PHP Common Commands

Once An algorithm are given for a problemand decided to being correct, an important step is To determine how much in the Resources,such as time or space, the algorithm would require.

The important things to know is:

1) It ' s very bad style to include constants or low-order terms inside a Big-oh

2) This means, in any analysis, that ignore lower-order terms and constants.

Example:do not say T (n) = O (2n^2) or t (n) = O (n^2 + N);

The correct form is T (N) = O (n^2).

General Rules:

rule1:for Loop:

The running time of a For loop are at the running time of the statements inside the for loop (including tests) times th E Number of iterations.

As an example, the following program fragment is O (N):

for (i=0; i<n; i++)       k++;

rule2:nested for Loop:

Analyze these inside out. The total running time of a statement inside a group of nested loops are the running time of the statement multiplied by th E Product of the sizes of the for loops.

As an example, the following program fragment is O (n^2):

for (i=0; i<n; i++) for    (j=0; j<n; j + +)        k++;

rule3:consecutive Statements:

These just add (which means that the maximum are the one that counts).

As an example, the following program fragment, which have O (N) work followed by O (n^2) work, is also O (n^2):

For (i=0, i<n; i++)    a[i] = 0;for (i=0; i<n; i++) for    (j=0; j<n; j + +)        A[i] + = a[j]+i+j;

Rule4:if/else:

for the Fragment

if (Condition)

S1

Else

S2

The running time of an if/else statement was never more than the running time of the test plus the larger of the running TI Mes of S1 and S2.

Notices:

A basic strategy of analyzing from the inside (or deepest part) to our works.

If There is function calls, these must be analyzed first.

Reference:

Data Structures and algorithm analysis in C. Second edtion

Than for reading!

--by Lzq at Nanyang may.26.2014