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4

^p^_[P

S(0) = 1+2+4+7+9 = 23

^p

S(1) = 1+1+3+6+9 = 20

^p

S(2) = 2+1+2+5+7 = 17

^p

S(3) = 4 + 3 + 2 + 3 + 5 = 17

^p

S(5) = 7 + 6 + 5 + 3 + 2 = 23

^p

S(6) = 9 + 8 + 7 + 5 + 2 = 31

^`

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j =0 (x i − x j ) + P n−1

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j = i (x j − x i−1 )

= (x _i − x _i −1 ) + (i − 1)(x _i − x _i −1 ) − (n − i − 1)(x _i −1 − x _i ) − (x _i − x _i −1 )

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i i 0 ≤ i<j<n x x i i i j x x i 0 ≤ i<n 0 ≤ x <x k =1 t ` s ( t,` ) s ( Y ) Y i d ( x ,Y ) i Y y ∈ Y i i j j j d ( x ,Y )=min { d ( x ,y ) | y ∈ Y } ( Y )= ( y ) P 0 1 n − 1 S ( Y )= d ( x ,Y )+ d ( x ,Y )+ ··· + d ( x ,Y )+ ( Y ) S ( Y ) i x Y k X i j i

∗

X = {x 0 , x 1 , . . . x n−1 }

n

n > 0

k

k > 0

y j

Y = {y 0 , y 1 , . . . y k −1 }

Y ⊆ X

d(x i , x j )

x i

x j

(x i )

x i

Y

k

X

S(Y )

S(Y ) = d(x 0 , Y ) + d(x 1 , Y ) + · · · + d(x n−1 , Y ) +

(Y )

d(x i , Y ) = min{d(x i , y j ) | y j ∈ Y }

(Y ) = P

y j ∈Y

(y j )

d(x i , Y )

i

Y

(Y )

Y

s

(t, `)

s

t

`

k = 1

x i

x i

i

0 ≤ i < n

0 ≤ x i < x j

0 ≤ i < j < n

x i

x i

∗

x m

S(m)

S(m) =

n−1 X

i=0

|x i − x m |

x m

X = {0, 1, 2, 4, 7, 9}

m

p

x i

x m

q

x i

x m

|p − q| ≤ 1

{ c , r , m }

c

m

r

x m = 4

cccrmrrcrc

x m = 2

S(m) =

n−1 X

i=0

|x i − x m | +

(x m )

m

s

n

s[i] = (x i , c i )

x i

x i

c i

Y = {y 0 , y 1 , . . . y _k −1 }

d(x _i , Y ) = min{d(x _i , y _j ) | y _j ∈ Y }

(y _j )

d(x _i , Y )

x _m

x _i

x _m

x _i

x _m

x _m = 2

(x _i )

m ⁰

x _m

x _m 0

(d, m, m ⁰ )

m ⁰

m ⁰

x m ⁰