AtCoder ARC 101 D Median of Medians(逆序对）

#include <map>
#include <set>
#include <cmath>
#include <ctime>
#include <queue>
#include <stack>
#include <vector>
#include <bitset>
#include <cstdio>
#include <cctype>
#include <string>
#include <cstring>
#include <cassert>
#include <climits>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <functional>
using namespace std ;

#define rep(i, a, b) for (int (i) = (a); (i) <= (b); (i)++)
#define Rep(i, a, b) for (int (i) = (a) - 1; (i) < (b); (i)++)
#define REP(i, a, b) for (int (i) = (a); (i) >= (b); (i)--)
#define clr(a) memset(a, 0, sizeof(a))
#define Sort(a, len, cmp) sort(a + 1, a + len + 1, cmp)
#define ass(a, sum) memset(a, sum, sizeof(a))

#define ls ((rt) << 1)
#define rs ((rt) << 1 | 1)
#define lowbit(x) (x & -x)
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define endl ‘\n‘
#define ENDL cout << endl
#define SZ(x) ((int)x.size())

typedef long long ll ;
typedef unsigned long long ull ;
typedef vector <int> vi ;
typedef pair <int, int> pii ;
typedef pair <ll, ll> pll ;
typedef map <int, int> mii ;
typedef map <string, int> msi ;
typedef map <ll, ll> mll ;

const int N = 100010 ;
const double eps = 1e-8 ;
const int iinf = INT_MAX ;
const ll linf = 2e18 ;
const double dinf = 1e30 ;
const int MOD = 1000000007 ;

inline int read(){
    int X = 0, w = 0 ;
    char ch = 0 ;
    while (!isdigit(ch)) { w |= ch == ‘-‘ ; ch = getchar() ; }
    while (isdigit(ch)) X = (X << 3) + (X << 1) + (ch ^ 48), ch = getchar() ;
    return w ? - X : X ;
}

void write(int x){
     if (x < 0) putchar(‘-‘), x = - x ;
     if (x > 9) write(x / 10) ;
     putchar(x % 10 + ‘0‘) ;
}

void print(int x) {
    cout << x << endl ;
    exit(0) ;
}

void PRINT(string x) {
    cout << x << endl ;
    exit(0) ;
}

void douout(double x){
     printf("%lf\n", x + 0.0000000001) ;
}

int a[N], sum[N * 10], bit[N * 10] ;
int n, l, r ;

void add(int a) {
    for (; a <= 2 * N; a += lowbit(a)) bit[a]++ ;
}

int query(int a){
    int res = 0 ;
    for (; a; a -= lowbit(a)) res += bit[a] ;
    return res ;
}

int check(int x) {
    for (int i = 0; i <= 2 * N; i++) bit[i] = 0 ;
    clr(sum) ;
    for (int i = 1; i <= n; i++) {
        sum[i] = sum[i - 1] + (a[i] >= x ? 1 : -1) ;
    }
    ll ans = 0 ;
    for (int i = 0; i <= n; i++) {
        ans += query(sum[i] + N) ;
        add(sum[i] + N) ;
    }
    return ans >= 1ll * n * (n + 1) / 4 ;
}

signed main(){
    scanf("%d", &n) ;
    for (int i = 1; i <= n; i++) scanf("%d", &a[i]), r = max(r, a[i]) ;
    while (l <= r) {
        int mid = (l + r) >> 1 ;
        if (check(mid)) l = mid + 1 ;
        else r = mid - 1 ;
    }
    printf("%d\n", r) ;
}

/*
写代码时请注意：
    1.是否要开Long Long？数组边界处理好了么？
    2.实数精度有没有处理？
    3.特殊情况处理好了么？
    4.做一些总比不做好。
思考提醒：
    1.最大值和最小值问题可不可以用二分答案？
    2.有没有贪心策略？否则能不能dp？
*/