Source: Hindu
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Understanding the P versus NP Problem
POLYNOMIAL TIME An algorithm is said to be solvable in polynomial time if the number of steps required to complete the algorithm for a given input is O(n^k) for some nonnegative integer k, where n is the complexity of the input. Polynomial-time algorithms are said to be "fast." Most familiar mathematical operations such as addition, subtraction, multiplication, and division, as well as computing square roots, powers, and logarithms, can be performed in polynomial time. Computing the digits of most interesting mathematical constants, including pi and e, can also be done in polynomial time. Significance and Applications:
The Clay Millennium Prize:
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Complex Issues in Healthcare
Implications for Healthcare
Impact Beyond Healthcare
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PRACTICE QUESTION Q. Discuss the significance of the P versus NP problem in the field of computer science and its potential implications for society. What are the challenges in resolving this longstanding problem, and how might its resolution impact fields beyond computer science?. (250 words) |
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