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
