Number Triangles
Consider the number triangle shown below. Write a program that calculates the highest sum of numbers that can be 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.
7 3 8 8 1 0 2 7 4 4 4 5 2 6 5
In the sample above, the route from 7 to 3 to 8 to 7 to 5 produces the highest sum: 30.
PROGRAM NAME: numtri
INPUT FORMAT
The first line contains R (1 <= R <= 1000), the number of rows. Each subsequent line contains the integers for that particular row of the triangle. All the supplied integers are non-negative and no larger than 100.
SAMPLE INPUT (file numtri.in)
5 7 3 8 8 1 0 2 7 4 4 4 5 2 6 5
OUTPUT FORMAT
A single line containing the largest sum using the traversal specified.
SAMPLE OUTPUT (file numtri.out)
30 題解: 數字三角形,dp中最簡單的問題
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/*
ID: cxq_xia1
PROG: numtri
LANG: C++
*/
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
using namespace std;
const int maxn=1002;
int a[maxn][maxn];
int dp[maxn];
int main()
{
freopen("numtri.in","r",stdin);
freopen("numtri.out","w",stdout);
int R;
memset(a,0,sizeof(a));
memset(dp,0,sizeof(dp));
cin >> R;
for(int i=1;i<=R;i++)
{
for(int j=1;j<=i;j++)
{
cin >> a[i][j];
}
}
for(int i=R;i>0;i--)
{
for(int j=1;j<=i;j++)
{
dp[j]=max(dp[j],dp[j+1])+a[i][j];
}
}
cout << dp[1] <<endl;
return 0;
}