UVA 10003 Cutting Sticks [线性结构dp] [最优矩阵链乘]

Cutting Sticks

Time Limit: 3000MS 64bit IO Format: %lld & %llu





最优矩阵链乘问题，阶段即使区间长度，因为长区间依赖于短区间，那么初始化dp[i][i+1]=0，因为只剩一段的时候不需要切割，同样k=2开始循环，避免修改dp[i][i+1]=0

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<cmath>
#include<vector>
#include<queue>
#include<stack>
#include<map>
#include<set>
#include<string>
#include<iomanip>
#include<ctime>
#include<climits>
#include<cctype>
#include<algorithm>
#ifdef WIN32
#define AUTO "%I64d"
#else
#define AUTO "%lld"
#endif
using namespace std;
#define smax(x,tmp) x=max((x),(tmp))
#define smin(x,tmp) x=min((x),(tmp))
#define maxx(x1,x2,x3) max(max(x1,x2),x3)
#define minn(x1,x2,x3) min(min(x1,x2),x3)
const int INF=0x3f3f3f3f;
const int maxn = 55;
int L,n;
int sum[maxn];
inline bool init()
{
if(!~scanf("%d%d",&L,&n) || !L) return false;
for(int i=1;i<=n;i++) scanf("%d",sum+i);
sum[n+1]=L;
return true;
}
int dp[maxn][maxn];
int dynamic()
{
memset(dp,0x3f,sizeof(dp));
for(int i=0;i<=n;i++) dp[i][i+1]=0;
for(int k=2;k<=n+1;k++)
for(int i=0;i<=n;i++)
{
int j=i+k;
if(j>n+1) break;
for(int p=i+1;p<j;p++)
smin(dp[i][j],dp[i][p]+dp[p][j]);
dp[i][j] += sum[j]-sum[i];
}
return dp[0][n+1];
}
int main()
{
#ifndef ONLINE_JUDGE
freopen("cut.in","r",stdin);
freopen("cut.out","w",stdout);
#endif
while(init())
printf("The minimum cutting is %d.\n",dynamic());
return 0;
}