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复习下树状数组
还是蛮有意思的一道题：
http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=501&page=show_problem&problem=4174
学到几点：
1、树状数组C[i]的构建，一则c[i]=s[i]-s[i-lowbit(i)];这是一直用的做法，现在学到一种新的，直接add(i,a[i])，（s[i]为a[1]到a[i]的和）
2、前缀和思想，树状数组的Sum本身就是基于前缀和的思想，本题把比某数小的数的个数，通过开大量空间+后缀数组，高效的统计出来比某数小的数的个数
3、其实我觉得通过这个题，可以做出来一种O(nlogn)的排序算法，当然不完善的地方就是只能是整数了，但是应该可以用vector+map解决？
贴自己的代码先，，，因为后面的Lrj大牛的代码太简洁...
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
#include <functional>using namespace std;#define MAXN 20010
#define SIZE 100015int a[MAXN],sma[SIZE],c[SIZE],s[SIZE],e[SIZE],tot[SIZE];
int n,mmax;int lowbit(int i)
{return i & (-i);
}int sum(int i)
{int ans=0;for(;i>0;i-=lowbit(i))ans+=c[i];return ans;
}void add(int x, int d) {while(x <= SIZE) {c[x] += d; x += lowbit(x);}}void Init()
{memset(c,0,sizeof(c));memset(a,0,sizeof(a));memset(sma,0,sizeof(sma));memset(s,0,sizeof(s));memset(e,0,sizeof(e));memset(tot,0,sizeof(tot));
}int main()
{//freopen("la4329.txt","r",stdin);int t;long long ans;scanf("%d",&t);while(t--){mmax=0;ans=0;Init();scanf("%d",&n);for(int i=1;i<=n;i++){scanf("%d",&a[i]);mmax=max(mmax,a[i]);add(a[i],1);//c[i]=sum(a[i]-1);e[a[i]]=1;sma[a[i]]=sum(a[i]-1);}memset(c,0,sizeof(c));for(int i=1;i<=mmax;i++){s[i] =s[i-1]+e[i];c[i]=s[i]-s[i-lowbit(i)];tot[i]=sum(i-1);}/////for(int i=1;i<=n;i++)//{// printf("sma[a[%d]] = %d tot(%d) = %d\n",i,sma[a[i]],a[i],tot[a[i]]);//}///for(int i=1;i<=n;i++){int tmp = tot[a[i]]-sma[a[i]];/*a[i]之后比a[i]小的个数*/ans+=(long long )tmp*(i-1-sma[a[i]])+(long long)sma[a[i]]*(n-i-tmp);}printf("%lld\n",ans);}return 0;
}
标程
// LA4329 Ping pong
// Rujia Liu
#include<cstdio>
#include<vector>
using namespace std;//inline int lowbit(int x) { return x&(x^(x-1)); }
inline int lowbit(int x) { return x&-x; }struct FenwickTree {int n;vector<int> C;void resize(int n) { this->n = n; C.resize(n); }void clear() { fill(C.begin(), C.end(), 0); }// ¼ÆËãA[1]+A[2]+...+A[x] (x<=n)int sum(int x) {int ret = 0;while(x > 0) {ret += C[x]; x -= lowbit(x);}return ret;}// A[x] += d (1<=x<=n)void add(int x, int d) {while(x <= n) {C[x] += d; x += lowbit(x);}}
};const int maxn = 20000 + 5;
int n, a[maxn], c[maxn], d[maxn];
FenwickTree f;int main() {freopen("la4329.txt","r",stdin);int T;scanf("%d", &T);while(T--) {scanf("%d", &n);int maxa = 0;for(int i = 1; i <= n; i++) { scanf("%d", &a[i]); maxa = max(maxa, a[i]); }f.resize(maxa);f.clear();for(int i = 1; i <= n; i++) {f.add(a[i], 1);c[i] = f.sum(a[i]-1);}f.clear();for(int i = n; i >= 1; i--) {f.add(a[i], 1);d[i] = f.sum(a[i]-1);}long long ans = 0;for(int i = 1; i <= n; i++)ans += (long long)c[i]*(n-i-d[i]) + (long long)(i-c[i]-1)*d[i];printf("%lld\n", ans);}return 0;
}
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