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An algorithm that completes in "polynomial time" is faster to solve than an algorithm that completes in "exponential time" in most of the important cases where it needs to be solved.
An algorithm that completes in "polynomial time" the time to solve is always determinable by a polynomial equation (e.g. x^2, x^4+7*x^3+12*x^2+x+19, x^8392).
An algorithm that completes in "exponential time" the time to solve can only be determined an exponential equation (e.g. 2^x, e^x, 10^x, 982301^x).
Exponential equations give larger value answers than polynomial equations after a certain input value and then increase progressively faster. This makes "exponential time" algorithms take much longer than "polynomial time" algorithms to solve, often making many of them effectively unsolvable for certain cases.
Many of the most important algorithms needed to solve real world problems are "exponential time" algorithms.
What else can I help you with?
What is independent variable in exponential growth and decay problems?
Time!
An exponential growth function represents a quantity that has a constant halving time?
That would be an exponential decay curve or negative growth curve.
Does an exponential growth function represents a quantity that has a constant doubling time?
False
What is growth factor in algebra?
Exponential growth occurs when a quantity increases exponentially over time.
An exponential decay function represents a quantity that has a constant doubling time?
depends it can be true or false Apex: False
What is exponential time complexity and polynomial time complexity?
Algorithms which have exponential time complexity grow much faster than polynomial algorithms. The difference you are probably looking for happens to be where the variable is in the equation that expresses the run time. Equations that show a polynomial time complexity have variables in the bases of their terms. Examples: n^3 + 2n^2 + 1. Notice n is in the base, NOT the exponent. In exponential equations, the variable is in the exponent. Examples: 2^n. As said before, exponential time grows much faster. If n is equal to 1000 (a reasonable input for an algorithm), then notice 1000^3 is 1 billion, and 2^1000 is simply huge! For a reference, there are about 2^80 hydrogen atoms in the sun, this is much more than 1 billion.
What is the difference between exponential and polynomial time complexity?
Algorithms which have exponential time complexity grow much faster than polynomial algorithms. The difference you are probably looking for happens to be where the variable is in the equation that expresses the run time. Equations that show a polynomial time complexity have variables in the bases of their terms. Examples: n^3 + 2n^2 + 1. Notice n is in the base, NOT the exponent. In exponential equations, the variable is in the exponent. Examples: 2^n. As said before, exponential time grows much faster. If n is equal to 1000 (a reasonable input for an algorithm), then notice 1000^3 is 1 billion, and 2^1000 is simply huge! For a reference, there are about 2^80 hydrogen atoms in the sun, this is much more than 1 billion.
What is the time complexity of backtracking algorithms?
The time complexity of backtracking algorithms is typically exponential, meaning the runtime grows rapidly as the input size increases.
Differentiate between polynomial algorithm and exponential algorithm?
Do you mean, "the difference between an algorithm that runs in polynomial time, and one that runs in exponential time".First a real quick review. A polynomial is any equation of the formy = cmxm + ... + c2x2 + c1x + c0 ,where ci are constantsAn exponential function is something of the formy = cxThese functions grow much faster than any polynomial function.So, if T(n) describes the runtime of an algorithm as a function of whatever (# of inputs, size of input, etc.)., and T(n) can be bound above by any polynomic function, then we say that algorithm runs in polynomial time.If it can't be bound above by a polynomial function, but can be bound above by an exponential function, we say it runs in exponential time.Note how ugly an exponential algorithm is. By adding one more input, we roughly double (or triple, whatever c is) the run-time.
How does the efficiency of algorithms in quasilinear time compare to those in linear time?
Algorithms in quasilinear time are more efficient than those in linear time because they have a slightly higher time complexity, but still grow at a relatively slow rate compared to linear time algorithms.
What is the significance of polynomial time in the context of computational complexity theory?
In computational complexity theory, polynomial time is significant because it represents the class of problems that can be solved efficiently by algorithms. Problems that can be solved in polynomial time are considered tractable, meaning they can be solved in a reasonable amount of time as the input size grows. This is important for understanding the efficiency and feasibility of solving various computational problems.
What is the difference between polynomial and non polynomial time complexity?
Polynomial vs non polynomial time complexity
Is the problem of determining the polynomial reducibility of a given function computationally feasible?
Determining the polynomial reducibility of a given function is computationally feasible, but it can be complex and time-consuming, especially for higher-degree polynomials. Various algorithms and techniques exist to tackle this problem, but it may require significant computational resources and expertise to efficiently solve it.
Is determining the minimum spanning tree of a graph an NP-complete problem?
Determining the minimum spanning tree of a graph is not an NP-complete problem. It can be solved in polynomial time using algorithms like Prim's or Kruskal's algorithm.
Can integer linear programming be solved in polynomial time?
No, integer linear programming is NP-hard and cannot be solved in polynomial time.
Compare the exponential model and the logistic model of population growth.?
An exponential model has a j-shaped growth rate that increases dramatically over a period of time with unlimited resources. A logistic model of population growth has a s-shaped curve with limited resources leading to a slow growth rate.
Compare the exponential model and the logistic model of population growth. (?
An exponential model has a j-shaped growth rate that increases dramatically over a period of time with unlimited resources. A logistic model of population growth has a s-shaped curve with limited resources leading to a slow growth rate.
