轮船装载问题解决

 **

• 描述:
  • 有一组物品，其重量分别是：
  • w1,w2…wn
  • 现在有两艘轮船，其容量分别是C1和C2，
  • 满足w1+w2+…+wn <= C1 + C2
  • 问怎么装载物品，才能够把物品全部装上轮船

**

代码实现：

public class shiploading {
    static int[] w = {12,18,21,14,9,10};
    static int c1 = 55;
    static int c2 = 30;

    static int[] x = new int[w.length];
    static int[] bestx = new int[w.length];
    static int bestw = Integer.MIN_VALUE;
    static int cw = 0;
    static int r = 0; // 记录物品i后面所有物品的总重量

    public static void main(String[] args) {
        for (int i = 0; i < w.length; i++) {
            r += w[i];
        }
        backstrace(0);

        int sum = 0;
        for (int i = 0; i < bestx.length; i++) {
            if(bestx[i] == 0){
                sum += w[i];
            }
        }
        if(sum > c2){
            System.out.println("物品无法装载到轮船!");
            return;
        }

        System.out.println("C1:" + c1 + "装载物品:");
        for (int i = 0; i < bestx.length; i++) {
            if(bestx[i] == 1){
                System.out.print(w[i] + " ");
            }
        }
        System.out.println();

        System.out.println("C2:" + c2 + "装载物品:");
        for (int i = 0; i < bestx.length; i++) {
            if(bestx[i] == 0){
                System.out.print(w[i] + " ");
            }
        }
        System.out.println();
    }

    private static void backstrace(int i) {
        if(i == w.length){
            if(cw > bestw){
                bestw = cw;
                for (int j = 0; j < x.length; j++) {
                    bestx[j] = x[j];
                }
            }
        } else {
            r -= w[i];
            if(cw + w[i] <= c1){
                cw += w[i];
                x[i] = 1;
                backstrace(i+1);  // 选择第i个节点
                cw -= w[i];
            }

            if(cw + r > bestw){
                x[i] = 0;      // 才有必要去往右边的i节点
                backstrace(i+1); // 没选择第i个节点
            }

            r += w[i];
        }
    }
}