محاسبه هزینه الگوریتم ها

2

1391:

space complexity .

time complexity .

2 - - - : (int, float, char, ) ( : ...)

: .3 - - - : 4 ansi ansi n a1n1s1in + 31sum_element(a[], n) {2 s = 03 for i=1 to n 4 s = s + a[i]5 return s6} - - - : [1] 5 : .

: a = 4 b = a + 3c = sin(b) * 3.14 / cos (a*2)Sum ( a , b) { c = a + b return c}11Tn = 2 - - - : 6 .1sum_element(a[], n) {2 s = 03 for i=1 to n 4 s = s + a[i]5 return s6}s=0i=1s= s + a[1]i=2s = s + a[2]i=ns = s + a[n]i = n+1return sn 111tn = 2n + 3 - - - : for7

for 1 . for i=1 to n { statement1 statementn } - - - : for8loop#iterationfor i=a to b b a + 1 for i=1 to n step p(n 1) / p + 1for (i=1; i r1 = (1+5)/2 , r2 =(1-5)/2

- - - : 1- ...21: r m- : (c0+c1n+c2n2++cm-1nm-1)rn ck .an = 6an-1 9an-2a0 = 0a1 = 1 - - - : 2- 22: k ai f(n) :a0tn+a1tn-1++aktn-k = f(n) k .

f(n) . - - - : 2- ...23: :a0tn+a1tn-1++aktn-k = bnp(n) :(a0rk+a1rk-1++akr0 )(r b)d+1 = 0 d p(n) . bnp(n) .an = anh + anp

: - - - : 24tn 3tn-1 = 4n(2n+1)for n>1t0 = 0 , t1 = 12

: (r-3)(r-4)1+1 = 0

: tn = c13n + c24n + c3n4n

=> tn = 20(3n) - 20(4n) + 8n4n

- - - : 25 .

n = 2m T(2m) = T(2m/2) + 1

T(2m) = S(m)S(m) = S(m/2) + 1 :S(1) = c S(m) = c + lg m :m = lg n T(n) = c + lg lg n

- - - : 26

1. :

: tn= n/(n+1) - - - :

27

2. m*n

: .3. .

A m*p * Bp*n - - - :