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    2007 SJTU 計算機復試上機試題(轉載)
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    Problem A. Old Bill
    Input file: standard input
    Output file: standard output

    Among grandfather's papers a bill was found.
    72 turkeys $_679_

    The first and the last digits of the number that obviously represented the
    total price of those turkeys are replaced here by blanks (denoted _), for
    they are faded and are illegible. What are the two faded digits and what
    was the price of one turkey?
    We want to write a program that solves a general version of the above
    problem.
    N turkeys $_XYZ_

    The total number of turkeys, N, is between 1 and 99, including both. The
    total price originally consisted of five digits, but we can see only the
    three digits in the middle. We assume that the first digit is nonzero, that
    the price of one turkeys is an integer number of dollars, and that all the
    turkeys cost the same price.
    Given N, X, Y, and Z, write a program that guesses the two faded digits and
    the original price. In case that there is more than one candidate for the
    original price, the output should be the most expensive one. That is, the
    program is to report the two faded digits and the maximum price per turkey
    for the turkeys.

    Input
    The first line of the input file contains an integer N (0<N<100), which
    represents the number of turkeys. In the following line, there are the
    three decimal digits X, Y, and Z., separated by a space, of the original
    price $_XYZ_.

    Output
    For the input case, there may be more than one candidate for the original
    price or there is none. In the latter case your program is to report 0.
    Otherwise, if there is more than one candidate for the original price, the
    program is to report the two faded digits and the maximum price per turkey
    for the turkeys.

    Sample input and output
    Standard input                         standard output
    72                                     3 2 511
    6 7 9

    5                                      9 5 18475
    2 3 7

    78                                     0
    0 0 5


    Problem B. Powerful Calculator
    Input file: standard input
    Output file: standard output

    Today, facing the rapid development of business, SJTU recognizes that more
    powerful calculator should be studied, developed and appeared in future
    market shortly. SJTU now invites you attending such amazing research and
    development work.
    In most business applications, the top three useful calculation operators
    are Addition (+), Subtraction (-) and Multiplication (×) between two given
    integers. Normally, you may think it is just a piece of cake. However,
    since some integers for calculation in business application may be very
    big, such as the GDP of the whole world, the calculator becomes harder to
    develop.
    For example, if we have two integers 20 000 000 000 000 000 and 4 000 000
    000 000 000, the exact results of addition, subtraction and multiplication
    are:
    20000000000000000 + 4000000000000000 = 24 000 000 000 000 000
    20000000000000000 - 4000000000000000 = 16 000 000 000 000 000
    20000000000000000 × 4000000000000000 = 80 000 000 000 000 000 000 000 000
    000 000

    Note: SJTU prefers the exact format of the results rather than the float
    format or scientific remark format. For instance, we need
    "24000000000000000" rather than 2.4×10^16.
    As a programmer in SJTU, your current task is to develop a program to
    obtain the exact results of the addition (a + b), subtraction (a - b) and
    multiplication (a × b) between two given integers a and b.

    Input
    The input file consist of two separate lines where the first line gives the
    integer a and the second gives b (|a| <10^200 and |b| < 10^200).

    Output
    For the input file, output three separate lines showing the exact results
    of addition (a + b), subtraction (a - b) and multiplication (a × b) of
    that case, one result per lines.

    Sample input and output
    Standard input                        standard output
    20000000000000000                     24000000000000000
    4000000000000000                      16000000000000000
                                          80000000000000000000000000000000


    Problem C. Sum of Factorials
    Input file: standard input
    Output file: standard output

    John von Neumann, b. Dec. 28, 1903, d. Feb. 8, 1957, was a
    Hungarian-American mathematician who made important contributions to the
    foundations of mathematics, logic, quantum physics, meteorology, science,
    computers, and game theory. He was noted for a phenomenal memory and the
    speed with which he absorbed ideas and solved problems. In 1925 he received
    a B.S. diploma in chemical engineering from Zurich Institute and in 1926 a
    Ph.D. in mathematics from the University of Budapest, His Ph.D.
    dissertation on set theory was an important contributions to the subject.
    At the age of 20, von Neumann proposed a new definition of ordinal numbers
    that was universally adopted. While still in his twenties, he made many
    contributions in both pure and applied mathematics that established him as
    a mathematician of unusual depth. His Mathematical Foundation of Quantum
    Mechanics (1932) built a solid framework for the new scientific discipline.
    During this time he also proved the mini-max theorem of GAME THEORY. He
    gradually expanded his work in game theory, and with coauthor Oskar
    Morgenstern he wrote Theory of Games and Economic Behavior (1944).
    There are some numbers which can be expressed by the sum of factorials. For
    example 9, 9 = 1! + 2! + 3! . Dr. von Neumann was very interested in such
    numbers. So, he gives you a number n, and wants you to tell whether or not
    the number can be expressed by the sum of some factorials.
    Well, it is just a piece of case. For a given n, you will check if there
    are some xi, and let n equal to
    ∑t (上標) i=1(下標) xi! (t≥1, xi≥0, xi = xj <==> i = j)
          t
    即  ∑    xi! (t≥1, xi≥0, xi = xj <==> i = j)
          i=1
    If the answer is yes, say "YES"; otherwise, print out
    "NO".

    Input
    You will get a non-negative integer n (n≤1,000,000) from input file.

    Output
    For the n in the input file, you should print exactly one word ("YES" or
    "NO") in a single line. No extra spaces are allowed.

    Sample input and output
    Standard input                      standard output
    9                                   YES
    2                                   YES


    Problem D. Zero-complexity Transposition
    Input file: standard input
    Output file: standard output

    You are given a sequence of integer numbers. Zero-complexity transposition
    of the sequence is the reverse of this sequence. Your task is to write a
    program that prints zero-complexity transposition of the given sequence.

    Input
    The first line of the input file contains one integer n-length of the
    sequence (0 < n ≤ 10 000). The second line contains n integers
    numbers-a1, a2, …, an (-1 000 000 000 000 000 ≤ ai ≤ 1 000 000 000 000
    000).

    Output
    On the first line of the output file print the sequence in the reverse
    order.

    Sample input and output
    Standard input                           standard output
    3                                        3 2 1
    1 2 3

    5                                        9 -8 6 4 -3
    -3 4 6 -8 9

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