DP -入门题1

最新推荐文章于 2025-09-20 20:36:20 发布

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在上面的数字三角形中寻找一条从顶部到底边的路径，使得路径上所经过的数字之和最大。路径上的每一步都只能往左下或右下走。只需要求出这个最大和即可，不必给出具体路径。三角形的行数大于1小于等于100，数字为 0 - 99

输入格式：

5 //表示三角形的行数接下来输入三角形

3 8

8 1 0

2 7 4 4

4 5 2 6 5

DP解法1

#include<iostream>
#include<algorithm>
using namespace std;
#define MAX 101

int buf[MAX][MAX];
int max_buf[MAX][MAX];


void solve(int pos_x,int pos_y,int &n)
{
    int i,j;
    for(i = n;i >= 1;i--)
    {
        if(i == pos_x)
        {
            j = pos_y;
            if(i == n)
            {
                max_buf[i][j] = buf[i][j];

            }
            else
            {
                int x,y;
                x = max_buf[i+1][j];
                y = max_buf[i+1][j+1];
                max_buf[i][j] = max(x,y) + buf[i][j];
            }
			cout <<max_buf[pos_x][pos_y];
        }
        else
        {
            for(j = 1;j <= i;j++)
            {
                if(i == n)
                {
                    max_buf[i][j] = buf[i][j];
                }
                else
                {
                    int x,y;
                    x = max_buf[i+1][j];
                    y = max_buf[i+1][j+1];
                    max_buf[i][j] = max(x,y) + buf[i][j];
                }
            }
        }
    }
	
}

int main()
{
    int i,j;
    int n;	
    cin >> n;
    for(i = 1;i <= n;i++)
    {
        for(j = 1;j <= i;j++)
        {
            cin >> buf[i][j];
        }
    }
    solve(1,1,n);
    system("pause");
    return 0;
}

#include<iostream>
#include<algorithm>
using namespace std;
#define MAX 101

int buf[MAX][MAX];
int max_buf[MAX][MAX];
int max_buf_p[MAX];//优化的solve2所用


void solve(int pos_x,int pos_y,int &n)
{
    int i,j;
    for(i = n;i >= 1;i--)
    {
        if(i == pos_x)
        {
            j = pos_y;
            if(i == n)
            {
                max_buf[i][j] = buf[i][j];

            }
            else
            {
                int x,y;
                x = max_buf[i+1][j];
                y = max_buf[i+1][j+1];
                max_buf[i][j] = max(x,y) + buf[i][j];
            }
			cout <<max_buf[pos_x][pos_y];
        }
        else
        {
            for(j = 1;j <= i;j++)
            {
                if(i == n)
                {
                    max_buf[i][j] = buf[i][j];
                }
                else
                {
                    int x,y;
                    x = max_buf[i+1][j];
                    y = max_buf[i+1][j+1];
                    max_buf[i][j] = max(x,y) + buf[i][j];
                }
            }
        }
    }
	
}

//空间再优化
void solve2(int pos_x,int pos_y,int &n)
{
	int i,j;
	for(i = n;i >= 1;i--)
    {
        if(i == pos_x)
        {
            j = pos_y;
            if(i == n)
            {
                max_buf_p[j] = buf[i][j];

            }
            else
            {
                int x,y;
                x = max_buf_p[j];
                y = max_buf_p[j+1];
                max_buf_p[j] = max(x,y) + buf[i][j];
            }
			cout <<max_buf_p[pos_x];
        }
        else
        {
            for(j = 1;j <= i;j++)
            {
				if(i == n)
				{
					max_buf_p[j] = buf[i][j];
				}
				else
				{
					int x,y;
					x = max_buf_p[j];
					y = max_buf_p[j+1];
					max_buf_p[j] = max(x,y) + buf[i][j];
				}
				cout <<max_buf_p[pos_x];
            }
        }
    }

}
int main()
{
    int i,j;
    int n;	
    cin >> n;
    for(i = 1;i <= n;i++)
    {
        for(j = 1;j <= i;j++)
        {
            cin >> buf[i][j];
        }
    }
    solve2(1,1,n);
    system("pause");
    return 0;
}