背包问题-两个背包问题

递归解法：

public class Main0 {
    static int n = 5;
    static int[] v={0,3,7,4,49,2};
    static int[] w={0,3,4,7,50,2};
    public static void main(String[] args){
        int AV = 10;
        int BV = 50;
        System.out.println(get(1,AV,BV));
    }
    public static int get(int i,int AV, int BV){
        if(i==n)if(AV>=v[n]||BV>=v[n])return w[n];
        else return 0;
        int res = 0;
        if(v[i]<=AV) res = Math.max(get(i+1,AV-v[i],BV)+w[i],res);
        if(v[i]<=BV) res = Math.max(get(i+1,0,BV-v[i])+w[i],res);
        res = Math.max(get(i+1,AV,BV),res);
        return res;
    }
}

二维数组解法：

public class Main{
    static int n  = 5;
    static int[] v = {0,3,7,4,49,2};
    static int[] w = {0,3,4,7,50,2};
    public static void main(String[] args){
        int AV = 10;int BV = 50;
        int[][] fA = new int[n+1][AV+1];
        int[][] fB = new int[n+1][BV+1];
        for(int i = 1;i<=n;i++)
            for (int j = 0; j <= AV; j++) {
                fA[i][j] = fA[i - 1][j];
                if (j >= v[i])
                    fA[i][j] = Math.max(fA[i][j], fA[i - 1][j - v[i]] + w[i]);
            }
        for(int i = 1;i<=n;i++)
            for(int j =0;j<=BV;j++){
                fB[i][j] = Math.max(fB[i-1][j],fA[i-1][AV]);
                if(v[i]<=j){
                fB[i][j] =  Math.max(fA[i-1][AV]+w[i],fB[i][j]);//启用b
                fB[i][j] = Math.max(fB[i-1][j-v[i]]+w[i],fB[i][j]);
                }
            }
        System.out.println(fB[n][BV]);

    }
}

压缩至一维（背包1从1-n装，背包2从n-1装）最后返回前i个用背包1装从i+1开始用背包2装的最大值

public class Main1 {
    static int n = 5;
    static int[] v = {0, 3, 7, 4, 49, 2};
    static int[] w = {0, 3, 4, 7, 50, 2};
    public static void main(String[] args) {
        int AV = 10;int BV = 50;
        int[] fA = new int[AV+1];
        int[] resA = new int[n + 1];
        for (int i = 1; i <= n; i++) {
            for (int j = AV; j >= v[i]; j--)
                fA[j] = Math.max(fA[j], fA[j - v[i]] + w[i]);
            resA[i] = fA[AV];//装至第i个物品价值的最大值为
        }
        int[] fB = new int[BV+1];int[] resB = new int[n+1];
        for(int i = n;i>0;i--){
            for(int j = BV;j>=v[i];j--)
                fB[j] = Math.max(fB[j],fB[j-v[i]]+w[i]);
            resB[i] = fB[BV];//小心越界（0,n,n-1....1）
        }
        int res = 0;
       // System.out.println(Arrays.toString(resA));System.out.println(Arrays.toString(resB));
        for(int i = 0;i<=n;i++)
            res = Math.max(resA[i]+resB[i],res);
        System.out.println(res);
    }
}