背包问题九讲

public class Package {
    public static void main(String[] args) {
        int W=10;
        int[] w={2,3,2,5};
        int[] v={3,4,5,6};
        int[] k={2,3,2,1};
        int U=8;
        int[] u={3,2,4,3};

        System.out.println(package01(W,w,v));//res=15
        System.out.println(packageFull(W,w,v));//res=25
        System.out.println(packageK(W,w,v,k));//res=18
        System.out.println(package2D(W,U,w,u,v));//res=13
        System.out.println(package2DFull(W,U,w,u,v));//res=13
        System.out.println(package2DK(W,U,w,u,v,k));//res=13
        //System.out.println(packageGroup(W,w,v));//res=13;
        System.out.println(packageSum(W,w,v));//res=15
    }
    public static int package01(int W,int[] w,int[] v){
        int len=w.length;
        int[][] dp=new int[len+1][W+1];
        for(int i=1;i<=len;i++){
            for(int j=1;j<=W;j++){
                if(w[i-1]>j){
                    dp[i][j]=dp[i-1][j];
                }else{
                    dp[i][j]=Math.max(dp[i-1][j],dp[i-1][j-w[i-1]]+v[i-1]);
                }
            }
        }
        return dp[len][W];
    }
    public static int package012(int W,int[] w,int[] v){
        int len=w.length;
        int[] dp=new int[W+1];
        for(int i=1;i<=len;i++){
            for(int j=W;j>=w[i-1];j--){
                //for (int j = W; j >=w[i - 1]; j--) {
                dp[j]=Math.max(dp[j],dp[j-w[i-1]]+v[i-1]);
            }
        }
        return dp[W];
    }
    public static int packageFull(int W,int[] w,int[] v){
        int len=w.length;
        int[][] dp=new int[len+1][W+1];
        for(int i=1;i<=len;i++){
            for(int j=1;j<=W;j++){
                if(w[i-1]>j){
                    dp[i][j]=dp[i-1][j];
                }else{
                    dp[i][j]=Math.max(dp[i-1][j],dp[i][j-w[i-1]]+v[i-1]);
                }
            }
        }
        return dp[len][W];
    }
    public static int packageFull2(int W,int[] w,int[] v){
        int len=w.length;
        int[] dp=new int[W+1];
        for(int i=1;i<=len;i++){
            for(int j=w[i-1];j<=W;j++){
                dp[j]=Math.max(dp[j],dp[j-w[i-1]]+v[i-1]);
            }
        }
        return dp[W];
    }
    public static int packageFull3(int W,int[] w,int[] v){
        int len=w.length;
        int[] dp=new int[W+1];
        for(int i=1;i<=len;i++){
            for (int j = W; j >= w[i-1]; j--) {
                for(int k=0;k*w[i-1] <= j;k++){
                    dp[j]=Math.max(dp[j],dp[j-k*w[i-1]]+k*v[i-1]);
                }
            }
        }
        return dp[W];
    }
    public static int packageK(int W,int[] w,int[] v,int[] K){
        int len=w.length;
        int[][] dp=new int[len+1][W+1];
        for(int i=1;i<=len;i++){
            for(int j=1;j<=W;j++){
                for(int k=0;k<= K[i-1] && k*w[i-1] <= j;k++) {
                    dp[i][j] = Math.max(dp[i][j], dp[i - 1][j - k*w[i-1]] + k*v[i-1]);
                }
            }
        }
        return dp[len][W];
    }
    public static int packageK2(int W,int[] w,int[] v,int[] K){
        int len=w.length;
        int[] dp=new int[W+1];
        for(int i=1;i<=len;i++){
            for (int j = W; j >=w[i - 1]; j--) {
                for(int k=0;k<= K[i-1] && k*w[i-1] <= j;k++) {
                    dp[j] = Math.max(dp[j], dp[j - k*w[i-1]] + k*v[i-1]);
                }
            }
        }
        return dp[W];
    }
    public static int package2D(int W,int U,int[] w,int[] u,int[] v){
        int len=w.length;
        int[][] dp=new int[W+1][U+1];
        for(int i=1;i<=len;i++) {
            for (int j = W; j >=w[i - 1]; j--) {
                for (int m = U; m >=u[i - 1]; m--) {
                    dp[j][m] = Math.max(dp[j][m], dp[j - w[i - 1]][m - u[i - 1]] + v[i - 1]);
                }
            }
        }
        return dp[W][U];
    }
    public static int package2DFull(int W,int U,int[] w,int[] u,int[] v){
        int len=w.length;
        int[][] dp=new int[W+1][U+1];
        for(int i=1;i<=len;i++) {
            for (int j = w[i - 1];j <= W; j++) {
                for (int m = u[i - 1]; m <= U; m++) {
                    dp[j][m] = Math.max(dp[j][m], dp[j - w[i - 1]][m - u[i - 1]] + v[i - 1]);
                }
            }
        }
        return dp[W][U];
    }
    public static int package2DK(int W,int U,int[] w,int[] u,int[] v,int[] K){
        int len=w.length;
        int[][] dp=new int[W+1][U+1];
        for(int i=1;i<=len;i++) {
            //for (int j = 1; j <= W; j++) {
            for (int j = W; j > 0; j--) {
                for (int m = U; m > 0; m--) {
                    for(int k=0;k<=K[i-1] && k*w[i-1] <= j && k*u[i-1] <= m;k++) {
                            dp[j][m] = Math.max(dp[j][m], dp[j - k*w[i - 1]][m - k*u[i - 1]] + k*v[i - 1]);
                    }
                }
            }
        }
        return dp[W][U];
    }
    public static int packageGroup(int W,int[] w,int[] v){
        int len=w.length;//比如第3个、第4个不能放在一起
        int groups=w.length-1;
        int[][]ww=new int[groups][2];
        int[][]vv=new int[groups][2];
        for(int i=0;i<w.length-1;i++){
            ww[i][0]=w[i];
            vv[i][0]=v[i];
        }
        ww[groups-1][1]=w[len-1];
        vv[groups-1][1]=v[len-1];

        int[] dp=new int[groups+1];
        for(int i=1;i<=groups;i++){
            for(int j=W;j>=0;j--){
                for(int group=0;group< 2 && j>= ww[i - 1][group] && ww[i - 1][group]>0 && vv[i - 1][group]>0;group++) {
                    System.out.println(j - ww[i - 1][group]+"ss");
                    dp[j] = Math.max(dp[j], dp[j - ww[i - 1][group]] + vv[i - 1][group]);//????
                }
            }
        }
        return dp[groups];
    }
    public static int packageSum(int W,int[] w,int[] v){
        int len=w.length;
        int[] ww=new int[w.length+1];
        for(int i=1;i<w.length+1;i++){
            ww[i]=w[i-1];
        }
        int[] vv=new int[w.length+1];
        for(int i=1;i<w.length+1;i++){
            vv[i]=v[i-1];
        }
        int[] dp=new int[W+1];
        dp[0]=1;
        for(int i=1;i<=len;i++){
            for(int j=W;j>=ww[i];j--){
                //for (int j = W; j >=w[i - 1]; j--) {
                dp[j]=dp[j]+dp[j-ww[i]];
            }
        }
        return dp[W];
    }
}