The Time Traveler's Dilemma

In a world where time travel exists, you're tasked with collecting historical artifacts while minimizing alterations to the timeline. Each artifact has historical significance and temporal alteration factors. You have a limited number of time machine uses and a maximum temporal alteration threshold. Item i has temporal alteration t$,$ and historical significance v$.$ The maximum number of time machine uses is denoted by M$,$ the total number of artifacts available is denoted by M$,$ and the maximum temporal alteration threshold is denoted by T$.$ Artifacts are represented by an array of tuples whose first element holds temporal alteration and the second element holds historical significance.

Your goal is to select a subset of artifacts that maximize the total historical significance you collect, while staying within the temporal alteration threshold and using the available time machine uses effectively. For example:

Suppose that; M $=3,$ N $=4,$ T $=9,$ Artifacts $=(2,50),(3,80),(9,180),(7,170)]$ The subset which maximizes the

total historical significance is $[(2,50),(7,170)].$

Write a program to find maximum historical significance that you can reach using dynamic programming. Also analyze the running time of your program.