quy (Recursion) c phn 1.3

Ging vin: Nguyn Mnh Hin Khoa Cng ngh thng tin Trng i hc Thy Li Email: hiennm@tlu.edu.vn

Hc k 2, nm hc 2014-2015

quy

Hm quy l mt hm c nh ngha bng bn thn n

VD: f(0) = 0 v f(x) = 2f(x - 1) + x2 vi x > 0

int f(int x) { if (x == 0) // trng hp c s return 0; else return 2*f(x-1) + x*x; // li gi quy }

V d v quy (tip) nh gi hm f(x) = 2f(x - 1) + x2:

f(4) = 2*f(3) + 4*4

f(3) = 2*f(2) + 3*3

f(2) = 2*f(1) + 2*2

f(1) = 2*f(0) + 1*1

f(0) = 0

f(1) = 2*0 + 1*1 = 1

f(2) = 2*1 + 2*2 = 6

f(3) = 2*6 + 3*3 = 21

f(4) = 2*21 + 4*4 = 58

Gp trng hp c s v bt u quay lui

quy c th khng kt thc

iu g xy ra nu ta gi f(-1) sau khi ci t hm f(x) = 2f(x - 1) + x2 nh lc trc?

Di y l mt hm quy khng kt thc:

iu g xy ra khi gi: - bad(1)? - bad(2)? - bad(3)?

m bo chng trnh quy kt thc

Hai quy tc vit chng trnh quy ng:

1. nh ngha trng hp c s

y l ni quy s kt thc

2. Li gi quy phi c s tin trin

Mi bc phi hng dn v pha trng hp c s