树状数组

A - 三元上升子序列

 

#include <bits/stdc++.h>
#define int long long int
#define IOS ios::sync_with_stdio(0), cin.tie(0), cout.tie(0)
using namespace std;

typedef long long LL;
typedef pair<int, int> PII;

const int N = 2e5 + 10;

int n;
int a[N], tr[N];
PII p[N];

int lowbit(int x)
{
    return x & -x;
}

void add(int id, int c)
{   
    for(int i = id; i <= N; i += lowbit(i))
        tr[i] += c;
}

int sum(int id)
{
    int ans = 0;
    for(int i = id; i; i -= lowbit(i))
        ans += tr[i];
    return ans;
}

int query(int l, int r)
{
    return (sum(r) - sum(l - 1));
} 

void sovle()
{
    int n;
    cin >> n;
    
    for(int i = 1; i <= n; i ++)
        cin >> a[i];

    for(int i = 1; i <= n; i ++)
    {
        add(a[i], 1);
        p[i].first = query(1, a[i] - 1);
    }

    memset(tr, 0, sizeof tr);
    for(int i = n; i; i --)
    {
        add(a[i], 1);
        p[i].second = query(a[i] + 1, N);
    }

    int ans = 0;
    for(int i = 1; i <= n; i ++)
        ans += (1LL * p[i].first * p[i].second);
    
    cout << ans << endl;
}

signed main(void)
{
    IOS;
    int t;
    t = 1;
    while(t --)
        sovle();
}

G - 逆序对 

#include<cstdio>
#include<iostream>
using namespace std;
int n,a[500010],c[500010];
long long ans;

void msort(int b,int e)//归并排序
{
    if(b==e)  
		return;
    int mid=(b+e)/2,i=b,j=mid+1,k=b;
    msort(b,mid),msort(mid+1,e);
    while(i<=mid&&j<=e)
    	if(a[i]<=a[j])
    		c[k++]=a[i++];
    	else
    		c[k++]=a[j++],ans+=mid-i+1;//统计答案
    while(i<=mid)
    	c[k++]=a[i++];
    while(j<=e)
    	c[k++]=a[j++];
    for(int l=b;l<=e;l++)
    	a[l]=c[l];
} 

int main()
{
    scanf("%d",&n); 
    for(int i=1;i<=n;i++)
    	scanf("%d",&a[i]);
    msort(1,n);
    printf("%lld",ans);
    return 0;
}

 H - 康托展开

#include<iostream>
#include<cstdio>
using namespace std;
typedef long long ll;//虽然不知道这题不开long long会不会见祖宗，但保险起见还是开一下吧
ll tree[1000005];//树状数组
int n;
  //树状数组的“老三件”：lowbit，修改，求和
int lowbit(int x){
	return x&-x;
}
void update(int x,int y){
	while(x<=n){
		tree[x]+=y;
		x+=lowbit(x);	
	}
}
ll query(int x){
	ll sum=0;
	while(x){
		sum+=tree[x];
		x-=lowbit(x);	
	}
	return sum;
}
const ll wyx=998244353;//懒人专用
ll jc[1000005]={1,1};//存阶乘的数组
int a[1000005];//存数的
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){//预处理阶乘数组和树状数组
		jc[i]=(jc[i-1]*i)%wyx;
		update(i,1);
	}
	ll ans=0;
	for(int i=1;i<=n;i++){
		scanf("%d",&a[i]);
		ans=(ans+((query(a[i])-1)*jc[n-i])%wyx)%wyx;//计算ans
		update(a[i],-1);//把a[i]变成0（原来是1，减1不就是0嘛）
	}
	printf("%lld",ans+1);//别忘了+1
   return /*2333333333*/ 0;
}