bzoj3675: [Apio2014]序列分割

  1 #include<cstdio>
  2 #include<cstring>
  3 #include<cstdlib>
  4 #include<algorithm>
  5 #include<iostream>
  6 
  7 using namespace std;
  8 
  9 void setIO(const string& s) {
 10     freopen((s + ".in").c_str(), "r", stdin);
 11     freopen((s + ".out").c_str(), "w", stdout);
 12 }
 13 template<typename Q> Q read(Q& x) {
 14     static char c, f;
 15     for(f = 0; c = getchar(), !isdigit(c); ) if(c == ‘-‘) f = 1;
 16     for(x = 0; isdigit(c); c = getchar()) x = x * 10 + c - ‘0‘;
 17     if(f) x = -x;
 18     return x;
 19 }
 20 template<typename Q> Q read() {
 21     static Q x; read(x); return x;
 22 }
 23 
 24 typedef long long LL;
 25 const int N = 100000 + 10;
 26 
 27 LL sqr(const LL& x) {
 28     return x * x;
 29 }
 30 
 31 LL f[N], g[N], sum[N];
 32 int q[N];
 33 
 34 LL up(int i) {
 35     return g[i] - sqr(sum[i]);
 36 }
 37 
 38 LL up(int i, int j) {
 39     return up(j) - up(i);
 40 }
 41 
 42 LL down(int i, int j) { // >= 0
 43     return sum[j] - sum[i];
 44 }
 45 
 46 double slope(int i, int j) {
 47     return up(i, j) / (double) down(i, j);
 48 }
 49 int n;
 50 
 51 struct Node {
 52     LL x, y;
 53     Node() {}
 54     Node(const LL& x, const LL& y) : x(x), y(y) {}
 55     Node operator - (const Node& rhs) const {
 56         return Node(x - rhs.x, y - rhs.y);
 57     }
 58 }p[N];
 59 
 60 LL Cross(const Node& a, const Node& b) {
 61     return a.x * b.y - b.x * a.y;
 62 }
 63 
 64 void dp(int st) {
 65     int L = 0, R = 0;
 66     q[R++] = st;
 67     for(int i = st + 1; i <= n; i++) {
 68 //        while(L + 1 < R && -sum[i] < slope(q[L], q[L + 1])) L++;
 69 //        while(L + 1 < R && -sum[i] * down(q[L], q[L + 1]) < up(q[L], q[L + 1])) L++;
 70         while(L + 1 < R && Cross(Node(1, -sum[i]), p[L + 1] - p[L]) >= 0) L++;
 71         int j = q[L];
 72         f[i] = g[j] + sum[j] * (sum[i] - sum[j]);
 73 //        while(L + 1 < R && slope(q[R - 2], q[R - 1]) < slope(q[R - 2], i)) R--;
 74 //        while(L + 1 < R && up(q[R - 2], q[R - 1]) * down(q[R - 2], i) < up(q[R - 2], i) * down(q[R - 2], q[R - 1])) R--;
 75         Node u(sum[i], up(i));
 76         while(L + 1 < R && Cross(p[R - 1] - p[R - 2], u - p[R - 2]) >= 0) R--;
 77         q[R] = i, p[R++] = u;
 78     }
 79     for(int i = st + 1; i <= n; i++) g[i] = f[i];
 80 }
 81 
 82 int main() {
 83 #ifdef DEBUG
 84     freopen("in.txt", "r", stdin);
 85     freopen("out.txt", "w", stdout);
 86 #endif
 87     
 88     read(n);
 89     int k = read<int>();
 90     
 91     for(int i = 1; i <= n; i++) {
 92         int x = read<int>();
 93         if(!x) i--, n--;
 94         else sum[i] = sum[i-1] + x;
 95 //        sum[i] = sum[i-1] + read<int>();
 96     }
 97     
 98     for(int i = 1; i <= k; i++) dp(i);
 99     
100     printf("%lld\n", g[n]);
101     
102     return 0;
103 }