斜率dp+滚动数组。
1 /* 3480 */ 2 #include <iostream> 3 #include <sstream> 4 #include <string> 5 #include <map> 6 #include <queue> 7 #include <set> 8 #include <stack> 9 #include <vector> 10 #include <deque> 11 #include <algorithm> 12 #include <cstdio> 13 #include <cmath> 14 #include <ctime> 15 #include <cstring> 16 #include <climits> 17 #include <cctype> 18 #include <cassert> 19 #include <functional> 20 #include <iterator> 21 #include <iomanip> 22 using namespace std; 23 //#pragma comment(linker,"/STACK:102400000,1024000") 24 25 #define sti set<int> 26 #define stpii set<pair<int, int> > 27 #define mpii map<int,int> 28 #define vi vector<int> 29 #define pii pair<int,int> 30 #define vpii vector<pair<int,int> > 31 #define rep(i, a, n) for (int i=a;i<n;++i) 32 #define per(i, a, n) for (int i=n-1;i>=a;--i) 33 #define clr clear 34 #define pb push_back 35 #define mp make_pair 36 #define fir first 37 #define sec second 38 #define all(x) (x).begin(),(x).end() 39 #define SZ(x) ((int)(x).size()) 40 #define lson l, mid, rt<<1 41 #define rson mid+1, r, rt<<1|1 42 43 const int maxn = 10005; 44 const int maxm = 5005; 45 int dp[2][maxn]; 46 int Q[maxn]; 47 int a[maxn]; 48 int n, m; 49 50 void solve() { 51 int l, r; 52 int p = 0, q = 1; 53 54 rep(i, 1, n+1) 55 dp[p][i] = (a[i] - a[1]) * (a[i] - a[1]); 56 57 rep(i, 2, m+1) { 58 l = r = 0; 59 Q[r++] = i-1; 60 rep(j, i, n+1) { 61 while (l+1 < r) { 62 int k1 = Q[l]; 63 int k2 = Q[l+1]; 64 int x1 = a[k1+1]; 65 int x2 = a[k2+1]; 66 int y1 = dp[p][k1] + x1 * x1; 67 int y2 = dp[p][k2] + x2 * x2; 68 if ((y2-y1)<=2*a[j]*(x2-x1)) 69 ++l; 70 else 71 break; 72 } 73 int k = Q[l]; 74 int x = a[k+1]; 75 dp[q][j] = dp[p][k] + (a[j]-x)*(a[j]-x); 76 while (l+1 < r) { 77 int k1 = j; 78 int k2 = Q[r-1]; 79 int k3 = Q[r-2]; 80 int x1 = a[k1+1]; 81 int x2 = a[k2+1]; 82 int x3 = a[k3+1]; 83 int y1 = dp[p][k1] + x1 * x1; 84 int y2 = dp[p][k2] + x2 * x2; 85 int y3 = dp[p][k3] + x3 * x3; 86 if ((y3-y2)*(x2-x1) >= (y2-y1)*(x3-x2)) 87 --r; 88 else 89 break; 90 } 91 Q[r++] = j; 92 #ifndef ONLINE_JUDGE 93 printf("l = %d, r = %d ", l, r); 94 #endif 95 } 96 q = p; 97 p ^= 1; 98 } 99 100 int ans = dp[p][n]; 101 printf("%d ", ans); 102 } 103 104 int main() { 105 ios::sync_with_stdio(false); 106 #ifndef ONLINE_JUDGE 107 freopen("data.in", "r", stdin); 108 freopen("data.out", "w", stdout); 109 #endif 110 111 int t; 112 113 scanf("%d", &t); 114 rep(tt, 1, t+1) { 115 scanf("%d %d", &n, &m); 116 rep(i, 1, n+1) 117 scanf("%d", &a[i]); 118 sort(a+1, a+1+n); 119 printf("Case %d: ", tt); 120 solve(); 121 } 122 123 #ifndef ONLINE_JUDGE 124 printf("time = %d. ", (int)clock()); 125 #endif 126 127 return 0; 128 }