poj_1163&&SDUT 1730 The Triangle

The Triangle

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 51049		Accepted: 30929

Description

7
3   8
8   1   0
2   7   4   4
4   5   2   6   5

(Figure 1)

Figure 1 shows a number triangle. Write a program that calculates the highest sum of numbers passed on a route that starts at the top and ends somewhere on the base. Each step can go either diagonally down to the left or diagonally down to the right. 

Input

Your program is to read from standard input. The first line contains one integer N: the number of rows in the triangle. The following N lines describe the data of the triangle. The number of rows in the triangle is > 1 but <= 100. The numbers in the triangle, all integers, are between 0 and 99.

Output

Your program is to write to standard output. The highest sum is written as an integer.

Sample Input

5
7
3 8
8 1 0 
2 7 4 4
4 5 2 6 5

Sample Output

30

#include <iostream>
#include <algorithm>
using namespace std;
int m=100;
int main()
{
    int array[m][m];
    int *getsum;//进一步优化空间，指针
    int n;
    cin>>n;
    for(int i=1;i<=n;++i)
        for(int j=1;j<=i;++j)
        cin>>array[i][j];
        getsum=array[n];
    for(int i=n-1;i>=1;--i)
        for(int j=1;j<=i;++j)
        getsum[j]=max(getsum[j],getsum[j+1])+array[i][j];
        //不理解的话可以用getsum[j]=max(array[i+1][j],array[i+1][j+1])+array[i][j];将数值代入就会发现rray每次计算的数值并没有与getsum的值联系在一起
        cout<<getsum[1]<<endl;
        return 0;
}

//递推，空间优化
#include <iostream>
#include <algorithm>
using namespace std;
int m=100;
int main()
{
    int array[m][m];
    int getsum[m];
    int n;
    cin>>n;
    for(int i=1;i<=n;++i)
        for(int j=1;j<=i;++j)
        cin>>array[i][j];
    for(int i=1;i<=n;++i)
        getsum[i]=array[n][i];
    for(int i=n-1;i>=1;--i)
        for(int j=1;j<=i;++j)
        getsum[j]=max(getsum[j],getsum[j+1])+array[i][j];
        //不理解的话可以用getsum[j]=max(array[i+1][j],array[i+1][j+1])+array[i][j];将数值代入就会发现rray每次计算的数值并没有与getsum的值联系在一起
        cout<<getsum[1]<<endl;
        return 0;
}
//超时
#include <iostream>
#include <algorithm>
#define m 100
using namespace std;
int n;
int array[m][m];
int getsum(int i,int j)
{
    if(i==n)
        return array[i][j];
    int x=getsum(i+1,j);
    int y=getsum(i+1,j+1);
    return max(x,y)+array[i][j];
}
int main()
{
    cin>>n;
    for(int i=1;i<=n;i++)
        for(int j=1;j<=i;j++)
        cin>>array[i][j];
    cout<<getsum(1,1)<<endl;
    return 0;
}
//递归
#include <iostream>
#include <algorithm>
#define m 100
using namespace std;
int n;
int array[m][m];
int maxsum[m][m];
int getsum(int i,int j)
{
    if(maxsum[i][j]!=-1)
        return maxsum[i][j];
    if(i==n)
        maxsum[i][j]=array[i][j];
    else
    {
    int x=getsum(i+1,j);
    int y=getsum(i+1,j+1);
     maxsum[i][j]=max(x,y)+array[i][j];
    }
    return maxsum[i][j];
}
int main()
{
    cin>>n;
    for(int i=1;i<=n;i++)
        for(int j=1;j<=i;j++)
        {
            cin>>array[i][j];
            maxsum[i][j]=-1;
        }
    cout<<getsum(1,1)<<endl;
    return 0;
}
//递推
#include <iostream>
#include <algorithm>
using namespace std;
int m=100;
int main()
{
    int array[m][m];
    int getsum[m][m];
    int n;
    cin>>n;
    for(int i=1;i<=n;++i)
        for(int j=1;j<=i;++j)
        cin>>array[i][j];
    for(int i=1;i<=n;++i)
        getsum[n][i]=array[n][i];
    for(int i=n-1;i>=1;--i)
        for(int j=1;j<=i;++j)
        getsum[i][j]=max(getsum[i+1][j],getsum[i+1][j+1])+array[i][j];
        cout<<getsum[1][1]<<endl;
        return 0;
}