public class sf { 
  public static void main(String[] args) { 
    // TODO Auto-generated method stub 
    int[] weight = {3,5,2,6,4}; //物品重量 
    int[] val = {4,4,3,5,3}; //物品价值 
    int m = 12; //背包容量 
    int n = val.length; //物品个数 
    int[][] f = new int[n+1][m+1]; //f[i][j]表示前i个物品能装入容量为j的背包中的最大价值 
    int[][] path = new int[n+1][m+1]; 
    //初始化第一列和第一行 
    for(int i=0;i<f.length;i++){ 
      f[i][0] = 0; 
    } 
    for(int i=0;i<f[0].length;i++){ 
      f[0][i] = 0; 
    } 
    //通过公式迭代计算 
    for(int i=1;i<f.length;i++){ 
      for(int j=1;j<f[0].length;j++){ 
        if(weight[i-1]>j) 
          f[i][j] = f[i-1][j]; 
        else{ 
          if(f[i-1][j]<f[i-1][j-weight[i-1]]+val[i-1]){ 
            f[i][j] = f[i-1][j-weight[i-1]]+val[i-1]; 
            path[i][j] = 1; 
          }else{ 
            f[i][j] = f[i-1][j]; 
          } 
          //f[i][j] = Math.max(f[i-1][j], f[i-1][j-weight[i-1]]+val[i-1]); 
        } 
      } 
    } 
    for(int i=0;i<f.length;i++){ 
      for(int j=0;j<f[0].length;j++){ 
        System.out.print(f[i][j]+" "); 
      } 
      System.out.println(); 
    } 
    int i=f.length-1; 
    int j=f[0].length-1; 
    while(i>0&&j>0){ 
      if(path[i][j] == 1){ 
        System.out.print("第"+i+"个物品装入 "); 
        j -= weight[i-1]; 
      } 
      i--; 
    } 
  } 
} 

0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 4 4 4 4 4 4 4 4 4 4 
0 0 0 4 4 4 4 4 8 8 8 8 8 
0 0 3 4 4 7 7 7 8 8 11 11 11 
0 0 3 4 4 7 7 7 8 9 11 12 12 
0 0 3 4 4 7 7 7 8 10 11 12 12 
第4个物品装入 第3个物品装入 第1个物品装入 

for i=1..N
  for v=V..0
    f[v]=max{f[v],f[v-c[i]]+w[i]};

public class sf { 
  public static void main(String[] args) { 
    // TODO Auto-generated method stub 
    int[] weight = {3,5,2,6,4}; //物品重量 
    int[] val = {4,4,3,5,3}; //物品价值 
    int m = 12; //背包容量 
    int n = val.length; //物品个数 
    int[] f = new int[m+1]; 
    for(int i=0;i<f.length;i++){   //不必装满则初始化为0 
      f[i] = 0; 
    } 
    for(int i=0;i<n;i++){ 
      for(int j=f.length-1;j>=weight[i];j--){ 
        f[j] = Math.max(f[j], f[j-weight[i]]+val[i]); 
      } 
    } 
    for(int i=0;i<f.length;i++){ 
      System.out.print(f[i]+" "); 
    } 
    System.out.println(); 
    System.out.println("最大价值为"+f[f.length-1]); 
  } 
} 

0 0 3 4 4 7 7 7 8 10 11 12 12 
最大价值为12

public class sf { 
  public static void main(String[] args) { 
    // TODO Auto-generated method stub 
    int[] weight = {3,5,2,6,4}; //物品重量 
    int[] val = {4,4,3,5,3}; //物品价值 
    int m = 12; //背包容量 
    int n = val.length; //物品个数 
    int[] f = new int[m+1]; 
    for(int i=1;i<f.length;i++){   //必装满则f[0]=0,f[1...m]都初始化为无穷小 
      f[i] = Integer.MIN_VALUE; 
    } 
    for(int i=0;i<n;i++){ 
      for(int j=f.length-1;j>=weight[i];j--){ 
        f[j] = Math.max(f[j], f[j-weight[i]]+val[i]); 
      } 
    } 
    for(int i=0;i<f.length;i++){ 
      System.out.print(f[i]+" "); 
    } 
    System.out.println(); 
    System.out.println("最大价值为"+f[f.length-1]); 
  } 
} 

0 -2147483648 3 4 3 7 6 7 8 10 11 12 11 
最大价值为11

for i=1..N
  for v=0..V
    f[v]=max{f[v],f[v-cost]+weight}

public class test{ 
   public static void main(String[] args){ 
      int[] weight = {3,4,6,2,5}; 
      int[] val = {6,8,7,5,9}; 
      int maxw = 10; 
      int[] f = new int[maxw+1]; 
      for(int i=0;i<f.length;i++){ 
        f[i] = 0; 
      } 
      for(int i=0;i<val.length;i++){ 
        for(int j=weight[i];j<f.length;j++){ 
          f[j] = Math.max(f[j], f[j-weight[i]]+val[i]); 
        } 
      } 
      System.out.println(f[maxw]); 
   } 
  } 

25