[{"type":"Heading1","children":[{"text":"👜 背包问题总结"}],"slateId":"5vIJ0L2Pnt8QdA8orzpag"},{"type":"Heading1","slateId":"Mom6TH05kgo1Kt_M8BOwx","children":[{"text":"一、统一抽象"}]},{"type":"Paragraph","children":[{"text":"所有背包问题都可以抽象为："}],"slateId":"acm67pqW9Pv1Mv4LyguD7"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"plainText","name":"","children":[{"text":"从前 i 个物品中选择，在“容量/约束 j”下，\n求：是否可达 / 最大值 / 最小值 / 方案数"}],"slateId":"rZ8u3cXSZwIbjzNsk2MWK"}],"slateId":"il-svdzxSjeOBhM1zeyKe"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"cptxLnQp8lbAs2oJhKIx2"},{"type":"Heading1","children":[{"text":"二、三大类型"}],"slateId":"YKrntQRlmIsPUetMdHgYS"},{"type":"Table","children":[{"type":"TableBody","children":[{"type":"TableRow","children":[{"type":"TableCell","children":[{"type":"TableContent","children":[{"type":"Paragraph","children":[{"text":"类型"}],"slateId":"WtKPeUCQ4ZoeMV3BGyzxd"}],"slateId":"C1WCF0MBUAnYoPjuyGbq7"}],"align":"left","slateId":"9RFQ9UyiU_wBabPErwsoM"},{"type":"TableCell","children":[{"type":"TableContent","children":[{"type":"Paragraph","children":[{"text":"dp含义"}],"slateId":"jJ4uhdSV4q-VWRiNoC4KU"}],"slateId":"nfKiI5OmpgiD6xt3GRfhA"}],"align":"left","slateId":"Dk1XlNXm4DK9YowFD0UX8"},{"type":"TableCell","children":[{"type":"TableContent","children":[{"type":"Paragraph","children":[{"text":"运算"}],"slateId":"tlZo-j655M7WIUygYek-8"}],"slateId":"-Us2z-ONVBI9POCUpT_pm"}],"align":"left","slateId":"Ck_4armLinb4lahk98pdt"}],"slateId":"3euDoMq_2N5RVBTvrNxQ7"},{"type":"TableRow","children":[{"type":"TableCell","children":[{"type":"TableContent","children":[{"type":"Paragraph","children":[{"text":"可达性"}],"slateId":"yWuP-tyKwf3v4cvw6nLsk"}],"slateId":"ubhzUnj-aAfXulH9N_ahx"}],"align":"left","slateId":"dCCx_rtRk-D9-NvrI5MAp"},{"type":"TableCell","children":[{"type":"TableContent","children":[{"type":"Paragraph","children":[{"text":"能不能凑出来"}],"slateId":"IDHFFQA268kpvfi3RzkE0"}],"slateId":"QYXAKbCQjjzx-wPISZFVR"}],"align":"left","slateId":"rAcxptjKTBcW09M0vuwIa"},{"type":"TableCell","children":[{"type":"TableContent","children":[{"type":"Paragraph","children":[{"text":"or / bool"}],"slateId":"ujBOZu5mn-JX8gvlCHd37"}],"slateId":"ROZ9GAyah8EDmj8oUCQw4"}],"align":"left","slateId":"ljkDY944MpAXxtApDJbUn"}],"slateId":"XzZDWh06YaWOvwtdm8ga6"},{"type":"TableRow","children":[{"type":"TableCell","children":[{"type":"TableContent","children":[{"type":"Paragraph","children":[{"text":"计数"}],"slateId":"585YMPQKSFu9CQB96vM19"}],"slateId":"nDg-xEeT44wjmgZ1t77Bj"}],"align":"left","slateId":"ztw7mvftgdz9kbuQfZ0pW"},{"type":"TableCell","children":[{"type":"TableContent","children":[{"type":"Paragraph","children":[{"text":"有多少种方案"}],"slateId":"2oibpdRL5fBXMb0P5JoH2"}],"slateId":"pRTQL0yv308TzhSEbJfN1"}],"align":"left","slateId":"-A5ovLZauTggZKWk6Ih2f"},{"type":"TableCell","children":[{"type":"TableContent","children":[{"type":"Paragraph","children":[{"text":"+"}],"slateId":"VWayzcE5wfMDTUZOOsgur"}],"slateId":"ZnomLFUt87I1KU8IqPmx7"}],"align":"left","slateId":"kqIeum0jOcXUjAVBwgd3H"}],"slateId":"kpgNaCXgryfoIbvsNIe9i"},{"type":"TableRow","children":[{"type":"TableCell","children":[{"type":"TableContent","children":[{"type":"Paragraph","children":[{"text":"最值"}],"slateId":"U2jM1b00JNpk7Evtiuz5c"}],"slateId":"AOZHCT0a_aT5BD_vQwYJ7"}],"align":"left","slateId":"9Ze9mMiTs1LG5q-YO1dJp"},{"type":"TableCell","children":[{"type":"TableContent","children":[{"type":"Paragraph","children":[{"text":"最优解（max/min）"}],"slateId":"N7GahJDsFE-5wnFIpwYIC"}],"slateId":"mqmrUj4jST-D36gJOdmf9"}],"align":"left","slateId":"3Hj9FZpuB3WKxmry70kdx"},{"type":"TableCell","children":[{"type":"TableContent","children":[{"type":"Paragraph","children":[{"text":"max / min"}],"slateId":"7tJkwFb0YuaSM18VkkpRI"}],"slateId":"LD0qJ5LE2tVNm-3sSRw7M"}],"align":"left","slateId":"Cs02lNJmWxX145XbOySR2"}],"slateId":"vyV703kKPK6YHa5j_7iJF"}],"slateId":"zjiWYaEM1i91KllNPSQHp"}],"slateId":"dKKcIKKiXFQ5WpNU6FwUq"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"AjEomr0t5Jr6kc6LmJ2NU"},{"type":"Heading1","children":[{"text":"三、DFS （递归）模板"}],"slateId":"sn_DhdHGPpC9oOI1oQEha"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"YiS2dISQ_BJ7A4m0itKso"},{"type":"Heading2","children":[{"text":"1️⃣ 0-1 背包（每个物品选 or 不选）"}],"slateId":"tILCx4CBKrrJNn_gjQh4c"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"python3","name":"","children":[{"text":"@cache\ndef dfs(i, j):\n if i < 0:\n return base # 看题意\n\n if j < 0:\n return 不合法\n\n return 合并(\n dfs(i - 1, j), # 不选\n dfs(i - 1, j - v[i]) # 选\n )"}],"slateId":"N8OLoqsDBgaPL_T4RdCad"}],"slateId":"8JN7JfU5lgdlCcimEWQg6"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"jisgYCFPAcY6-ZyUSosrZ"},{"type":"Heading2","children":[{"text":"2️⃣ 完全背包（可以重复选）"}],"slateId":"ZImMxhZr65VtQO6uUubXu"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"python3","name":"","children":[{"text":"@cache\ndef dfs(i, j):\n if i < 0:\n return base\n\n if j < 0:\n return 不合法\n\n return 合并(\n dfs(i - 1, j), # 不选\n dfs(i, j - v[i]) # 继续选 i\n )"}],"slateId":"gWfdXWJR9mc91euOLZO1m"}],"slateId":"31NYkWPTV1Tsv827c03DZ"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"J2bvB0g8kYyVEBpgTZ9Rj"},{"type":"Heading2","children":[{"text":"3️⃣ 多重背包（最多选 cnt 次）"}],"slateId":"GkK56HybWmMJdeohQI8Fo"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"python3","name":"","children":[{"text":"@cache\ndef dfs(i, j):\n if i < 0:\n return base\n\n res = 0\n for k in range(0, cnt[i] + 1):\n if j - k * v[i] >= 0:\n res += dfs(i - 1, j - k * v[i])\n return res"}],"slateId":"wtp9EdPd9EtbRPwyE29wd"}],"slateId":"THsR0M5tESxhOuFacUA8M"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"eEt1157ro7hVp8J8aHSw1"},{"type":"Heading2","children":[{"text":"4️⃣ 分组背包（每组必须选一个）"}],"slateId":"ngPmQ9_j061Xc3uQvgNjW"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"python3","name":"","children":[{"text":"@cache\ndef dfs(i, j):\n if i < 0:\n return base\n\n res = 0\n for x in group[i]:\n if j - x >= 0:\n res += dfs(i - 1, j - x)\n return res"}],"slateId":"ScMetUYOIiOTbnNBy4T5_"}],"slateId":"OJF5sQUz_WloNYVnxOtIU"},{"type":"Paragraph","children":[{"text":"👉 注意："}],"slateId":"EUvFZBl6utIKixDU46_Kn"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"plainText","name":"","children":[{"text":"没有“不选”分支 ❗（必须选）"}],"slateId":"H4M2U5g0CwothGKQxc-kg"}],"slateId":"c-xMLOTgMrRZg3O1_grwi"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"tQlNnfgxDz10dmihAuoR9"},{"type":"Heading1","children":[{"text":" 四、DP（递推）模板"}],"slateId":"sOq__AUPTsqDQNSHpaO_N"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"GcFP7xKLBQtwShAFwrfGP"},{"type":"Heading2","children":[{"text":"1️⃣ 0-1 背包"}],"slateId":"838-QYurGKBvoFkPc15_M"},{"type":"Paragraph","children":[{"text":""},{"type":"Mention","item":{"type":"question","href":"https://leetcode.cn/problems/last-stone-weight-ii/description/","name":"1049. 最后一块石头的重量 II"},"children":[{"text":""}],"slateId":"H4043ghCt0kzwTBXLM6cQ"},{"text":""}],"slateId":"7LnoUpM6LIK2L-CKXW0YT"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"python","name":"","children":[{"text":"for v in nums:\n for j in range(target, v - 1, -1):\n dp[j] = 合并(dp[j], dp[j - v])"}],"slateId":"n8Qg1QbMf7nMAUVef4VGi"}],"slateId":"N3DqqDvsmM7pALMQyE0AJ"},{"type":"Paragraph","children":[{"text":"👉 倒序原因："}],"slateId":"oJF2cpSfLfzIEjbMNmAXq"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"plainText","name":"","children":[{"text":"防止重复选同一个物品"}],"slateId":"y8FE9L1BxkMweDG6-smpJ"}],"slateId":"XfOSNV4HB00I3DtUwSLTy"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"iIuIeYYQ75bHVT1j1oTu2"},{"type":"Heading2","children":[{"text":"2️⃣ 完全背包"}],"slateId":"nHX1IUtJ4O22ynCZ-Bkp4"},{"type":"Paragraph","children":[{"text":""},{"type":"Mention","item":{"type":"question","href":"https://leetcode.cn/problems/coin-change/description/","name":"322. 零钱兑换"},"children":[{"text":""}],"slateId":"PrxsxVxIbTlRGsyunhxk2"},{"text":""}],"slateId":"fEqI1v2GW2_yU4FgOohfT"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"python","name":"","children":[{"text":"for v in nums:\n for j in range(v, target + 1):\n dp[j] = 合并(dp[j], dp[j - v])"}],"slateId":"kitRuMBTXDgpma9Dg9lSO"}],"slateId":"HRwwVmQmjIlUqATX9NkaM"},{"type":"Paragraph","children":[{"text":"👉 正序原因："}],"slateId":"errzumnGvCDCzs6Yfg2S2"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"plainText","name":"","children":[{"text":"允许重复使用"}],"slateId":"9BuankyxSYayMWwm16kaG"}],"slateId":"UM8_AxB23-WnynYNnoYvB"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"MvmiMYa2ytBzJtPMEtK-Y"},{"type":"Heading2","children":[{"text":"3️⃣ 多重背包"}],"slateId":"Vn-zYvpuTJHtF8An3pzv5"},{"type":"Paragraph","children":[{"text":""},{"type":"Mention","item":{"type":"question","href":"https://leetcode.cn/problems/number-of-ways-to-earn-points/","name":"2585. 获得分数的方法数"},"children":[{"text":""}],"slateId":"pvEWDNvTRK1GrZY2nX2Zw"},{"text":""}],"slateId":"020II9tI9K-R0ZQv4KDGq"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"python","name":"","children":[{"text":"for v, cnt in items:\n for j in range(target, v - 1, -1):\n for k in range(1, cnt + 1):\n if j >= k * v:\n dp[j] += dp[j - k * v]"}],"slateId":"SnmxtNhs3jDi3t0xJ1cw4"}],"slateId":"0dVzfHr8eaw7amP4V8rud"},{"type":"Paragraph","children":[{"text":"👉 或优化："}],"slateId":"YE27slGcDVaCRqCIqTU8Y"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"plainText","name":"","children":[{"text":"二进制拆分 / 单调队列"}],"slateId":"oyZZuTrD_GE5qjBnROcYT"}],"slateId":"Y5vmPZJaYslF7DbCdW20N"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"5T_mxglVEMRl7sixBRVc2"},{"type":"Heading2","children":[{"text":"4️⃣ 分组背包"}],"slateId":"xhjb5EH-jc-Sn0ZW9xImi"},{"type":"Paragraph","children":[{"text":""},{"type":"Mention","item":{"type":"question","href":"https://leetcode.cn/problems/number-of-dice-rolls-with-target-sum/description/","name":"1155. 掷骰子等于目标和的方法数"},"children":[{"text":""}],"slateId":"qFx6O6NkNK_8Tov2PhrWE"},{"text":""}],"slateId":"B-YYMWjtblcCvKV7MCuyT"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"python","name":"","children":[{"text":"for group in groups:\n for j in range(target, -1, -1):\n dp[j] = 0\n for x in group:\n if j >= x:\n dp[j] += dp[j - x]"}],"slateId":"mKpc0hD5Zjapiu1xMxsxf"}],"slateId":"cf4wrqEhOBYB59U3eH4Qd"},{"type":"Paragraph","children":[{"text":"👉 特点："}],"slateId":"sIwyKC9HzSbCi3nMPGC3T"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"plainText","name":"","children":[{"text":"必须清零（覆盖）"}],"slateId":"WFaiiN2DQw_xM6i_viS_E"}],"slateId":"8NaNMhneu3o369fSOHGem"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"5AEP96Rq0uqJ1wqXXYMYk"},{"type":"Heading1","children":[{"text":"五、j 的范围判定"}],"slateId":"xswfUE1I3WZKQl2bePm2H"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"LrRPwspz76qsZG0XOSyhJ"},{"type":"Heading2","children":[{"text":"🔥 总规则"}],"slateId":"NcNcSRtKd9Xr48UA37KzL"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"plainText","name":"","children":[{"text":"看转移：dp[j] ← dp[j - ???]\n\n??? 的最小值 → 决定 j 的起点"}],"slateId":"QeT_mlJakMYXVMA_Ql1L1"}],"slateId":"UNRV1DEDT_rIHszv2rum0"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"wFdjggao8nvzBEmVMARDN"},{"type":"Heading2","children":[{"text":"🔷 情况1：dp[j] ← dp[j - v]"}],"slateId":"cDUQXjdxOZBHEcjGXvbW5"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"plainText","name":"","children":[{"text":"v ≥ 1\n→ j ≥ v\n→ j ∈ [v, target]"}],"slateId":"MhhDZBdLEKoRZASv_Yk_7"}],"slateId":"zZ73H0zzmk6b5UQ-aY5z5"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"sUv9sdf1xWksKQ7CBOSVJ"},{"type":"Heading2","children":[{"text":"🔷 情况2：dp[j] ← dp[j - k * v]"}],"slateId":"GRHqgesMmuN0tnmcL2fbj"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"plainText","name":"","children":[{"text":"k ≥ 1\n→ j ≥ v\n→ j ∈ [v, target]"}],"slateId":"lelKayeWgkzeWV3jBoYnl"}],"slateId":"lckuQbE1cP0UNp2t666QZ"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"ryY3t63N9JOC7Yuq048-9"},{"type":"Heading2","children":[{"text":"🔷 情况3：dp[j] ← dp[j - x]（x ∈ [1, k]）"}],"slateId":"e1kezGanRU8Mu4-aWbj6W"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"plainText","name":"","children":[{"text":"x 最小 = 1\n→ j ≥ 1\n→ j ∈ [0, target]"}],"slateId":"QDuxAaI25RF7m-19f2wek"}],"slateId":"FtgpUzKC35U0bKVhfVZ7p"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"nq1xiZSZzDmFLPGoxBXSr"},{"type":"Heading2","children":[{"text":"🔷 分组背包"}],"slateId":"RXDZlGowITuZ4denfuF_d"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"plainText","name":"","children":[{"text":"dp[j] ← dp[j - x]\n\nx ∈ group[i]\n→ j ≥ min(group[i])"}],"slateId":"4lHHu2qbs9Z0HhvXibr1b"}],"slateId":"aL8zhDyMgyQdPEFELEuBD"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"pNyIvgGnF-e689UBMxOxJ"},{"type":"Heading1","children":[{"text":"六、是否需要清零"}],"slateId":"nvbfaifKBftTJeZ_ySFK5"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"_KraPheHuUR94zkVXCKui"},{"type":"Heading2","children":[{"text":"✅ 需要清零（覆盖型）"}],"slateId":"nv3rlGfJrIzyCtzlWdikI"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"plainText","name":"","children":[{"text":"分组背包 / 每轮必须选"}],"slateId":"7M7tv1wRNLAV6ngvJGsY5"}],"slateId":"PSR89L5fgVilwz-hHMS6B"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"python","name":"","children":[{"text":"dp[j] = 0"}],"slateId":"DAelSEAXFEWMV5hgaSuGB"}],"slateId":"JpD3rozluDNFP1QInU8Fi"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"Q7W526Xz_SUAfVKFW0xma"},{"type":"Heading2","children":[{"text":"❌ 不清零（累加型）"}],"slateId":"cLyEy6JJgJu-y8qcCLCkc"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"plainText","name":"","children":[{"text":"0-1 / 完全 / 多重"}],"slateId":"NirHj6NcSHjmkDY8-fSDG"}],"slateId":"aNWsPBDziJ4V654EuIL3u"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"python","name":"","children":[{"text":"dp[j] += ..."}],"slateId":"EuLEKfHDIehmZIvlTj7TM"}],"slateId":"-5OAETGRxP33SuJ24T_66"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"orCisrYCqlveVz-3OSR0Z"},{"type":"Heading1","children":[{"text":"七、顺序判定"}],"slateId":"-_8IvJZRFtatXuN4nVQPx"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"3V3Ggop9UejkGveOTmELn"},{"type":"Heading2","children":[{"text":"🔷 倒序"}],"slateId":"UXsp-KUowv7_NfbipVMdr"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"plainText","name":"","children":[{"text":"dp[j] ← dp[j - v]\n且不能重复选\n→ 倒序"}],"slateId":"TTiULfzeTTJ1y-ek7VJal"}],"slateId":"wGgVHkN8fIguj6KaoKKTl"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"nX4bS-ShpCZoRvzFR5LN7"},{"type":"Heading2","children":[{"text":"🔷 正序"}],"slateId":"vn4G2owIXRIFObbfIJI6X"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"plainText","name":"","children":[{"text":"允许重复选\n→ 正序"}],"slateId":"G8A4eTa-tg_dNUwSYTAiy"}],"slateId":"pJrvnygUidztfMy3X5lxI"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"42pW_8KGNESlu4USOKSqK"},{"type":"Heading2","children":[{"text":"🔷 必须 new_dp / 覆盖"}],"slateId":"QpslNQWytoFiEZ-BCI3NM"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"plainText","name":"","children":[{"text":"dp[j] 依赖多个 dp[j-x]\n→ 分组背包 / 骰子"}],"slateId":"Qmi6o05u9Sxuz_kwWB4NH"}],"slateId":"8g0U3v_r2BMSddpbzdYGt"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"SFwmJpwTYkeRIbOXTy1pu"},{"type":"Heading1","children":[{"text":"八、bitset 适用场景"}],"slateId":"vMrB5Hc7uBg2yF28J5dbx"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"asKVfjIbW57YpU9ARkj2f"},{"type":"Heading2","children":[{"text":"✅ 可达性问题"}],"slateId":"43hqt-8wYQjAvym39O3Co"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"python","name":"","children":[{"text":"dp |= dp << v"}],"slateId":"G94HKIP9Psag1wRrzUvpK"}],"slateId":"SljCaX8zUIINoQTjIE4P3"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"soWqTSlM-HAVjt5EcPo7P"},{"type":"Heading2","children":[{"text":"✅ 分组背包"}],"slateId":"IAGY2FHGCwdq4EBLc3kcW"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"python","name":"","children":[{"text":"g = 0\nfor x in group:\n g |= dp << x\ndp = g"}],"slateId":"Fdy988LuOauvWHdj28VG5"}],"slateId":"MKy4fWh-OKULe-jYkp7CI"},{"type":"HorizontalRule","children":[{"text":""}],"slateId":"72or6q6t_x3_MpxZ_53eR"},{"type":"Heading1","children":[{"text":"九、统一理解"}],"slateId":"DLleW2p1U1w3jjAzjKbaL"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"plainText","name":"","children":[{"text":"背包问题 = “状态压缩的枚举选择”"}],"slateId":"dbOuNZEeRScy8n5LMlGRe"}],"slateId":"HKb7vfxk_2Ee1ezDu6xRV"},{"type":"CodeBlock","activeTabIndex":0,"children":[{"type":"CodeTab","language":"plainText","name":"","children":[{"text":"是否可选 → 决定是否 +=\n\n是否必须选 → 决定是否清零\n\n是否可重复 → 决定正序 or 倒序\n\n转移减多少 → 决定 j 的起点\n\n状态稀疏 → 用 set / bitset"}],"slateId":"ZxnniGde9_AdSQ5titMXy"}],"slateId":"T5daf31mYn6osyGkPhfhx"},{"type":"Paragraph","children":[{"text":""}],"slateId":"LdmFa387dTvEDwZqGQtLN"}]