Hihocoder1636Pangu and Stones(区间DP)
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题意:N堆石子,每次可以合并连续的长度从L到R的若干堆石子为1堆,费用为选择的石子总个数,求将N堆合并成1堆的最小总花费,无解输出0
思路:dp[i][j][k]表示将i到j这段区间合并为k堆的最小代价
[ 初始条件 dp[i][j][j-i+1]=0 ]
[ dp[i][j][k]=min(dp[i][x][y-1]+dp[x+1][j][1]+s[j]-s[i-1] (k=1,i<=x<=j-1,L<=y<=R) ]
[ dp[i][j][k]=min(dp[i][x][k-1]+dp[x+1][j][1] (k>=2,i<=x<=j-1) ]
1 #include<cstdio> 2 #include<cstring> 3 #include<string> 4 #include<cmath> 5 #include<iostream> 6 #include<algorithm> 7 #include<map> 8 #include<set> 9 #include<queue> 10 #include<vector> 11 using namespace std; 12 typedef long long ll; 13 typedef unsigned int uint; 14 typedef unsigned long long ull; 15 typedef pair<int,int> PII; 16 typedef vector<int> VI; 17 #define fi first 18 #define se second 19 #define MP make_pair 20 #define N 150 21 #define M 6100000 22 #define eps 1e-8 23 #define pi acos(-1) 24 #define oo 1e9 25 26 ll dp[N][N][N],a[N],s[N]; 27 28 int main() 29 { 30 //freopen("hihocoder1636.in","r",stdin); 31 //freopen("hihocoder1636.out","w",stdout); 32 int n,L,R; 33 while(scanf("%d%d%d",&n,&L,&R)!=EOF) 34 { 35 s[0]=0; 36 for(int i=1;i<=n;i++) 37 { 38 scanf("%lld",&a[i]); 39 s[i]=s[i-1]+a[i]; 40 } 41 memset(dp,0x3f,sizeof(dp)); 42 for(int i=1;i<=n;i++) 43 for(int j=i;j<=n;j++) dp[i][j][j-i+1]=0; 44 for(int len=2;len<=n;len++) 45 for(int i=1;i<=n-len+1;i++) 46 { 47 int j=i+len-1; 48 for(int x=i;x<=j-1;x++) 49 for(int y=L;y<=R;y++) 50 dp[i][j][1]=min(dp[i][j][1],dp[i][x][y-1]+dp[x+1][j][1]+s[j]-s[i-1]); 51 for(int k=2;k<=len;k++) 52 for(int x=i;x<=j-1;x++) 53 dp[i][j][k]=min(dp[i][j][k],dp[i][x][k-1]+dp[x+1][j][1]); 54 } 55 if(dp[1][n][1]>oo) printf("0 "); 56 else printf("%lld ",dp[1][n][1]); 57 } 58 return 0; 59 }
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