Detailed explanation of algorithm time complexity

In general, the number of repeated executions of the basic operation in an algorithm is a function with the problem scale N.F (N)Algorithm Time Measurement
T (n) = O (f (n ))He indicates the algorithm execution time growth andF (N)With the same growth rate.Progressive time complexity(Asymptotic time complexity), shortTime Complexity.

The algorithm time complexity is from small to large:
O (1) <O (logn) <O (n) <O (nlogn) <O (n2) <O (N3) <O (2n) <O (N !) <O (NN)

The higher the time complexity, the higher the CPU consumption of the algorithm, and the slower the execution speed.

The time complexity analysis code is as follows:

Int sum = 1, n = 100;

O (1 ):

Sum = (1 + n) * n/2;

O (logn ):

While (sum <n ){

Sum = sum * 2;

}

O (n ):

For (INT I = 0; I <n; I ++ ){

Sum + = N;

}

O (N^{2 ):}

For (INT I = 0; I <n; I ++ ){

For (Int J = 0; j <n; j ++ ){

Sum + = 1;

}

}

For (INT I = 0; I <n; I ++ ){

For (Int J = I; j <n; j ++ ){

Sum + = 1;

}

}

// The above loop is actually not executed to N square times, executed N + (n-1) + (n-2) +... + 1 = n (n + 1)/2 = N^{2/2 times}

Because constants do not need to be calculated, n^{2/2 the final time complexity is O (n2)}

The algorithm has the best time complexity, worst and average complexity. For example, to search for a number in a data set, the best time complexity is O (1), the worst time complexity is O (n), and the average complexity is n/2.

The time complexity of this algorithm is O (n). Generally, the time complexity of this algorithm is the worst time complexity.