Number Triangles - USACO 1.5.1

numbertriangles - codetrick

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

https://github.com/leonlu/USACOJavaSolution/blob/master/USACOSection1/src/numtri.java

DP题。newRow[j]+= max(oldRow[j-1], oldRow[j])。从上至下。边读边计算，状态只需保存当前行和上一行。每一行首尾补零，为了方便计算。



public static void main(String[] args) throws IOException {
  BufferedReader in = new BufferedReader(new FileReader("numtri.in"));
  PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter(
    "numtri.out")),true);
  
  int[] oldRow = null;
  int[] newRow = null;
  
  // initialize
  int N = Integer.parseInt(in.readLine());
  for(int i = 1; i <= N; i++){
   // exchange oldRow with newRow
   if(i != 1) oldRow = newRow; 
   // read in newRow
   newRow = new int[N+2];
   newRow[0] = 0;
   newRow[N+1] = 0;
   StringTokenizer st = new StringTokenizer(in.readLine());
   for(int j = 1; j <= i; j++)
    newRow[j] = Integer.parseInt(st.nextToken());
   // calculate
   if(i != 1)
    for(int j = 1; j <=i; j++)
     newRow[j]+= max(oldRow[j-1], oldRow[j]);
  }
   
  // output
  int maxValue = 0;
  for(int i = 0; i < newRow.length; i++)
   maxValue = max(newRow[i],maxValue);
  out.println(maxValue);
  
  System.exit(0);
 }

http://mangogao.com/read/90.html
http://jackneus.com/programming-archives/number-triangles/
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