Given n open intervals (a1, b1), (a2, b2), . . . , (an, bn) on
the real line, each representing start and end times of some activity requiring the same resource, the task is to find the largest number of these intervals so that no two of them overlap. Investigate the three greedy algorithms based on
a. earliest start first.
b. shortest duration first.
c. earliest finish first.
For each of the three algorithms, either prove that the algorithm always yields an optimal solution or give a counterexample showing this not to be the case.

Consider the following statements, then select one of the answers below: the signal() function shown below registers "sig_handler()" as the signal handler function for the sigkill signal, without the complexity of using when the sigkill signal is sent to a process running this code, by a user typing "kill -kill ", where the correct process id is used for to target the process, sig_handler() will be executed.

Write a function balancechemical to balance chemical reactions by solving a linear set of equations. the inputs arguments are: reagents: symbols of reagents in string row array products: symbols of products in string row array elements: elements in the reaction in string row array elcmpreag: elemental composition of reactants in two dimensional numeric array elcmpprdcts: elemental composition of prducts in two dimensional numeric array hint: the first part of the problem is setting up the set of linear equations that should be solve. the second part of the problem is to find the integers from the solution. one way to do this is to mulitiply the rational basis for the nullspace by increasing larger integers until both the left-and right-side integers exist. for example, for the reaction that involves reacting with to produce and : reagents=["ch4", "o2"]; products =["co2", "h2o"]; elements =["c","h", "o"] elcmpreag=[1,4,0;

Use a physical stopwatch to record the length of time it takes to run the program. calculate the difference obtained by calls to the method system.currenttimemillis() just before the start of the algorithm and just after the end of the algorithm. calculate the difference obtained by calls to the method system.currenttimemillis() at the start of the program and at the end of the program so that the elapsed time includes the display of the result. use the value returned by the method system.currenttimemillis() just after the end of the algorithm as the elapsed time.