【DP】UVA 10003 Cutting Sticks 类似矩阵链乘

记忆化搜索

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <math.h>
#include <string>
#include <iostream>
#include <algorithm>
using namespace std;
#include <queue>
#include <stack>
#include <vector>
#include <deque>
#include <set>
#include <map>
#define IN     freopen ("in.txt" , "r" , stdin);
#define OUT  freopen ("out.txt" , "w" , stdout);
typedef long long  LL;
const int MAXN = 55;//点数的最大值
const int MAXM = 20006;//边数的最大值
const int INF = 11521204;
const int mod=1000000007;
int dp[MAXN][MAXN],x[MAXN],a;
int find(int l,int r)
{
    if(l+1==r)
        return 0;
    if(dp[l][r]!=-1)    return dp[l][r];
    dp[l][r]=INF;
    for(int i=l+1; i<r; i++)
        dp[l][r]=min(dp[l][r],find(l,i)+find(i,r)+x[r]-x[l]);
    return dp[l][r];
}
int main()
{
    int n;
    while(scanf("%d",&n),n)
    {
        memset(dp,-1,sizeof(dp));
        scanf("%d",&a);
        x[0]=0;
        x[a+1]=n;
        for(int i=1; i<=a; i++)
            scanf("%d",&x[i]);
        printf("The minimum cutting is %d.\n",find(0,a+1));

    }
    return 0;
}

递推

按照r-l的间隔递增转移状态

#include<stdio.h>
#include<string.h>
int main()
{

    int n,l,i,j,k,c;
    while (scanf("%d",&l))
    {
        if (l==0) break;
        scanf("%d",&n);
        int dp[52][52],p[52];
        memset(a,0,sizeof(a));
        for (i=1; i<=n; i++)
            scanf("%d",&p[i]);
        p[0]=0;
        p[++n]=l;
        for (c=2; c<=n; c++)//间隔
            for (i=0; i<=n-c; i++)
            {
                j=i+c;
                for (k=i+1; k<j; k++)
                    if (dp[i][j]==0 || dp[i][j]>dp[i][k]+dp[k][j]+p[j]-p[i])
                        dp[i][j]=dp[i][k]+dp[k][j]+p[j]-p[i];
            }
        printf("The minimum cutting is %d.\n",a[0][n]);
    }
    return 0;
}