CS447/CS547/EE667    Fall 2008    Assignment 1    Due September 4 (in class)
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1.  Recall the SS_100_k problem.  There is an array S of positive
integers, whose size is n, and a positive integer k.  We want to determine
if there is a subset of S, the sum of whose elements is equivalent to k
mod 100.  Assume the function SS_100,k has been run, as given below.
Write a function to take S, A_new and k as inputs and print out the subset
determined by SS_100_k. 

2A.  Recall the original SUBSET SUM problem.  There is an array S of
positive integers, whose size is n, and a positive integer k.  We want to
determine if there is a subset of S whose elements add up to k.  Write an
algorithm to solve SUBSET SUM which runs in time O(n k).  

2B.  Explain why your algorithm from part A is not polynomial in the size
of the input.

3.  Suppose we have a group of n men and n women, along with their
    heights.  Write an algorithm to determine if it is posible for every
    man to marry a woman taller than him.  No woman is allowed to marry
    more than one man.

4.  Problem 3 in the textbook, page 22.


SS_100_k(int S[1..n], int k)
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int A[0..99]

for j = 0 to 99
  A[j] = -0

for i = 1 to n

  for j = 0 to 99
    if A[j] != 0 and A[j] != i
      new_pos = (j + S[i]) mod 100
      if A[new_pos] = 0
        A[new_pos] = i

  if A[S[i] mod 100] = 0
    A[S[i] mod 100] = i

if A[k mod 100] != 0
  print YES
else 
  print NO