https://dandansad.com/tags/%E8%83%8C%E5%8C%85%E9%97%AE%E9%A2%98/Recent content in 背包问题 on 蛋蛋忧桑Hugo -- gohugo.iozhSat, 22 Mar 2025 10:31:12 +0800https://dandansad.com/2025/03/22/%E8%83%8C%E5%8C%85%E9%97%AE%E9%A2%98/Sat, 22 Mar 2025 10:31:12 +0800https://dandansad.com/2025/03/22/%E8%83%8C%E5%8C%85%E9%97%AE%E9%A2%98/<h2 id="01背包问题"><a href="#01%e8%83%8c%e5%8c%85%e9%97%ae%e9%a2%98" class="header-anchor"></a><a class="link" href="https://www.acwing.com/problem/content/2/" target="_blank" rel="noopener" >01背包问题</a> </h2><div class="highlight"><pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;-webkit-text-size-adjust:none;"><code class="language-cpp" data-lang="cpp"><span style="display:flex;"><span><span style="color:#75715e">#include </span></span></span><span style="display:flex;"><span><span style="color:#75715e">#include </span></span></span><span style="display:flex;"><span><span style="color:#75715e">#include </span></span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span><span style="color:#66d9ef">using</span> <span style="color:#66d9ef">namespace</span> std; </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span><span style="color:#66d9ef">const</span> <span style="color:#66d9ef">int</span> N <span style="color:#f92672">=</span> <span style="color:#ae81ff">1010</span>; </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span><span style="color:#66d9ef">int</span> n, m; </span></span><span style="display:flex;"><span><span style="color:#66d9ef">int</span> v[N], w[N]; </span></span><span style="display:flex;"><span><span style="color:#66d9ef">int</span> f[N]; </span></span><span style="display:flex;"><span><span style="color:#66d9ef">int</span> g[N]; </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span><span style="color:#66d9ef">int</span> <span style="color:#a6e22e">main</span>() </span></span><span style="display:flex;"><span>{ </span></span><span style="display:flex;"><span> scanf(<span style="color:#e6db74">&#34;%d %d&#34;</span>, <span style="color:#f92672">&amp;</span>n, <span style="color:#f92672">&amp;</span>m); </span></span><span style="display:flex;"><span> <span style="color:#66d9ef">for</span> (<span style="color:#66d9ef">int</span> i <span style="color:#f92672">=</span> <span style="color:#ae81ff">1</span>; i <span style="color:#f92672">=</span> <span style="color:#ae81ff">1</span>; i<span style="color:#f92672">--</span>) </span></span><span style="display:flex;"><span> <span style="color:#75715e">// { </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// for (int j = 0; j = v[i]) </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// { </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// g[j] = max(f[j], f[j - v[i]] + w[i]); </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// } </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// } </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// memcpy(f, g, sizeof g); </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// } </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// cout= v[i]) </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// { </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// g[j] = max(f[j], f[j - v[i]] + w[i]); </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// } </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// } </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// memcpy(f, g, sizeof g); </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// } </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// cout = 0; j--) </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// { </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// if (j &gt;= v[i]) </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// { </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// f[j] = max(f[j], f[j - v[i]] + w[i]); </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// } </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// } </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// } </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// cout = 1; i--) </span></span></span><span style="display:flex;"><span> { </span></span><span style="display:flex;"><span> <span style="color:#66d9ef">for</span> (<span style="color:#66d9ef">int</span> j <span style="color:#f92672">=</span> m; j <span style="color:#f92672">&gt;=</span> <span style="color:#ae81ff">0</span>; j<span style="color:#f92672">--</span>) </span></span><span style="display:flex;"><span> { </span></span><span style="display:flex;"><span> <span style="color:#66d9ef">if</span> (j <span style="color:#f92672">&gt;=</span> v[i]) </span></span><span style="display:flex;"><span> { </span></span><span style="display:flex;"><span> f[j] <span style="color:#f92672">=</span> max(f[j], f[j <span style="color:#f92672">-</span> v[i]] <span style="color:#f92672">+</span> w[i]); </span></span><span style="display:flex;"><span> } </span></span><span style="display:flex;"><span> } </span></span><span style="display:flex;"><span> } </span></span><span style="display:flex;"><span> cout </span></span><span style="display:flex;"><span><span style="color:#66d9ef">using</span> <span style="color:#66d9ef">namespace</span> std; </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span><span style="color:#66d9ef">const</span> <span style="color:#66d9ef">int</span> N <span style="color:#f92672">=</span> <span style="color:#ae81ff">1010</span>; </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span><span style="color:#66d9ef">int</span> n, m; </span></span><span style="display:flex;"><span><span style="color:#66d9ef">int</span> v[N], w[N]; </span></span><span style="display:flex;"><span><span style="color:#66d9ef">int</span> mem[N][N]; </span></span><span style="display:flex;"><span><span style="color:#66d9ef">int</span> f[N][N]; </span></span><span style="display:flex;"><span><span style="color:#66d9ef">int</span> g[N]; </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span><span style="color:#66d9ef">int</span> dfs(<span style="color:#66d9ef">int</span> x, <span style="color:#66d9ef">int</span> spV) </span></span><span style="display:flex;"><span>{ </span></span><span style="display:flex;"><span> <span style="color:#66d9ef">if</span> (mem[x][spV]) </span></span><span style="display:flex;"><span> <span style="color:#66d9ef">return</span> mem[x][spV]; </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span> <span style="color:#66d9ef">int</span> sum <span style="color:#f92672">=</span> <span style="color:#ae81ff">0</span>; </span></span><span style="display:flex;"><span> <span style="color:#66d9ef">if</span> (x <span style="color:#f92672">&gt;</span> n) </span></span><span style="display:flex;"><span> sum <span style="color:#f92672">=</span> <span style="color:#ae81ff">0</span>; </span></span><span style="display:flex;"><span> <span style="color:#66d9ef">else</span> <span style="color:#66d9ef">if</span> (spV <span style="color:#f92672">&gt;</span> n <span style="color:#f92672">&gt;&gt;</span> m; </span></span><span style="display:flex;"><span> <span style="color:#66d9ef">for</span> (<span style="color:#66d9ef">int</span> i <span style="color:#f92672">=</span> <span style="color:#ae81ff">1</span>; i <span style="color:#f92672">&gt;</span> v[i] <span style="color:#f92672">&gt;&gt;</span> w[i]; </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span> <span style="color:#75715e">// int res=dfs(1,m); </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// cout </span></span></span><span style="display:flex;"><span><span style="color:#66d9ef">using</span> <span style="color:#66d9ef">namespace</span> std; </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span><span style="color:#66d9ef">const</span> <span style="color:#66d9ef">int</span> N <span style="color:#f92672">=</span> <span style="color:#ae81ff">1010</span>; </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span><span style="color:#66d9ef">int</span> n, V, M; </span></span><span style="display:flex;"><span><span style="color:#66d9ef">int</span> v[N], m[N], w[N]; </span></span><span style="display:flex;"><span><span style="color:#66d9ef">int</span> mem[N][<span style="color:#ae81ff">110</span>][<span style="color:#ae81ff">110</span>]; </span></span><span style="display:flex;"><span><span style="color:#66d9ef">int</span> f[N][<span style="color:#ae81ff">110</span>][<span style="color:#ae81ff">110</span>]; </span></span><span style="display:flex;"><span><span style="color:#66d9ef">int</span> g[<span style="color:#ae81ff">110</span>][<span style="color:#ae81ff">110</span>]; </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span><span style="color:#66d9ef">int</span> dfs(<span style="color:#66d9ef">int</span> x, <span style="color:#66d9ef">int</span> spV, <span style="color:#66d9ef">int</span> spM) </span></span><span style="display:flex;"><span>{ </span></span><span style="display:flex;"><span> <span style="color:#66d9ef">if</span> (mem[x][spV][spM]) </span></span><span style="display:flex;"><span> <span style="color:#66d9ef">return</span> mem[x][spV][spM]; </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span> <span style="color:#66d9ef">int</span> sum <span style="color:#f92672">=</span> <span style="color:#ae81ff">0</span>; </span></span><span style="display:flex;"><span> <span style="color:#66d9ef">if</span> (x <span style="color:#f92672">&gt;</span> n) </span></span><span style="display:flex;"><span> sum <span style="color:#f92672">=</span> <span style="color:#ae81ff">0</span>; </span></span><span style="display:flex;"><span> <span style="color:#66d9ef">else</span> <span style="color:#66d9ef">if</span> (spV <span style="color:#f92672">&gt;</span> n <span style="color:#f92672">&gt;&gt;</span> V <span style="color:#f92672">&gt;&gt;</span> M; </span></span><span style="display:flex;"><span> <span style="color:#66d9ef">for</span> (<span style="color:#66d9ef">int</span> i <span style="color:#f92672">=</span> <span style="color:#ae81ff">1</span>; i <span style="color:#f92672">&gt;</span> v[i] <span style="color:#f92672">&gt;&gt;</span> m[i] <span style="color:#f92672">&gt;&gt;</span> w[i]; </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span> <span style="color:#75715e">// int res=dfs(1,V,M); </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// cout= 1; i--) </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// for (int j = 0; j = v[i]; j--) </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// for (int k = M; k &gt;= m[i]; k--) </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// { </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// g[j][k] = max(g[j][k], g[j - v[i]][k - m[i]] + w[i]); </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// } </span></span></span><span style="display:flex;"><span> <span style="color:#75715e">// cout = 1; i--) </span></span></span><span style="display:flex;"><span> <span style="color:#66d9ef">for</span> (<span style="color:#66d9ef">int</span> j <span style="color:#f92672">=</span> V; j <span style="color:#f92672">&gt;=</span> v[i]; j<span style="color:#f92672">--</span>) </span></span><span style="display:flex;"><span> <span style="color:#66d9ef">for</span> (<span style="color:#66d9ef">int</span> k <span style="color:#f92672">=</span> M; k <span style="color:#f92672">&gt;=</span> m[i]; k<span style="color:#f92672">--</span>) </span></span><span style="display:flex;"><span> { </span></span><span style="display:flex;"><span> g[j][k] <span style="color:#f92672">=</span> max(g[j][k], g[j <span style="color:#f92672">-</span> v[i]][k <span style="color:#f92672">-</span> m[i]] <span style="color:#f92672">+</span> w[i]); </span></span><span style="display:flex;"><span> } </span></span><span style="display:flex;"><span> cout <span style="color:#f92672">&lt;&lt;</span> g[V][M] <span style="color:#f92672">&lt;&lt;</span> endl; </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span> <span style="color:#66d9ef">return</span> <span style="color:#ae81ff">0</span>; </span></span><span style="display:flex;"><span>} </span></span></code></pre></div><h2 id="背包问题求具体方案"><a href="#%e8%83%8c%e5%8c%85%e9%97%ae%e9%a2%98%e6%b1%82%e5%85%b7%e4%bd%93%e6%96%b9%e6%a1%88" class="header-anchor"></a><a class="link" href="https://www.acwing.com/problem/content/12/" target="_blank" rel="noopener" >背包问题求具体方案</a> </h2>