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#include #include #include #include #include #define fi first#define se second#define pii pair #define mp make_pair#define pb push_back#define space putchar(' ')#define enter putchar('\n')#define MAXN 100005//#define ivorysiusing namespace std;typedef long long int64;template 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 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;}