Codeforces Round #267 (Div. 2) C George and Job

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題目大意：從n個數中選出m段不相交的子串，子串的長度均為k，問所有選出來的子串的所有數的和最大為多少。

DP題，DP還是太弱，開始時的dp方程居然寫成了O(n^3)...  

dp[i][j]:  以num[i]結尾的序列，分成j段的最大和

dp[i][j]=max(dp[k][j-1]+sum[i]-sum[i-m])  這樣的話，其實只要第一重迴圈是選的段數，第二重迴圈時數字個數

我又換了種思路

dp[i][j]: 前i個數，分成j段的最大和

dp[i][j]=max(dp[i-1][j],dp[i-m][j-1]+sum[i]-sum[i-m])

思路：二維嘛，所以寫出來的dp方程肯定是要麼從第一維變化轉移過來的，要麼從第二維的變化轉移過來的

AC代碼：

//#pragma comment(linker, "/STACK:102400000,102400000")#include <cstdio>#include <cstring>#include <algorithm>#include <string>#include <iostream>#include <iomanip>#include <cmath>#include <map>#include <set>#include <queue>using namespace std;#define ls(rt) rt*2#define rs(rt) rt*2+1#define ll long long#define ull unsigned long long#define rep(i,s,e) for(int i=s;i<e;i++)#define repe(i,s,e) for(int i=s;i<=e;i++)#define CL(a,b) memset(a,b,sizeof(a))#define IN(s) freopen(s,"r",stdin)#define OUT(s) freopen(s,"w",stdout)const ll ll_INF = ((ull)(-1))>>1;const double EPS = 1e-8;const double pi = acos(-1);const int INF = 100000000;const int MAXN = 5000+100;ll num[MAXN],dp[MAXN][MAXN],pp[MAXN];int n,m,k;ll solve(){    CL(dp,0);    for(int i=m;i<=n;i++)        for(int j=1;j<=k;j++)            dp[i][j]=max(dp[i-m][j-1]+pp[i]-pp[i-m],dp[i-1][j]);    return dp[n][k];}int main(){    //IN("C.txt");    while(~scanf("%d%d%d",&n,&m,&k))    {        pp[0]=0;        for(int i=1;i<=n;i++)        {            scanf("%I64d",&num[i]);            pp[i]=pp[i-1]+num[i];        }        printf("%I64d\n",solve());    }    return 0;}

第一種思路的AC代碼（摘自 http://blog.csdn.net/qian99/article/details/39397101）：

#include<iostream>  #include<cstdio>  #include<cstring>  #include<string>  #include<algorithm>  #include<map>  #include<queue>  #include<stack>  #include<set>  #include<cmath>  #include<vector>  #define inf 0x3f3f3f3f  #define Inf 0x3FFFFFFFFFFFFFFFLL  #define eps 1e-8  #define pi acos(-1.0)  using namespace std;  typedef long long ll;  const int maxn = 5000 + 5;  int a[maxn];  ll sum[maxn],dp[maxn][maxn],maxv[maxn];  int main()  {  //    freopen("in.txt","r",stdin);  //    freopen("out.txt","w",stdout);      int n,m,k;      scanf("%d%d%d",&n,&m,&k);      for(int i = 1;i <= n;++i)          scanf("%d",&a[i]);      sum[0] = 0;      for(int i = 1;i <= n;++i)          sum[i] = sum[i-1] + a[i];      memset(dp,0xff,sizeof(dp));      memset(maxv,0,sizeof(maxv));      dp[0][0] = 0;      for(int j = 1;j <= k;++j)      {          for(int i = 1;i <= n;++i)          {              if(i - m >= 0)              {                  dp[i][j] = max(dp[i][j],maxv[i-m] + sum[i] - sum[i-m]);              }          }          for(int i = 1;i <= n;++i)              maxv[i] = max(maxv[i-1],dp[i][j]);      }      ll ans = 0;      for(int i = 1;i <= n;++i)          if(dp[i][k] != -1)              ans = max(ans,dp[i][k]);      printf("%I64d\n",ans);      return 0;  }  

Codeforces Round #267 (Div. 2) C George and Job