Write a program that solves Exercise 2.19. You need to modify the programs for each of the 4 algorithms for the maximum-subsequence-sum problem so that the program not only returns the maximum sums of subsequences of the given integer array but also returns/outputs the actual subsequence where the sum of integers is maximum. Run each algorithm on three randomly generated integer arrays of sizes N=1,000, 10,000, and 100,000, measure the running times, and determine if they are consistent with the theoretical analysis results of those algorithms given in class, i.e., if the running time of algorithm 1 for the MSS problem is proportional to N3 and that for Algorithm 2 is proportional to N2, etc. Include a table in your report that summarizes the actual running times (in appropriate time units) and narrative about your observations regarding whether the implemented algorithms indeed demonstrate behaviors entailed by theoretical analysis.

Exercise 2.19: The maximum contiguous subsequence sum algorithms in the text do not give any indication of the actual sequence. Modify them so that they return in a single object the value of the maximum subsequence and the indices of the actual sequence.

Algo1:

Algo 2:

Algo 3(focus on this specially):

Algo 4:

2 Cubic maximum contiguous subsequence sum algorithm 4 int maxSubSum1( const vector int> & a ) int maxSum 0; for( int i 0; i maxSum) maxSum thisSum; return maxSum; Figure 2.5 Algorithm 1 2 Cubic maximum contiguous subsequence sum algorithm 4 int maxSubSum1( const vector int> & a ) int maxSum 0; for( int i 0; i maxSum) maxSum thisSum; return maxSum; Figure 2.5 Algorithm 1