Dynamic Programming for partation and backtracing
CSE 3318 Lab Assignment 3
Due March 27
Goal:
1. Understanding of dynamic programming.
2. Understanding of subset sums.
Requirements:
1. Design, code, and test a C program that uses dynamic programming to partition (if possible) a
sequence of n positive integers into three subsequences such that the sum of each subsequence is the
same. For example, if the input were (10, 20, 30, 40, 40, 50, 80), with a total of m = 270, the three
m/3 = 90 subsequences could be (10, 80), (20, 30, 40), and (40, 50). If the input were (20, 20, 30, 50),
then no solution is possible even though the values yield a sum (m = 120) divisible by 3 (m/3 = 40).
The input should be read from standard input (which will be one of 1. keyboard typing, 2. a shell
redirect (<) from a file, or 3. cut-and-paste. Do NOT prompt for a file name!). The first line of the
input is n, the length of the sequence. Each of the remaining lines will include one sequence value.
Your program should echo the input sequence in all cases. The dynamic programming table should be
output when m/3 < 10, but in no other cases. Error messages should be displayed if m is not divisible
by 3 or if the problem instance does not have a solution. When a solution exists, it should be
displayed with each subsequence in a separate column:
i 0 1 2
1 10
2 20
3 30
4 40
5 40
6 50
7 80
2. Submit your C program on Canvas by 3:45 p.m. on Wednesday, March 27. One of the comment lines
should include the compilation command used on OMEGA (5 point penalty for omitting this).
Another comment should indicate the asymptotic worst-case time in terms of m and n.
Getting Started:
1. If you wanted two sequences summing to m/2, then the backtrace part of subsetSum.c could easily
be modified. By finding one subsequence that sums to m/2, the remaining elements would be another
subsequence that sums to m/2. Similarly, your program should use dynamic programming to find two
subsequences that each sum to m/3 and then take the leftover values as the third subsequence. Thus,
this is a two-dimensional DP situation, not one-dimensional like ordinary subset sums in Notes 7.F.
2. Dynamic programming is the only acceptable method for doing this lab.
