Hdu 2829 Lawrence (DP_四边形优化、斜率优化)(二)

2014-11-24 10:45:29 · 作者: · 浏览: 2
for (i = 1; i <= n; ++i)
scanf("%d",&arr[i]),sum[i] = arr[i] + sum[i-1];


Initial();
int ans = Solve_DP();
printf("%d\n",ans);
}
}


[cpp]
//cost[k+1][i]=cost[1][i]-cost[1][k]-sum[k]*(sum[i]-sum[k])
//dp[i][j]=dp[k][j-1]+cost[1][i]-cost[1][k]-sum[k]*(sum[i]-sum[k])
// =dp[k][j-1]-cost[1][k]+sum[k]^2-sum[i]*sum[k]+cost[1][i]
//斜率优化一
#include
#include
#define MAX 1100
#define INF (1<<30)


struct point {

int x,y;
}pot[MAX];
int head,tail,qu[MAX];
int n,m,arr[MAX],cost[MAX];
int sum[MAX],sum2[MAX],dp[MAX][MAX];


void Initial() {

for (int i = 1; i <= n; ++i) {

sum[i] = arr[i] + sum[i-1];
cost[i] = cost[i-1] + arr[i] * sum[i-1];
dp[i][0] = cost[i];
}
}
int CheckIt(point p0,point p1,point p2) {

return (p0.x-p1.x) * (p0.y-p2.y) - (p0.y-p1.y) * (p0.x-p2.x) <= 0;
}
int NotBest(point p0,point p1,int k) {

return p0.y - k * p0.x > p1.y - k * p1.x;
}
int Solve_DP() {


int i,j,k;


for (j = 1; j <= m; ++j) {

head = 0,tail = 0;
qu[tail] = 0;
for (i = j + 1; i <= n; ++i) {

pot[i].x = sum[i-1];
pot[i].y = dp[i-1][j-1] - cost[i-1] + sum[i-1] * sum[i-1];
while (head <= tail - 1 &&
CheckIt(pot[qu[tail-1]],pot[qu[tail]],pot[i])) tail--;


qu[++tail] = i;
while (head + 1 <= tail &&
NotBest(pot[qu[head]],pot[qu[head+1]],sum[i])) head++;
k = qu[head];
//dp[i][j] = y - k * x + c
dp[i][j] = pot[k].y - sum[i] * pot[k].x + cost[i];
}
}


return dp[n][m];
}


int main()
{
int i,j,k;


while (scanf("%d%d",&n,&m),n+m) {

for (i = 1; i <= n; ++i) www.2cto.com
scanf("%d",&arr[i]),sum[i] = arr[i] + sum[i-1];


Initial();
int ans = Solve_DP();
printf("%d\n",ans);
}
}