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BZOJ 1911 特别行动队(斜率优化DP)
应该可以看出这是个很normal的斜率优化式子。推出公式搞一搞即可。
# include <cstdio> # include <cstring> # include <cstdlib> # include <iostream> # include <vector> # include <queue> # include <stack> # include <map> # include <set> # include <cmath> # include <algorithm> using namespace std; # define lowbit(x) ((x)&(-x)) # define pi 3.1415926535 # define eps 1e-9 # define MOD 10000 # define INF 1000000000 # define mem(a,b) memset(a,b,sizeof(a)) # define FOR(i,a,n) for(int i=a; i<=n; ++i) # define FO(i,a,n) for(int i=a; i<n; ++i) # define bug puts("H"); # define lch p<<1,l,mid # define rch p<<1|1,mid+1,r # define mp make_pair # define pb push_back typedef pair<int,int> PII; typedef vector<int> VI; # pragma comment(linker, "/STACK:1024000000,1024000000") typedef long long LL; int Scan() { int res=0, flag=0; char ch; if((ch=getchar())==‘-‘) flag=1; else if(ch>=‘0‘&&ch<=‘9‘) res=ch-‘0‘; while((ch=getchar())>=‘0‘&&ch<=‘9‘) res=res*10+(ch-‘0‘); return flag?-res:res; } void Out(int a) { if(a<0) {putchar(‘-‘); a=-a;} if(a>=10) Out(a/10); putchar(a%10+‘0‘); } const int N=1000005; //Code begin... int a[N], que[N], head, tail, A, B, C; LL dp[N], sum[N]; bool check(int x, int y, int z){ return dp[x]-dp[y]+A*(sum[x]*sum[x]-sum[y]*sum[y])>=(2*A*sum[z]+B)*(sum[x]-sum[y]); } bool sol(int x, int y, int z){ return (dp[x]-dp[y]+A*(sum[x]*sum[x]-sum[y]*sum[y]))*(sum[y]-sum[z])>=(dp[y]-dp[z]+A*(sum[y]*sum[y]-sum[z]*sum[z]))*(sum[x]-sum[y]); } int main () { int n; scanf("%d%d%d%d",&n,&A,&B,&C); FOR(i,1,n) scanf("%d",a+i), sum[i]=sum[i-1]+a[i]; head=-1; tail=0; que[++head]=0; FOR(i,1,n) { while (head>tail&&check(que[tail+1],que[tail],i)) ++tail; int v=que[tail]; dp[i]=dp[v]+A*(sum[i]-sum[v])*(sum[i]-sum[v])+B*(sum[i]-sum[v])+C; while (head>tail&&sol(i,que[head],que[head-1])) --head; que[++head]=i; } printf("%lld\n",dp[n]); return 0; }
BZOJ 1911 特别行动队(斜率优化DP)
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