforms lakes into bogs and marshes over time. Natural eutrophication is usually quite slow, often measured in thousands of years before major changes occur. What human activity has done is rapidly accelerate this process (called "cultural eutrophication") by introducing large quantities of nutrients. Sources of nutrients include municipal wastewater, industrial wastes, and runoff from fertilized agricultural land. The introduction of superfluous nutrients disturbs the natural balance of the system, causing excessive algae growth and water quality deterioration. Algal blooms are the unsightly and often malodorous clumps of rotting debris along the shoreline and thick mats of dead organic matter in the lake. A nutrient of major importance that enter fresh water bodies such as lakes from the aforementioned sources is phosphorous. C = 20% C = 15% Q = 100 L/min C = 4% bypass centrifuge C = 0.1% ("centrate") 2 Consider a phosphorus-limited lake with a surface area equal to 8 x 107 m 2 that is being fed by a stream with a flow rate of 15 m3 /s and a phosphorus concentration of 0.01 mg/L. An outfall from a wastewater treatment plant also adds 1 g/s of phosphorus to the lake, but its volumetric flow rate is small and can be ignored. The outflow rate from the lake is the same as the inflow (15 m3 /s). Because phosphorus can attach to suspended particles in lake water, the phosphorus in the lake can also be removed through particle settling (to sediment), which occurs at a rate of 10 m/yr. For the questions below, assume the lake is a cylindrical CSTR.

(a) Draw a diagram to represent the processes involved in phosphorus mass balance. List all sources and sinks. Estimate the steady-state phosphorus concentration in the lake.

(b) An acceptable level of phosphorus in the lake is 0.01 mg/L, above which eutrophication is considered likely. By what percent must the wastewater treatment plant reduce its phosphorous discharge into the lake to achieve this concentration?

3. A textile finishing process involves drying fabric that has been treated with a volatile solvent. The drying process involves evaporation of solvent and removal of solvent vapor by air. The wet fabric entering the dryer contains 50% solvent by weight. Air enters the dryer at a rate of 8 kg per kg of solvent-free fabric. The drying process is 92% efficient; i.e., 92% of entering solvent is removed from fabric and carried out by air. What is the weight % of solvent in the dried fabric? What is the mole % of solvent vapor in the exhaust? The molecular weight of the solvent is 46 g/mol.(Note: Dried fabric still contains some solvent; i.e., dried fabric is not solvent-free).

4. A process heater burns 4.8 kg of natural gas per minute, and the air supply rate is 20% higher than the stoichiometric rate. Exhaust from the heater is sent to a heat exchanger, where water vapor is condensed and removed from the exhaust. Assume natural gas is all methane (CH4), air contains 21% O2 and 79% N2, and the combustion of CH4 is complete, what is the mole % of CO2 in the cooled exhaust?

CISC 365 Lecture Notes - Lecture 1: The Algorithm

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