USACO Number Triangles
2014-02-02 09:45
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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 diagonallydown 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 than100.
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
/* ID: qhn9992 PROG: numtri LANG: C++ */ #include <iostream> #include <cstring> #include <cstdio> #include <algorithm> using namespace std; int a[1200][1200],dp[1200][1200]; int main() { freopen("numtri.in","r",stdin); freopen("numtri.out","w",stdout); int n; scanf("%d",&n); for(int i=0;i<n;i++) { for(int j=0;j<=i;j++) { scanf("%d",&a[i][j]); } } for(int i=0;i<n;i++) { for(int j=0;j<=i;j++) { int A=0,B=0; if(i-1>=0) { if(j-1>=0) A=dp[i-1][j-1]; B=dp[i-1][j]; } dp[i][j]=max(A,B)+a[i][j]; } } int ans=0; for(int i=0;i<n;i++) { ans=max(ans,dp[n-1][i]); } printf("%d\n",ans); return 0; }
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