## Rate of Growth in Data Structure and Algorithm

**Rate of Growth** refers to the **percentage** change of a specific variable within a specific time period.

# What is the Rate of Growth?

The rate at which The running time increases as a function of input is called the rate of growth.

Let us assume that you go to a shop to buy a car and a bicycle. If your friend sees you there and asks what you are buying, then, in general, you say buying a car. This is because the cost of the car is high compared to the cost of the bicycle (approximating the cost of The bicycle to the cost of the car).

Total Cost = cost_of_car + cost_of _blcycle Total Cost = cost_of _car (approximation)

For the above-mentioned example, we can represent the cost of the car and the cost of the bicycle in terms of function, and for a given function ignore the low order terms that are relatively insignificant (for large value of input size, n). For example, in the case below, n^{4}, 2n^{2}, 100n, and 500 are the individual costs of some function and approximate to n4 since n4^{ is the highest }**rate of ****growth**.

n4 + 2n2 + 100n + 500 = n4

# Commonly Used Rates of Growth

The diagram below shows the relationship between different rates of growth.

Below is the list of growth rates you can be seen anywhere:

Time Complexity | Name | Example |

1 | Constant | Adding an Element to the front of the linked list. |

logn | Logarithmic | Finding an Element in sorted Array. |

n | Linear | Finding an Element in Unsorted Array. |

nlogn | Linear Logarithmic | Sorting n items by divide-and-conquer – Merge sort. |

n^{2} | Quadratic | The shortest path between two nodes in a graph. |

n^{3} | Cubic | Matrix Multiplication. |

2^{n} | Exponential | The Towers of Hanoi problem. |

Learn more about the Rate of Growth.

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Source: Abhiyantriki