http://codeforces.com/contest/1197
A. DIY Wooden Ladder
贪心水题
1 #include<iostream> 2 #include<sstream> 3 #include<fstream> 4 #include<algorithm> 5 #include<cstring> 6 #include<iomanip> 7 #include<cstdlib> 8 #include<cctype> 9 #include<vector> 10 #include<string> 11 #include<cmath> 12 #include<ctime> 13 #include<stack> 14 #include<queue> 15 #include<map> 16 #include<set> 17 #define mem(a,b) memset(a,b,sizeof(a)) 18 #define random(a,b) (rand()%(b-a+1)+a) 19 #define ll long long 20 #define ull unsigned long long 21 #define e 2.71828182 22 #define Pi acos(-1.0) 23 using namespace std; 24 const int MAXN=1e5+5; 25 int a[MAXN]; 26 int n; 27 int read() 28 { 29 int s=1,x=0; 30 char ch=getchar(); 31 while(!isdigit(ch)) {if(ch=='-') s=-1;ch=getchar();} 32 while(isdigit(ch)) {x=10*x+ch-'0';ch=getchar();} 33 return x*s; 34 } 35 int solve() 36 { 37 sort(a+1,a+n+1,greater<int>()); 38 if(n==2) return 0; 39 int high=min(a[1],a[2]); 40 if(high==1) return 0; 41 return high-1<n-2?high-1:n-2; 42 } 43 int main() 44 { 45 int T;cin>>T; 46 while(T--) 47 { 48 cin>>n; 49 for(int i=1;i<=n;++i) cin>>a[i]; 50 cout<<solve()<<endl; 51 } 52 return 0; 53 } 54
B.Pillars
找到最大值的下标，必须向两侧递减
1 #include<iostream> 2 #include<sstream> 3 #include<fstream> 4 #include<algorithm> 5 #include<cstring> 6 #include<iomanip> 7 #include<cstdlib> 8 #include<cctype> 9 #include<vector> 10 #include<string> 11 #include<cmath> 12 #include<ctime> 13 #include<stack> 14 #include<queue> 15 #include<map> 16 #include<set> 17 #define mem(a,b) memset(a,b,sizeof(a)) 18 #define random(a,b) (rand()%(b-a+1)+a) 19 #define ll long long 20 #define ull unsigned long long 21 #define e 2.71828182 22 #define Pi acos(-1.0) 23 using namespace std; 24 const int MAXN=2e5+5; 25 int imax,a[MAXN]; 26 int read() 27 { 28 int s=1,x=0; 29 char ch=getchar(); 30 while(!isdigit(ch)) {if(ch=='-') s=-1;ch=getchar();} 31 while(isdigit(ch)) {x=10*x+ch-'0';ch=getchar();} 32 return x*s; 33 } 34 int main() 35 { 36 int n=read(); 37 for(int i=1;i<=n;++i) 38 { 39 a[i]=read(); 40 if(a[i]==n) imax=i; 41 } 42 bool flag=true; 43 for(int i=1;i<=imax-1&&flag;++i) 44 if(a[i]>a[i+1]) flag=false; 45 for(int i=imax;i<=n-1&&flag;++i) 46 if(a[i]<a[i+1]) flag=false; 47 if(flag) cout<<"YES "; 48 else cout<<"NO "; 49 }
C.Array Splitting
a[n]-a[1]=(a[n]-a[n-1])+(a[n-1]-a[n-2])+...+(a[2]-a[1])。划分k个区间相当于从(a[2]-a[1],a[3]-a[2],...,a[n]-a[n-1])中去掉k-1个值。排序后减去前k-1个打的。
1 #include<iostream> 2 #include<sstream> 3 #include<fstream> 4 #include<algorithm> 5 #include<cstring> 6 #include<iomanip> 7 #include<cstdlib> 8 #include<cctype> 9 #include<vector> 10 #include<string> 11 #include<cmath> 12 #include<ctime> 13 #include<stack> 14 #include<queue> 15 #include<map> 16 #include<set> 17 #define mem(a,b) memset(a,b,sizeof(a)) 18 #define random(a,b) (rand()%(b-a+1)+a) 19 #define ll long long 20 #define ull unsigned long long 21 #define e 2.71828182 22 #define Pi acos(-1.0) 23 using namespace std; 24 const int MAXN=3e5+5; 25 int a[MAXN],b[MAXN]; 26 int read() 27 { 28 int s=1,x=0; 29 char ch=getchar(); 30 while(!isdigit(ch)) {if(ch=='-') s=-1;ch=getchar();} 31 while(isdigit(ch)) {x=10*x+ch-'0';ch=getchar();} 32 return x*s; 33 } 34 int main() 35 { 36 int n=read(); 37 int k=read(); 38 for(int i=1;i<=n;++i) 39 a[i]=read(); 40 int ans=a[n]-a[1]; 41 for(int i=2;i<=n;++i) 42 b[i]=a[i]-a[i-1]; 43 sort(b+2,b+n+1,greater<int>()); 44 //for(int i=2;i<=n;++i) cout<<b[i]<<' ';cout<<endl; 45 for(int i=2+0;i<2+k-1;++i) 46 ans-=b[i]; 47 cout<<ans<<endl; 48 }
一开始想用Dp，但复杂度不允许。令dp[i][j]表示前i个数划分成j个子数组（第j个数位于第j个子数组），那么dp[i][j]=min(dp[i-1][j-1],dp[i-1][j]+a[i]-a[i-1])。初始化dp中的值为无穷大，dp[1][1]=0。
D.Yet Another Subarray Problem
令dp[i]表示右边界为a[i]时的最佳答案。
，根据该公式将j（左边界）分为两种情况：
1、i-j+1<=m即i-j+1<m+1，即i-j<m，此时dp[i]=sum[i]-sum[j-1]-k
2、i-j>=m，此时dp[i]=dp[i-m]+sum[i]-sum[i-m]-k
取较大值（最佳值）即可。
1 #include<iostream> 2 #include<sstream> 3 #include<fstream> 4 #include<algorithm> 5 #include<cstring> 6 #include<iomanip> 7 #include<cstdlib> 8 #include<cctype> 9 #include<vector> 10 #include<string> 11 #include<cmath> 12 #include<ctime> 13 #include<stack> 14 #include<queue> 15 #include<map> 16 #include<set> 17 #define mem(a,b) memset(a,b,sizeof(a)) 18 #define random(a,b) (rand()%(b-a+1)+a) 19 #define ll long long 20 #define ull unsigned long long 21 #define e 2.71828182 22 #define Pi acos(-1.0) 23 using namespace std; 24 const int MAXN=3e5+5; 25 const int INF=1<<30; 26 int a[MAXN]; 27 ll dp[MAXN],sum[MAXN]; 28 int n,m,k; 29 ll read() 30 { 31 ll s=1,x=0; 32 char ch=getchar(); 33 while(!isdigit(ch)) {if(ch=='-') s=-1;ch=getchar();} 34 while(isdigit(ch)) {x=10*x+ch-'0';ch=getchar();} 35 return x*s; 36 } 37 int main() 38 { 39 n=read();m=read();k=read(); 40 ll ans=-INF; 41 for(int i=1;i<=n;++i) a[i]=read(),sum[i]=sum[i-1]+a[i]; 42 for(int i=1;i<=n;++i) 43 { 44 for(int j=max(i-m+1,1);j<=i;++j) dp[i]=max(dp[i],sum[i]-sum[j-1]-k); 45 if(i>=m) dp[i]=max(dp[i],dp[i-m]+sum[i]-sum[i-m]-k); 46 ans=dp[i]>ans?dp[i]:ans; 47 } 48 cout<<ans<<endl; 49 return 0; 50 }