BZOJ 5125: [Lydsy1712月赛]小Q的书架

5125: [Lydsy1712月赛]小Q的书架
思路：
分治优化决策单调性dp
代码：

#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize(4)
#include<bits/stdc++.h>
using namespace std;
#define y1 y11
#define fi first
#define se second
#define pi acos(-1.0)
#define LL long long
//#define mp make_pair
#define pb push_back
#define ls rt<<1, l, m
#define rs rt<<1|1, m+1, r
#define ULL unsigned LL
#define pll pair<LL, LL>
#define pli pair<LL, int>
#define pii pair<int, int>
#define piii pair<pii, int>
#define pdd pair<double, double>
#define mem(a, b) memset(a, b, sizeof(a))
#define debug(x) cerr << #x << " = " << x << "\n";
#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
//head

const int N = 4e4 + 10;
const int INF = 0x3f3f3f3f;
int dp[N][11], s[N][11], a[N], bit[N], n, k, tot, l, r;
inline void add(int x, int a) {
    while(x <= n) bit[x] += a, x += x&-x;
}
inline int sum(int x) {
    int ans = 0;
    while(x) ans += bit[x], x -= x&-x;
    return ans;
}
inline void move(int L, int R) {
    while(l < L) add(a[l++], -1), tot -= sum(a[l-1]-1);
    while(l > L) add(a[--l], 1), tot += sum(a[l]-1);
    while(r < R) add(a[++r], 1), tot += r-l+1-sum(a[r]);
    while(r > R) add(a[r--], -1), tot -= r-l+1-sum(a[r+1]);
}
void solve(int L, int R, int l, int r, int k) {
    if(L > R) return ;
    int mid = L+R >> 1, up = min(mid-1, r), id = up;
    dp[mid][k] = INF;
    for (int i = up; i >= l; --i) {
        move(i+1, mid);
        if(dp[i][k-1] + tot < dp[mid][k]) {
            dp[mid][k] = dp[i][k-1] + tot;
            id = i;
        }
    }
    solve(L, mid-1, l, id, k);
    solve(mid+1, R, id, r, k);
}
int main() {
    scanf("%d %d", &n, &k);
    for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
    for (int i = 1; i <= n; ++i) dp[i][0] = INF;
    l = 1, r = 0;
    for (int i = 1; i <= k; ++i) solve(1, n, 0, n-1, i);
    printf("%d\n", dp[n][k]);
    return 0;
}