DFS之剪枝与优化 AcWing 165. 小猫爬山

素颜马尾好姑娘i 2024-04-07 11:11 24阅读 0赞

## AcWing 165. 小猫爬山 ##

### 原题链接 ###

[AcWing 165. 小猫爬山][AcWing 165.]

### 算法标签 ###

搜索 深度优先搜索 DFS

### 思路 ###

![在这里插入图片描述][03e3f88a426240378d267510ce5bd94e.png]

### 代码 ###

#pragma GCC optimize(2)
    #pragma GCC optimize(3)
    #include<bits/stdc++.h>
    #define int long long
    #define x first
    #define y second
    #define ump unordered_map
    #define pq priority_queue
    #define rep(i, a, b) for(int i=a;i<b;++i)
    #define Rep(i, a, b) for(int i=a;i>b;--i)
    using namespace std;
    typedef pair<int, int> PII;
    const int N = 18;
    int n, ww;
    int w[N];
    int sum[N];
    int ans=N;
    //int t, n, m, cnt, ans; 
    inline int rd(){
       int s=0,w=1;
       char ch=getchar();
       while(ch<'0'||ch>'9'){if(ch=='-')w=-1;ch=getchar();}
       while(ch>='0'&&ch<='9') s=s*10+ch-'0',ch=getchar();
       return s*w;
    }
    void put(int x) {
        if(x<0) putchar('-'),x=-x;
        if(x>=10) put(x/10);
        putchar(x%10^48);
    }
    void dfs(int a, int b){
        // 最优性剪枝
        if(b>=ans){
            return;
        }
        if(a==n){
            ans=b;
            return ;
        }
        rep(i, 0, b){
            // 可行性剪枝
            if(sum[i]+w[a]<=ww){
                sum[i]+=w[a];
                dfs(a+1, b);
                // 恢复现场
                sum[i]-=w[a];
            }
        }
        // 新开一辆车
        sum[b]=w[a];
        dfs(a+1, b+1);
        // 恢复现场
        sum[b]=0;
    }
    signed main(){
    	ios::sync_with_stdio(false);
    	cin.tie(0);
    	cout.tie(0);
    	n=rd(), ww=rd();
    	rep(i, 0, n){
    	    w[i]=rd();
    	}
    	sort(w, w+n);
    	reverse(w, w+n);
    	dfs(0, 0);
    	printf("%lld", ans);
    	return 0;
    }

参考文献  
[AcWing 165. 小猫爬山（算法提高课）y总视频讲解][AcWing 165. _y]

[AcWing 165. 小猫爬山题解][AcWing 165. 1]

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![在这里插入图片描述][9cb4cb80a18345158f8a69e2f196e5b9.png]

[AcWing 165.]: https://www.acwing.com/problem/content/167/
[03e3f88a426240378d267510ce5bd94e.png]: https://image.dandelioncloud.cn/pgy_files/images/2024/04/07/460127eac5e04c1792460792056ba7ee.png
[AcWing 165. _y]: https://www.acwing.com/video/478/
[AcWing 165. 1]: https://www.acwing.com/solution/content/32118/
[9cb4cb80a18345158f8a69e2f196e5b9.png]: https://image.dandelioncloud.cn/pgy_files/images/2024/04/07/608624d447f849b8b28cf6428e40f756.png