PKU 2299
题型：求逆序数
解法一：正统做法，归并排序，375MS。
1
#include
"
stdio.h
"
2
#define
N 500000
3
int
num[N], temp[N];
4
__int64 sum;
5
6
void
Merge(
int
*
a,
int
start,
int
mid,
int
end)
7
{
8
int
i
=
start, j
=
mid
+
1
, k
=
0
;
9
while
(i
<=
mid
&&
j
<=
end) {
10
if
(a[i]
<=
a[j])
11
temp[k
++
]
=
a[i
++
];
12
else
{
13
temp[k
++
]
=
a[j
++
];
14
sum += mid-i+1
; //出现逆序时，交换的次数
15
}
16
}
17
while
(i
<=
mid)
18
temp[k
++
]
=
a[i
++
];
19
while
(j
<=
end)
20
temp[k
++
]
=
a[j
++
];
21
for
(i
=
0
; i
<
k; i
++
)
22
a[start
+
i]
=
temp[i];
23
}
24
25
void
MergeSort(
int
*
a,
int
start,
int
end)
26
{
27
int
mid;
28
mid
=
(end
+
start)
>>
1
;
29
if
(start
<
end) {
30
MergeSort(a, start, mid);
31
MergeSort(a, mid
+
1
, end);
32
Merge(a, start, mid, end);
33
}
34
}
35
36
int
main()
37
{
38
int
n, i;
39
while
(scanf(
"
%d
"
,
&
n), n) {
40
for
(i
=
0
; i
<
n; i
++
)
41
scanf(
"
%d
"
,
&
num[i]);
42
sum
=
0
;
43
MergeSort(num,
0
, n
-
1
);
44
printf(
"
%I64d\n
"
, sum);
45
}
46
return
0
;
47
}
48
解法二：树状数组，需要先离散化，因为用到qsort()，比归并排序稍慢，516MS。
1
#include
<
stdio.h
>
2
#include
<
stdlib.h
>
3
#include
<
string
.h
>
4
#define
NL 500000
5
#define
LL long long
6
7
struct
A {
8
int
a, id;
9
}q[NL];
10
int
f[NL], p[NL]; //f数组的意义：数字p[i]后边比其小的数的个数。
11
int
n;
12
13
int
cmp(
const
void
*
a,
const
void
*
b)
14
{
15
return
((
struct
A
*
)a)
->
a
-
((
struct
A
*
)b)
->
a;
16
}
17
18
int
sum(
int
idx)
19
{
20
int
cnt
=
0
;
21
while
(idx
>
0
) {
22
cnt
+=
f[idx];
23
idx
-=
idx
&
(
-
idx);
24
}
25
return
cnt;
26
}
27
28
void
update(
int
idx,
int
c)
29
{
30
while
(idx
<=
n) {
31
f[idx]
+=
c;
32
idx
+=
idx
&
(
-
idx);
33
}
34
}
35
36
int
main()
37
{
38
int
i;
39
LL cnt;
40
while
(scanf(
"
%d
"
,
&
n)
!=
EOF) {
41
if
(
!
n)
break
;
42
for
(i
=
1
; i
<=
n; i
++
) {
43
scanf(
"
%d
"
,
&
q[i].a);
44
q[i].id
=
i;
45
}
46
qsort(q
+
1
, n,
sizeof
(q[
0
]), cmp);
47
for
(i
=
1
; i
<=
n; i
++
) {
48
p[q[i].id]
=
i;
49
f[i]
=
0
;
50
}
51
cnt
=
0
;
52
for
(i
=
n; i
>
0
; i
--
) {
53
cnt
+=
sum(p[i]
-
1
);
54
update(p[i],
1
);
55
}
56
printf(
"
%lld\n
"
, cnt);
57
}
58
return
0
;
59
60
}
61