【魔改】树状数组 牛客多校第五场I vcd 几何+阅读理解

https://www.nowcoder.com/acm/contest/143/I

vc-dimension 

题解：分三种情况，组合数学算一下，其中一种要用树状数组维护

技巧（来自UESTC）：1.循环技巧i主j滑

2.树状数组：一个数列从左到右分别维护某个元素左边比它大num的与右边比他大的num时，从上往下扫， 对每个点的x坐标离散化累加1到X轴上，然后就会发现sum(p[i].x-1)就是左边比它大的，i-1-sum(p[i])就是右边比它大的。 注意y相同的点，需要一起更新（我已开始一个一个更新，根本写不出来）

orz太屌了

坑点：我循环写错了+公式里i,j写反了，wa了20发

比赛时x,y轴都看反了orz

 

#define _CRT_SECURE_NO_WARNINGS
#include<cmath>
#include<iostream>
#include<stdio.h>
#include<algorithm>
#include<cstring>
#include<stack>
#include<vector>
#include<string.h>
#include<queue>
#include<string>
#include<set>
using namespace std;
#define rep(i,t,n)  for(int i =(t);i<=(n);++i)
#define per(i,n,t)  for(int i =(n);i>=(t);--i)
#define mmm(a,b) memset(a,b,sizeof(a))
#define eps 1e-6
#define pb push_back
#define lowbit(x) ((x)&(-(x)))
const int maxn = 3e5 + 5;
const int inf = 1e7 + 5;//0x7fffffff;   //无限大
const int MOD = 1013;
typedef long long ll;
const int mod = 998244353;
int power(int a, int b) {
    int c = 1; a %= mod;
    while (b) {
        if (b & 1) c = 1ll * c*a%mod;
        a = 1ll * a*a%mod; b >>= 1;
    }
    return c;
}


struct node {
    int x, y;
    void sc() { scanf("%d%d", &x, &y); }
}p[maxn];

int n;
bool cmp(node a, node b) {
    return a.x > b.x;
}


bool cmpy(node a, node b) {
    return a.y < b.y;
}

int f[maxn];
int idx;
void add(int x, int y) { for (; x <= idx; x += lowbit(x)) f[x] += y; }
int sum(int x) { int ans = 0; for (; x; x -= lowbit(x)) ans += f[x]; return ans; }

int main() {
    int div2 = power(2, mod - 2);
    cin >> n;
    rep(i, 1, n) {
        p[i].sc();
    }
    int ans = n;
     ans +=  1ll*n * (n - 1)%mod*div2 % mod;
    if (ans >= mod)ans -= mod; else if (ans < 0)ans += mod;
    sort(p + 1, p + 1 + n, cmpy);
     idx = 0;
    for (int i = 1, j; i <= n; i = j + 1) {
        for (j = i ; j < n&&p[i].y == p[j+1].y; j++);
        ++idx;
        rep(k, i, j)p[k].y = idx;
        ans -=1ll* (j - i)*(j - i + 1)%mod*div2%mod;
        if (ans >= mod)ans -= mod; else if (ans < 0)ans += mod;
    }
    mmm(f, 0);
    sort(p + 1, p + 1 + n, cmp);
    for (int i = 1, j; i <= n; i = j + 1) {
        for (j = i ; j < n&&p[i].x == p[j+1].x; j++);
        rep(k, i, j) {
            int t1 = sum(p[k].y - 1); int t2 = i - 1 - sum(p[k].y);
            ans += 1ll * t1*t2%mod;
            if (ans >= mod)ans -= mod; else if (ans < 0)ans += mod;
        }
        rep(k, i, j)add(p[k].y, 1);
    }
    cout << ans << endl;
    cin >> n;
    return 0;
}

/*

*/

一开始无脑分别前后维护

#define _CRT_SECURE_NO_WARNINGS
#include<cmath>
#include<iostream>
#include<stdio.h>
#include<algorithm>
#include<cstring>
#include<stack>
#include<vector>
#include<string.h>
#include<queue>
#include<string>
#include<set>
using namespace std;
#define rep(i,t,n)  for(int i =(t);i<=(n);++i)
#define per(i,n,t)  for(int i =(n);i>=(t);--i)
#define mmm(a,b) memset(a,b,sizeof(a))
#define eps 1e-6
#define pb push_back
const int maxn = 1e5 + 5;
const int inf = 1e7 + 5;//0x7fffffff;   //无限大
const int MOD = 1013;
typedef long long ll;
const long long mod = 998244353;
int power(int a,int b){
    int c=1; a%=mod;
    while (b) {
        if (b&1) c=1ll*c*a%mod;
        a=1ll*a*a%mod; b>>=1;
    }
    return c;
}

ll div2 = power(2, mod - 2);
struct node {
    int x, y;
    int id;
    void sc() { scanf("%d%d", &x, &y); }
}P[maxn];

ll n;
bool cmp(node a, node b) {
    if (a.x != b.x)
    return a.x < b.x;
    else return a.y < b.y;
}
bool cmpx(node a, node b) {
    if (a.x != b.x)
        return a.x > b.x;
    else return a.y < b.y;
}

bool cmpy(node a, node b) {
    return a.y < b.y;
}
int cnt[maxn];
ll l[maxn], r[maxn];
int d[maxn];
int lowbit(int x) { return x & (-x); }
int fr[maxn], bk[maxn];
void add(int x, int v) {//a[x]+=v;
    while (x <= maxn) {
        d[x] += v;
        x += lowbit(x);
    }

}
int query(int x) {
    int res = 0;
    while (x) {
        res += d[x];
        x -= lowbit(x);
    }
    return res;
}

int main() {
    cin >> n;
    rep(i, 1, n) {
        P[i].sc();
        P[i].id = i;
    }
    sort(P + 1, P + n + 1, cmp);

    int idx = 0;
    int now = 0;
    rep(i, 1, n) {
        if (P[i].x != now) {
            cnt[++idx]++;
            now = P[i].x;
        }
        else {
            cnt[idx]++;
        }
    }
    ll ans = n;
    ll tmp = n * (n - 1) %mod*div2;
    rep(i, 1, idx)if (cnt[i] > 1) { tmp = (tmp - cnt[i] * (cnt[i] - 1) % mod *div2) % mod; }
    ans = (ans + tmp) % mod;
    //维护每个点左右比它高的点
    sort(P + 1, P + n + 1, cmpy);
    idx = 0;
    now = 0;
    rep(i, 1, n) {
        if (P[i].y != now) {
            P[i].y = ++idx;
            now = P[i].y;
        }
        else {
            P[i].y = idx;
        }
    }
    sort(P + 1, P + n + 1, cmp);
     now = 0;
    rep(i, 1, n)
    {
        if (P[i].x != P[i - 1].x)fr[i] =now= i - 1;
        else fr[i] = now;
    }
    now = 0;
    per(i, n, 1)
    {
        if (P[i].x != P[i + 1].x)bk[i] = now = i + 1;
        else bk[i] = now;
    }
    rep(i, 1, n) {
        if(P[i].x!=P[i-1].x)l[i] =ll( i-1-query(P[i].y));
        else {
            if (P[i].y >= P[fr[i]].y || P[i].y >= P[bk[i]].y)l[i] = 0;
            else l[i] = l[i - 1];
        }
        add(P[i].y, 1);    
    }
    mmm(d, 0);
    //sort(P + 1, P + n + 1, cmpx);
    int first = 1;
    per(i, n, 1) {
        if (P[i].x != P[i + 1].x)r[i] = ll(n-i - query(P[i].y)),first=1;
        else {
            if (P[i].y >= P[fr[i]].y || P[i].y >= P[bk[i]].y)r[i] = 0;
            else {
                if (first) 
                { 
                    first = 0; 
                    r[i] = ll(n - i -1- query(P[i].y));
                }
                else r[i] = r[i + 1]; 
            }
        }
        add(P[i].y, 1);
    }
    tmp = 0;
    rep(i, 1, n) {
        tmp = (tmp + l[i] * r[i] % mod) % mod;
    }
    ans = (ans + tmp) % mod;
        cout << ans<<endl;


        //sort(P + 1, P + n + 1, cmp);
        rep(i, 1, n) {
            //cout << l[i] << ' ' << r[i] << endl;
        }
    cin >> n;
}

/*

*/