动态规划解决矩阵路径问题

从矩阵左上角走到矩阵右下角，求最短路径

import java.lang.Math;

public class Dynamic_1{
  static int m = 4;
  static int n = 4;
  static int sum = 0;
  static int[][] state = {{1, 3, 5, 9}, {2, 1, 3, 4}, {5, 2, 6, 7}, {6, 8, 4, 3}};
  static int[][] matrix = new int[m][n];

  public static void dynamic_1(){
    for(int i = 0; i < m; i++){
      sum = sum + state[i][0];
      matrix[i][0] = sum;
    }
    sum = 0;
    for(int j = 0; j < n; j++){
      sum = sum + state[0][j];
      matrix[0][j] = sum;
    }

    for(int i = 1; i < m; i++){
      for(int j = 1; j < n; j++){
        matrix[i][j] = state[i][j] + Math.min(matrix[i - 1][j], matrix[i][j - 1]); 
      }
    }

    for(int i = 0; i < m; i++){
      for(int j = 0; j < n; j++){
        System.out.print(matrix[i][j] + " ");
      }
      System.out.println();
    }
  }
  
  public static void main(String[] argv){
    dynamic_1();
  }

}