## Editorial for VM 12 Bài 18 - Đổi chỗ

Remember to use this editorial only when stuck, and not to copy-paste code from it. Please be respectful to the problem author and editorialist.
Submitting an official solution before solving the problem yourself is a bannable offence.

Lưu ý: Các code mẫu dưới đây chỉ mang tính tham khảo và có thể không AC được bài tập này

#### Code mẫu của flashmt

#include <iostream>
#include <algorithm>
using namespace std;

int brute(int a[],int n)
{
int best=0;
for (int l=n-1;l;l--)
for (int i=0;i+l<n;i++)
{
int j=i+l;
if ((l-1)*2+1<=best) break;
if (a[j]>a[i]) continue;
int inc=0;
for (int k=i+1;k<j;k++)
{
if (a[k]>a[i]) inc--; else inc++;
if (a[k]<a[j]) inc--; else inc++;
}
best=max(best,inc+1);
}
return best;
}

int main()
{
int n,a[1000],inv=0;
cin >> n;
for (int i=0;i<n;i++) cin >> a[i];

for (int i=0;i<n;i++)
for (int j=i+1;j<n;j++)
inv+=a[i]>a[j];

cout << inv-brute(a,n) << endl;
}


program VMSWAP;
uses    math;
const   fi='';
maxn=1111;
var     f,g:array[1..maxn,0..maxn] of longint;
a:array[1..maxn] of longint;
n,i,j,res,s,t:longint;
inp:text;
begin
assign(inp,fi);reset(inp);
for i:=1 to n do read(inp,a[i]);
for i:=1 to n do
for j:=n downto 1 do
if i>a[j] then f[i,j]:=f[i,j+1]+1
else f[i,j]:=f[i,j+1];
for i:=1 to n do
for j:=1 to n do
if a[j]>i then g[i,j]:=g[i,j-1]+1
else g[i,j]:=g[i,j-1];
for i:=1 to n do inc(s,f[a[i],i]);
res:=s;
for i:=1 to n-1 do
for j:=i+1 to n do begin
t:=s+f[a[i],j+1]+f[a[j],i+1]-f[a[i],i]-f[a[j],j];
t:=t+g[a[i],j]-g[a[i],i]-g[a[j],j]+g[a[j],i];
res:=min(res,t);
end;
write(res);
end.


#### Code mẫu của RR

#include <sstream>
#include <iomanip>
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#include <stack>
#include <queue>
#include <string>
#include <deque>
#include <complex>

#define FOR(i,a,b) for(int i=(a),_b=(b); i<=_b; i++)
#define FORD(i,a,b) for(int i=(a),_b=(b); i>=_b; i--)
#define REP(i,a) for(int i=0,_a=(a); i<_a; i++)
#define FORN(i,a,b) for(int i=(a),_b=(b);i<_b;i++)
#define DOWN(i,a,b) for(int i=a,_b=(b);i>=_b;i--)
#define SET(a,v) memset(a,v,sizeof(a))
#define sqr(x) ((x)*(x))
#define ll long long
#define F first
#define S second
#define PB push_back
#define MP make_pair

#define DEBUG(x) cout << #x << " = "; cout << x << endl;
#define PR(a,n) cout << #a << " = "; FOR(_,1,n) cout << a[_] << ' '; cout << endl;
#define PR0(a,n) cout << #a << " = "; REP(_,n) cout << a[_] << ' '; cout << endl;
using namespace std;

int INP,AM,REACHEOF;
#define BUFSIZE (1<<12)
char BUF[BUFSIZE+1], *inp=BUF;
#define GETCHAR(INP) { \
if(!*inp) { \
if (REACHEOF) return 0;\
memset(BUF,0,sizeof BUF);\
if (inpzzz != BUFSIZE) REACHEOF = true;\
inp=BUF; \
} \
INP=*inp++; \
}
#define DIG(a) (((a)>='0')&&((a)<='9'))
#define GN(j) { \
AM=0;\
GETCHAR(INP); while(!DIG(INP) && INP!='-') GETCHAR(INP);\
if (INP=='-') {AM=1;GETCHAR(INP);} \
j=INP-'0'; GETCHAR(INP); \
while(DIG(INP)){j=10*j+(INP-'0');GETCHAR(INP);} \
if (AM) j=-j;\
}

const long double PI = acos((long double) -1.0);

int a[1011], n;

int main() {
scanf("%d", &n);
FOR(i,1,n) scanf("%d", &a[i]);

int inv = 0;
FOR(i,1,n) FOR(j,i+1,n) if (a[i] > a[j]) ++inv;

int best = inv;

FORD(l,n-1,1) FOR(i,1,n-l) {
int j = i + l;
if (a[i] < a[j]) continue;

if (inv - l - l + 1 >= best) continue;

int cur = inv - 1;

FOR(k,i+1,j-1) {
if (a[k] < a[i] && a[k] > a[j]) cur -= 2;
}
best = min(best, cur);
}
cout << best << endl;
return 0;
}


#### Code mẫu của hieult

#include <set>
#include <map>
#include <list>
#include <cmath>
#include <ctime>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <cctype>
#include <cstdio>
#include <string>
#include <vector>
#include <cassert>
#include <cstdlib>
#include <cstring>
#include <sstream>
#include <iomanip>
#include <iostream>
#include <algorithm>

using namespace std;

typedef long long ll;
typedef long double ld;
typedef unsigned int ui;
typedef unsigned long long ull;

#define Rep(i,n) for(typeof(n) i = 0; i < (n); ++i)
#define Repd(i,n) for(typeof(n) i = (n)-1; i >= 0; --i)
#define For(i,a,b) for(typeof(b) i = (a); i <= (b); ++i)
#define Ford(i,a,b) for(typeof(a) i = (a); i >= (b); --i)
#define Fit(i,v) for(typeof((v).begin()) i = (v).begin(); i != (v).end(); ++i)
#define Fitd(i,v) for(typeof((v).rbegin()) i = (v).rbegin(); i != (v).rend(); ++i)
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define sz(a) ((int)(a).size())
#define all(a) (a).begin(), (a).end()
#define ms(a,x) memset(a, x, sizeof(a))
#define nl puts("")
#define sp printf(" ")
#define ok puts("ok")

template<class F, class T> T convert(F a, int p = -1) { stringstream ss; if (p >= 0) ss << fixed << setprecision(p); ss << a; T r; ss >> r; return r; }
template<class T> void db(T a, int p = -1) { if (p >= 0) cout << fixed << setprecision(p); cout << a << " "; }
template<class T> T gcd(T a, T b) { T r; while (b != 0) { r = a % b; a = b; b = r; } return a; }
template<class T> T lcm(T a, T b) { return a / gcd(a, b) * b; }
template<class T> T sqr(T x) { return x * x; }
template<class T> T cube(T x) { return x * x * x; }
template<class T> struct Triple { T x, y, z; Triple() {} Triple(T _x, T _y, T _z) : x(_x), y(_y), z(_z) {} };
template<class T> Triple<T> euclid(T a, T b) { if (b == 0) return Triple<T>(1, 0, a); Triple<T> r = euclid(b, a % b); return Triple<T>(r.y, r.x - a / b * r.y, r.z); }
template<class T> int getbit(T s, int i) { return (s >> i) & 1; }
template<class T> T onbit(T s, int i) { return s | (T(1) << i); }
template<class T> T offbit(T s, int i) { return s & (~(T(1) << i)); }
template<class T> int cntbit(T s) { return s == 0 ? 0 : cntbit(s >> 1) + (s & 1); }
const int bfsz = 1 << 16; char bf[bfsz + 5]; int rsz = 0;int ptr = 0;
char gc() { if (rsz <= 0) { ptr = 0; rsz = fread(bf, 1, bfsz, stdin); if (rsz <= 0) return EOF; } --rsz; return bf[ptr++]; }
void ga(char &c) { c = EOF; while (!isalpha(c)) c = gc(); }
int gs(char s[]) { int l = 0; char c = gc(); while (isspace(c)) c = gc(); while (c != EOF && !isspace(c)) { s[l++] = c; c = gc(); } s[l] = '\0'; return l; }
template<class T> bool gi(T &v) {
v = 0; char c = gc(); while (c != EOF && c != '-' && !isdigit(c)) c = gc(); if (c == EOF) return false; bool neg = c == '-'; if (neg) c = gc();
while (isdigit(c)) { v = v * 10 + c - '0'; c = gc(); } if (neg) v = -v; return true;
}

const double PI = 2 * acos(0);
const string months[] = {"January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"};
const int days[] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
const int dr[] = {-1, 0, +1, 0};
const int dc[] = {0, +1, 0, -1};
const int inf = (int)1e9 + 5;
const ll linf = (ll)1e16 + 5;
const double eps = 1e-9;

#define maxn 1005

int n, a[maxn], front_smaller[maxn][maxn], back_smaller[maxn][maxn], front_bigger[maxn][maxn], back_bigger[maxn][maxn];

int main() {
//    freopen("in.txt", "r", stdin);

ms(front_smaller, 0); ms(back_smaller, 0);
ms(front_bigger, 0); ms(back_bigger, 0);

gi(n); For(i, 1, n) gi(a[i]);

For(i, 1, n) {
For(x, 1, n) {
front_smaller[i][x] = front_smaller[i - 1][x];
front_bigger[i][x] = front_bigger[i - 1][x];
if (a[i] < x) ++front_smaller[i][x];
if (a[i] > x) ++front_bigger[i][x];
}
}

Ford(i, n, 1) {
For(x, 1, n) {
back_smaller[i][x] = back_smaller[i + 1][x];
back_bigger[i][x] = back_bigger[i + 1][x];
if (a[i] < x) ++back_smaller[i][x];
if (a[i] > x) ++back_bigger[i][x];
}
}

int res = 0;
For(i, 1, n) res += back_smaller[i + 1][a[i]];

int original = res;
For(i, 1, n - 1) For(j, i + 1, n) {
int x = back_smaller[i + 1][a[i]] - back_smaller[j][a[i]];
int y = back_bigger[i + 1][a[i]] - back_bigger[j][a[i]];
int z = front_bigger[j - 1][a[j]] - front_bigger[i][a[j]];
int t = front_smaller[j - 1][a[j]] - front_smaller[i][a[j]];
int changes = original - x + y - z + t;
if (a[i] > a[j]) --changes;
else if (a[i] < a[j]) ++changes;
res = min(res, changes);
}

printf("%d\n", res);

return 0;
}


#### Code mẫu của skyvn97

#include<cstdio>
#define MAX   3030
int a[MAX];
int h[MAX][MAX];
int l[MAX][MAX];
int n;
int fst,best;
int min(const int &x,const int &y) {
if (x<y) return (x); else return (y);
}
void init(void) {
scanf("%d",&n);
int i;
for (i=1;i<=n;i=i+1) scanf("%d",&a[i]);
}
void count(void) {
int i,j;
fst=0;
for (i=1;i<n;i=i+1)
for (j=i+1;j<=n;j=j+1)
fst=fst+(a[i]>a[j]);
for (i=1;i<=n;i=i+1) {
h[i][0]=0;
l[i][0]=0;
for (j=1;j<=n;j=j+1) {
h[i][j]=h[i][j-1]+(a[j]>a[i]);
l[i][j]=l[i][j-1]+(a[j]<a[i]);
}
}
}
void process(void) {
best=fst;
int i,j;
for (i=1;i<n;i=i+1)
for (j=i+1;j<=n;j=j+1) {
best=min(best,fst+(h[i][j-1]-h[i][i])+(l[j][j-1]-l[j][i])-(l[i][j-1]-l[i][i])-(h[j][j-1]-h[j][i])-(a[i]>a[j])+(a[i]<a[j]));
//  printf("%d %d %d\n",i,j,best);
}
printf("%d",best);
}
int main(void) {
init();
count();
process();
return 0;
}