CodeForces868F. Yet Another Minimization Problem

Posted 2022-03-18 ivorysi

原题链接

题目大意是有N个数，分成K段，每一段的花费是这个数里相同的数的数对个数，要求花费最小

如果只是区间里相同数对个数的话，莫队就够了

而这里是！边单调性优化边莫队（只是类似莫队）！而移动的次数和分治的复杂度是一样的！

这个时候就不能用单调栈+二分了，得用分治

分治的方法就是\(Solve(l,r,ql,qr)\)表示我想计算区间\([l,r]\)的答案，然后转移过来的区间在\([ql,qr]\)

暴力计算出\(f[mid]\)的值，找到最优转移点是\(k\)，然后分成\(Solve(l,mid,ql,k)\)和\(Solve(mid +1,r,k,qr)\)做下去

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <vector>
#include <bitset>
#define fi first
#define se second
#define pii pair<int,int>
#define mp make_pair
#define pb push_back
#define space putchar(' ')
#define enter putchar('\n')
#define MAXN 100005
//#define ivorysi
using namespace std;
typedef long long int64;
template<class T>
void read(T &res) 
    res = 0;T f = 1;char c = getchar();
    while(c < '0' || c > '9') 
        if(c == '-') f = -1;
        c = getchar();
    
    while(c >= '0' && c <= '9') 
        res = res * 10 + c - '0';
        c = getchar();
    
    res *= f;

template<class T>
void out(T x) 
    if(x < 0) x = -x;putchar('-');
    if(x >= 10) out(x / 10);
    putchar('0' + x % 10);

int N,K,a[MAXN],cnt[MAXN];
int64 f[22][MAXN],w = 0;
int nw,p,q;
int64 work(int l,int r) 
    while(q < r) w += cnt[a[++q]]++;
    while(p > l) w += cnt[a[--p]]++;
    while(p < l) w -= --cnt[a[p++]];
    while(q > r) w -= --cnt[a[q--]];
    return w;

int64 Calc(int a,int b) 
    return f[nw - 1][a] + work(a + 1,b);

void Solve(int l,int r,int ql,int qr) 
    if(l > r) return;
    int mid = (l + r) >> 1,p = min(qr,mid - 1);
    int k;
    f[nw][mid] = Calc(ql,mid);k = ql;
    for(int i = ql + 1 ; i <= p ; ++i) 
        int64 x = Calc(i,mid);
        if(x <= f[nw][mid]) 
            f[nw][mid] = x;k = i;
        
    
    Solve(l,mid - 1,ql,k);
    Solve(mid + 1,r,k,qr);

int main() 
#ifdef ivorysi
    freopen("f1.in","r",stdin);
#endif
    read(N);read(K);
    for(int i = 1 ; i <= N ; ++i) read(a[i]);f[1][i] = f[1][i - 1] + cnt[a[i]]++;
    
    for(int i = 2 ; i <= K ; ++i) 
        memset(cnt,0,sizeof(cnt));
        p = 1;q = 0;w = 0;
        nw = i;
        Solve(0,N,0,N);
    
    out(f[K][N]);enter;