POJ-1163-The Triangle: DP入门 递归 递推

递归思路 超时算法

#include<iostream>
using namespace std;
#define Size 101
int Triangle[Size][Size];
int n;

int GetAns( int i, int j )
{
        if( i==n )
            return Triangle[i][j];
        int x=GetAns( i+1, j );
        int y=GetAns( i+1, j+1 );
        return max(x, y)+Triangle[i][j];
}

int main()
{
        cin>>n;
        for( int i=1; i<=n; i++ )
            for( int j=1; j<=i; j++ )
                cin>>Triangle[i][j];

        cout<<GetAns(1, 1)<<endl;
        return 0;
}

上述算法优化: 记忆型递归

#include<iostream>
using namespace std;
#define Size 101
int Triangle[Size][Size];
int Table[Size][Size];
int n;

int GetAns( int i, int j )
{
        if( Table[i][j]!=-1 )
            return Table[i][j];
        if( i==n )
            Table[i][j] = Triangle[i][j];
        else{
                int x=GetAns( i+1, j );
                int y=GetAns( i+1, j+1 );
                Table[i][j] =  max(x, y)+Triangle[i][j];
        }
        return Table[i][j];
}

int main()
{
        cin>>n;
        for( int i=1; i<=n; i++ )
            for( int j=1; j<=i; j++ ){
                cin>>Triangle[i][j];
                Table[i][j]=-1;
            }
        cout<<GetAns(1, 1)<<endl;
        return 0;
}
/*通过引入记忆表 Table 当每算出一个Table(i,j)就保存起来，下次用到其值的时候直接取用，则可免去重复计算。*/

上述递归算法 转 递推(“人人为我”型)

#include<iostream>
using namespace std;
#define Size 101
int Triangle[Size][Size];
int Table[Size][Size];
int n;

int main()
{
        cin>>n;
        for( int i=1; i<=n; i++ )
            for( int j=1; j<=i; j++ )
                cin>>Triangle[i][j];

        for( int i=1; i<=n; i++ )
            Table[n][i] = Triangle[n][i];

        for( int i=n-1; i>=1; i-- )
            for( int j=1; j<=i; j++ )
                        Table[i][j] = max(Table[i+1][j] , Table[i+1][j+1]) + Triangle[i][j];

        cout<<Table[1][1]<<endl;
        return 0;
}