1 File de priorité - implantation par Tas

n T T [1] T[n]
•1≤i≤n T [i]
•
•T[i] 2i2i+ 1
2≤i≤n T [i]T[i/2]
•i > n/2T[i]
•n
2T[n/2]
•
•
•
•

18
8
3
11
96
45215
7
18
8
3
11
915
4526
7
18
8
3
15
911
4526
7
6
8
3
15
911
452
7
15
8
3
6
911
452
7
15
8
3
11
96
452
7
•T[i]
T[i/2]
•T[i]
T[i]
O(1) n/2
O(log n)
O(n)
n/2O(1) O(1) A B
2i−1
2i+1 −1A B v O(i)

b
•
•
n
k=dlog2(n+ 1)en=Pk−1
i=0 ni2in ni
n k A0, . . . , Ak−1Ai2i
ni= 1 ni= 0 Ai
A0= [e]A1= [,]A2= [a, c, i, l]A3= [b, d, f, g, h, j, k]
k Ai
T2k−1 2n
T T = [A0, A1, . . .]Ai2i
T
<
dlog2(n+ 1)e
<0...2j−1−1 2j...2j−1
T
0. . . 2j−1−1 2j. . . 2j−1
m1≤2j−1m2≤2jm1+m2
T[0 . . . m1+m2−1]
O(nlog n)
O(log n)
n O(n2)
O(nlog n)
2n T
O(n)O(nlog n)

log2n Aii=k−
1, . . . , 0
Aini6= 0 log2kAik=
i
Plog n
i=0 i=O(log2n)
n= 2k−1ni= 1 i
n
Ai2i
n≤2i−kcR(n= 2k−1)
cR(n)≤(Ak−1) + 1
2.cR(2k−1−1)
≤log22k−1+1
2log22k−2+. . . +1 2ilog22k−i−1+. . . +1 2k−1
≤2 log2n.
Θ(log2n)
Ak−1Ak−2
j nj= 0 ni= 1 i= 0 . . . j −1
Aj
A0Aj−1Aj
AjA0A1
Aj−12i2i+1
Pj−1
i=0 2i+1 ≤2j−1
n ni= 0 0 ≤i < j nj= 1
Ai
j=k−1O(n)
n0= 0
O(1) n
•n
2j= 0 20−1 = 0
•n
22j= 1 21−1 = 1
•n
23j= 2 22−1 = 3
•n
2ij=i2i−1
•. . .
•j= log2n n −1
n
c(n)≤Plog2n
j=0
n
2j+1 .2j
n=O(log2n).
Ad
j≤d nj= 1 ni= 0 0 ≤i < j
•Ajy Aj
2j−1AjA0, . . . , Aj−1O(2j)
•Adx y
Ady
O(2d)
•n ni= 1 0 ≤i < j nj= 0
O(n)
Aj

j= 0 Ad
d=k n/4
O(n)
O(log n)
Θ(log n)
i O(log i)
Pn
i=1 log i≡Rn
1log t= [tlog t−t]n
1≡nlog n O(nlog n)
0. . . 2j−1−1
2j. . . 2j−1 2jΘ(2j)
Plog2n
j=1 2j≡2nΘ(n)
Θ(nlog n)