hdu 2829 Lawrence， hdu 3045 Picnic Cows，hdu 3480 Division ， 斜率dp

斜率dp的几题.

hdu2829

//#pragma warning (disable: 4786)//#pragma comment (linker, "/STACK:16777216")//HEAD#include <cstdio>#include <ctime>#include <cstdlib>#include <cstring>#include <queue>#include <string>#include <set>#include <stack>#include <map>#include <cmath>#include <vector>#include <iostream>#include <algorithm>using namespace std;//LOOP#define FF(i, a, b) for(int i = (a); i < (b); ++i)#define FD(i, b, a) for(int i = (b) - 1; i >= (a); --i)#define FE(i, a, b) for(int i = (a); i <= (b); ++i)#define FED(i, b, a) for(int i = (b); i>= (a); --i)#define REP(i, N) for(int i = 0; i < (N); ++i)#define CLR(A,value) memset(A,value,sizeof(A))#define RI(n) scanf("%d", &n)#define RII(n, m) scanf("%d%d", &n, &m)#define RIII(n, m, k) scanf("%d%d%d", &n, &m, &k)#define RIV(n, m, k, p) scanf("%d%d%d%d", &n, &m, &k, &p)#define RV(n, m, k, p, q) scanf("%d%d%d%d%d", &n, &m, &k, &p, &q)#define RS(s) scanf("%s", s)//OUTPUT#define WI(n) printf("%d\n", n)#define WS(s) printf("%s\n", s)typedef long long LL;typedef vector <int> VI;const int INF = 1000000000;const double eps = 1e-10;const int MAXN = 1005;int n, m;int s[MAXN];int a[MAXN];int tol;int q[MAXN], be, ed;int dp[MAXN][MAXN];int getUp(int i, int j, int k){//    return -1 * dp[k - 1][j] + s[j] * s[j] - (-1 * dp[k - 1][i] + s[i] * s[i]);    return s[j] * s[j] - dp[k - 1][j] - (s[i] * s[i] - dp[k - 1][i]);}int getDown(int i, int j){    return s[j] - s[i];}void solve(){    FE(i, 1, m)    {        be = 1;        ed = 0;        q[++ed] = i;        FE(j, i + 1, n)        {            while (be < ed)            {                int p1= q[be];                int p2 = q[be + 1];                int x1 = getDown(p1, p2);                int y1 = getUp(p1, p2, i);                if (y1 <= s[j] * x1) be++;                else break;            }            int p = q[be];            dp[i][j] = dp[i - 1][p] + s[p] * (s[j] - s[p]);            while(be < ed)            {                int p1 = q[ed - 1];                int p2 = q[ed];                int x1 = getDown(p1, p2);                int x2 = getDown(p2, j);                int y1 = getUp(p1, p2, i);                int y2 = getUp(p2, j, i);                if (y1 * x2 >= y2 * x1) ed--;                else break;            }            q[++ed] = j;        }    }    printf("%d\n", tol - dp[m][n]);}int main (){    while (~RII(n, m) && (n || m))    {        s[0] = 0;        FE(i, 1, n)        {            RI(a[i]);            s[i] = s[i - 1] + a[i];        }        tol = 0;        FED(i, n, 2)        {            tol += a[i] * s[i - 1];        }        CLR(dp, 0);        solve();    }    return 0;}

hdu3045

//#pragma warning (disable: 4786)//#pragma comment (linker, "/STACK:16777216")//HEAD#include <cstdio>#include <ctime>#include <cstdlib>#include <cstring>#include <queue>#include <string>#include <set>#include <stack>#include <map>#include <cmath>#include <vector>#include <iostream>#include <algorithm>using namespace std;//LOOP#define FF(i, a, b) for(int i = (a); i < (b); ++i)#define FD(i, b, a) for(int i = (b) - 1; i >= (a); --i)#define FE(i, a, b) for(int i = (a); i <= (b); ++i)#define FED(i, b, a) for(int i = (b); i>= (a); --i)#define REP(i, N) for(int i = 0; i < (N); ++i)#define CLR(A,value) memset(A,value,sizeof(A))//INPUT#define RI(n) scanf("%d", &n)#define RII(n, m) scanf("%d%d", &n, &m)#define RIII(n, m, k) scanf("%d%d%d", &n, &m, &k)#define RIV(n, m, k, p) scanf("%d%d%d%d", &n, &m, &k, &p)#define RV(n, m, k, p, q) scanf("%d%d%d%d%d", &n, &m, &k, &p, &q)#define RS(s) scanf("%s", s)//OUTPUT#define WI(n) printf("%d\n", n)#define WS(s) printf("%s\n", s)typedef long long LL;typedef vector <int> VI;const int INF = 1000000000;const double eps = 1e-10;const int MAXN = 400005;int q[MAXN];LL dp[MAXN];LL a[MAXN], s[MAXN];int be, ed;int n, k;LL getUp(int i, int j){    return dp[j] - s[j] + j * a[j + 1] - (dp[i] - s[i] + i * a[i + 1]);}LL getDown(int i, int j){    return a[j + 1] - a[i + 1];}void solve(){    CLR(dp, 0);///    be = 1;    ed = 0;    q[++ed] = 0;    FE(i, k, n)///    {        while (be < ed)        {            int p1 = q[be];            int p2 = q[be + 1];            LL x1 = getDown(p1, p2);            LL y1 = getUp(p1, p2);            if (y1 <= i * x1) be++;            else break;        }        int p = q[be];        dp[i] = dp[p] + s[i] - s[p] - (i - p) * a[p + 1];        int j = i - k + 1;        if (j < k) continue;///!!!!!!!!!!!!!!!!!!!!!!!!!        while (be < ed)        {            int p1 = q[ed - 1];            int p2 = q[ed];            LL x1 = getDown(p1, p2);            LL x2 = getDown(p2, j);            LL y1 = getUp(p1, p2);            LL y2 = getUp(p2, j);            if (y1 * x2 >= y2 * x1) ed--;            else break;        }        q[++ed] = j;    }    printf("%I64d\n", dp[n]);}int main (){    while (~RII(n, k))    {        FE(i, 1, n) scanf("%I64d", &a[i]);        sort(a + 1, a + 1 + n);        s[0] = 0;        FE(i, 1, n) s[i] = s[i - 1] + a[i];        solve();    }    return 0;}

hdu3480

//#pragma warning (disable: 4786)//#pragma comment (linker, "/STACK:16777216")//HEAD#include <cstdio>#include <ctime>#include <cstdlib>#include <cstring>#include <queue>#include <string>#include <set>#include <stack>#include <map>#include <cmath>#include <vector>#include <iostream>#include <algorithm>using namespace std;//LOOP#define FF(i, a, b) for(int i = (a); i < (b); ++i)#define FD(i, b, a) for(int i = (b) - 1; i >= (a); --i)#define FE(i, a, b) for(int i = (a); i <= (b); ++i)#define FED(i, b, a) for(int i = (b); i>= (a); --i)#define REP(i, N) for(int i = 0; i < (N); ++i)#define CLR(A,value) memset(A,value,sizeof(A))#define CPY(a, b) memcpy(a, b, sizeof(a))#define FC(it, c) for(__typeof((c).begin()) it = (c).begin(); it != (c).end(); it++)//STL#define SZ(V) (int)V.size()#define PB push_back#define EQ(a, b) (fabs((a) - (b)) <= 1e-10)#define ALL(c) (c).begin(), (c).end()//INPUT#define RI(n) scanf("%d", &n)#define RII(n, m) scanf("%d%d", &n, &m)#define RIII(n, m, k) scanf("%d%d%d", &n, &m, &k)#define RIV(n, m, k, p) scanf("%d%d%d%d", &n, &m, &k, &p)#define RV(n, m, k, p, q) scanf("%d%d%d%d%d", &n, &m, &k, &p, &q)#define RS(s) scanf("%s", s)//OUTPUT#define WI(n) printf("%d\n", n)#define WS(s) printf("%s\n", s)typedef long long LL;typedef unsigned long long ULL;typedef vector <int> VI;const int INF = 1000000000;const double eps = 1e-10;const int MAXN = 10005;int q[MAXN], be, ed;int a[MAXN];int dp[5005][MAXN];int n, m;int getUp(int i, int j, int k){    return dp[k - 1][j] - dp[k - 1][i] + a[j + 1] * a[j + 1] - a[i + 1] * a[i + 1];}int getDown(int i, int j){    return a[j + 1] - a[i + 1];}int solve(){    FE(i, 1, n)        dp[1][i] = (a[i] - a[1]) * (a[i] - a[1]);    FE(i, 2, m)    {        be = 1;        ed = 0;        q[++ed] = i - 1;        FE(j, i, n)        {            while (be < ed)            {                int p1 = q[be];                int p2 = q[be + 1];                int x1 = getDown(p1, p2);                int y1 = getUp(p1, p2, i);                if (y1 <= 2 * a[j] * x1) be++;                else break;            }            int p = q[be];            dp[i][j] = dp[i - 1][p] + (a[j] - a[p + 1]) * (a[j] - a[p + 1]);            while (be < ed)            {                int p1 = q[ed - 1];                int p2 = q[ed];                int p3 = j;                int x1 = getDown(p1, p2);                int x2 = getDown(p2, p3);                int y1 = getUp(p1, p2, i);                int y2 = getUp(p2, p3, i);                if (x1 * y2 <= x2 * y1) ed--;                else break;            }            q[++ed] = j;        }    }    printf("%d\n", dp[m][n]);}int main (){    int T;    RI(T);    int iCase = 1;    while (T--)    {        RII(n, m);//        a[0] = 0;        FE(i, 1, n)            RI(a[i]);        sort(a + 1, a + 1 + n);//        CLR(dp, 0);        printf("Case %d: ",iCase++);        solve();    }    return 0;}