| {"id": "f1-c0-en", "family": 1, "increment": 0, "language": "en", "items": [{"id": "A", "weight": 2, "value": 24}, {"id": "B", "weight": 8, "value": 9}, {"id": "C", "weight": 3, "value": 3}, {"id": "D", "weight": 9, "value": 5}, {"id": "E", "weight": 5, "value": 5}, {"id": "F", "weight": 9, "value": 17}], "capacity": 18, "optimum": 46, "optimal_sets": [["A", "E", "F"]], "prompt": "Select a subset of these six indivisible items. Each item may be selected at most once. Total weight must be at most 18. Maximize total value.\nID | weight | value\nA | 2 | 24\nB | 8 | 9\nC | 3 | 3\nD | 9 | 5\nE | 5 | 5\nF | 9 | 17\nExplain your calculation briefly, then give exactly one final line using this format (example only): FINAL_JSON: {\"value\": 12, \"items\": [\"A\", \"C\"]}. Report the maximum value and one optimal subset."} | |
| {"id": "f1-c0-zh", "family": 1, "increment": 0, "language": "zh", "items": [{"id": "A", "weight": 2, "value": 24}, {"id": "B", "weight": 8, "value": 9}, {"id": "C", "weight": 3, "value": 3}, {"id": "D", "weight": 9, "value": 5}, {"id": "E", "weight": 5, "value": 5}, {"id": "F", "weight": 9, "value": 17}], "capacity": 18, "optimum": 46, "optimal_sets": [["A", "E", "F"]], "prompt": "从以下六个不可分割的物品中选择一个子集。每个物品最多选一次，总重量不能超过18。请使总价值最大。\n编号 | 重量 | 价值\nA | 2 | 24\nB | 8 | 9\nC | 3 | 3\nD | 9 | 5\nE | 5 | 5\nF | 9 | 17\n简要说明计算过程，然后严格用以下格式给出唯一的最终行（仅为格式示例）：FINAL_JSON: {\"value\": 12, \"items\": [\"A\", \"C\"]}。报告最大价值和一个最优子集。"} | |
| {"id": "f1-c1-en", "family": 1, "increment": 1, "language": "en", "items": [{"id": "A", "weight": 2, "value": 24}, {"id": "B", "weight": 8, "value": 9}, {"id": "C", "weight": 3, "value": 3}, {"id": "D", "weight": 9, "value": 5}, {"id": "E", "weight": 5, "value": 5}, {"id": "F", "weight": 9, "value": 17}], "capacity": 19, "optimum": 50, "optimal_sets": [["A", "B", "F"]], "prompt": "Select a subset of these six indivisible items. Each item may be selected at most once. Total weight must be at most 19. Maximize total value.\nID | weight | value\nA | 2 | 24\nB | 8 | 9\nC | 3 | 3\nD | 9 | 5\nE | 5 | 5\nF | 9 | 17\nExplain your calculation briefly, then give exactly one final line using this format (example only): FINAL_JSON: {\"value\": 12, \"items\": [\"A\", \"C\"]}. Report the maximum value and one optimal subset."} | |
| {"id": "f1-c1-zh", "family": 1, "increment": 1, "language": "zh", "items": [{"id": "A", "weight": 2, "value": 24}, {"id": "B", "weight": 8, "value": 9}, {"id": "C", "weight": 3, "value": 3}, {"id": "D", "weight": 9, "value": 5}, {"id": "E", "weight": 5, "value": 5}, {"id": "F", "weight": 9, "value": 17}], "capacity": 19, "optimum": 50, "optimal_sets": [["A", "B", "F"]], "prompt": "从以下六个不可分割的物品中选择一个子集。每个物品最多选一次，总重量不能超过19。请使总价值最大。\n编号 | 重量 | 价值\nA | 2 | 24\nB | 8 | 9\nC | 3 | 3\nD | 9 | 5\nE | 5 | 5\nF | 9 | 17\n简要说明计算过程，然后严格用以下格式给出唯一的最终行（仅为格式示例）：FINAL_JSON: {\"value\": 12, \"items\": [\"A\", \"C\"]}。报告最大价值和一个最优子集。"} | |
| {"id": "f2-c0-en", "family": 2, "increment": 0, "language": "en", "items": [{"id": "A", "weight": 3, "value": 7}, {"id": "B", "weight": 4, "value": 8}, {"id": "C", "weight": 3, "value": 9}, {"id": "D", "weight": 8, "value": 16}, {"id": "E", "weight": 3, "value": 5}, {"id": "F", "weight": 5, "value": 9}], "capacity": 13, "optimum": 29, "optimal_sets": [["A", "B", "C", "E"]], "prompt": "Select a subset of these six indivisible items. Each item may be selected at most once. Total weight must be at most 13. Maximize total value.\nID | weight | value\nA | 3 | 7\nB | 4 | 8\nC | 3 | 9\nD | 8 | 16\nE | 3 | 5\nF | 5 | 9\nExplain your calculation briefly, then give exactly one final line using this format (example only): FINAL_JSON: {\"value\": 12, \"items\": [\"A\", \"C\"]}. Report the maximum value and one optimal subset."} | |
| {"id": "f2-c0-zh", "family": 2, "increment": 0, "language": "zh", "items": [{"id": "A", "weight": 3, "value": 7}, {"id": "B", "weight": 4, "value": 8}, {"id": "C", "weight": 3, "value": 9}, {"id": "D", "weight": 8, "value": 16}, {"id": "E", "weight": 3, "value": 5}, {"id": "F", "weight": 5, "value": 9}], "capacity": 13, "optimum": 29, "optimal_sets": [["A", "B", "C", "E"]], "prompt": "从以下六个不可分割的物品中选择一个子集。每个物品最多选一次，总重量不能超过13。请使总价值最大。\n编号 | 重量 | 价值\nA | 3 | 7\nB | 4 | 8\nC | 3 | 9\nD | 8 | 16\nE | 3 | 5\nF | 5 | 9\n简要说明计算过程，然后严格用以下格式给出唯一的最终行（仅为格式示例）：FINAL_JSON: {\"value\": 12, \"items\": [\"A\", \"C\"]}。报告最大价值和一个最优子集。"} | |
| {"id": "f2-c1-en", "family": 2, "increment": 1, "language": "en", "items": [{"id": "A", "weight": 3, "value": 7}, {"id": "B", "weight": 4, "value": 8}, {"id": "C", "weight": 3, "value": 9}, {"id": "D", "weight": 8, "value": 16}, {"id": "E", "weight": 3, "value": 5}, {"id": "F", "weight": 5, "value": 9}], "capacity": 14, "optimum": 32, "optimal_sets": [["A", "C", "D"]], "prompt": "Select a subset of these six indivisible items. Each item may be selected at most once. Total weight must be at most 14. Maximize total value.\nID | weight | value\nA | 3 | 7\nB | 4 | 8\nC | 3 | 9\nD | 8 | 16\nE | 3 | 5\nF | 5 | 9\nExplain your calculation briefly, then give exactly one final line using this format (example only): FINAL_JSON: {\"value\": 12, \"items\": [\"A\", \"C\"]}. Report the maximum value and one optimal subset."} | |
| {"id": "f2-c1-zh", "family": 2, "increment": 1, "language": "zh", "items": [{"id": "A", "weight": 3, "value": 7}, {"id": "B", "weight": 4, "value": 8}, {"id": "C", "weight": 3, "value": 9}, {"id": "D", "weight": 8, "value": 16}, {"id": "E", "weight": 3, "value": 5}, {"id": "F", "weight": 5, "value": 9}], "capacity": 14, "optimum": 32, "optimal_sets": [["A", "C", "D"]], "prompt": "从以下六个不可分割的物品中选择一个子集。每个物品最多选一次，总重量不能超过14。请使总价值最大。\n编号 | 重量 | 价值\nA | 3 | 7\nB | 4 | 8\nC | 3 | 9\nD | 8 | 16\nE | 3 | 5\nF | 5 | 9\n简要说明计算过程，然后严格用以下格式给出唯一的最终行（仅为格式示例）：FINAL_JSON: {\"value\": 12, \"items\": [\"A\", \"C\"]}。报告最大价值和一个最优子集。"} | |
| {"id": "f3-c0-en", "family": 3, "increment": 0, "language": "en", "items": [{"id": "A", "weight": 7, "value": 8}, {"id": "B", "weight": 3, "value": 9}, {"id": "C", "weight": 8, "value": 19}, {"id": "D", "weight": 2, "value": 5}, {"id": "E", "weight": 5, "value": 21}, {"id": "F", "weight": 6, "value": 6}], "capacity": 15, "optimum": 45, "optimal_sets": [["C", "D", "E"]], "prompt": "Select a subset of these six indivisible items. Each item may be selected at most once. Total weight must be at most 15. Maximize total value.\nID | weight | value\nA | 7 | 8\nB | 3 | 9\nC | 8 | 19\nD | 2 | 5\nE | 5 | 21\nF | 6 | 6\nExplain your calculation briefly, then give exactly one final line using this format (example only): FINAL_JSON: {\"value\": 12, \"items\": [\"A\", \"C\"]}. Report the maximum value and one optimal subset."} | |
| {"id": "f3-c0-zh", "family": 3, "increment": 0, "language": "zh", "items": [{"id": "A", "weight": 7, "value": 8}, {"id": "B", "weight": 3, "value": 9}, {"id": "C", "weight": 8, "value": 19}, {"id": "D", "weight": 2, "value": 5}, {"id": "E", "weight": 5, "value": 21}, {"id": "F", "weight": 6, "value": 6}], "capacity": 15, "optimum": 45, "optimal_sets": [["C", "D", "E"]], "prompt": "从以下六个不可分割的物品中选择一个子集。每个物品最多选一次，总重量不能超过15。请使总价值最大。\n编号 | 重量 | 价值\nA | 7 | 8\nB | 3 | 9\nC | 8 | 19\nD | 2 | 5\nE | 5 | 21\nF | 6 | 6\n简要说明计算过程，然后严格用以下格式给出唯一的最终行（仅为格式示例）：FINAL_JSON: {\"value\": 12, \"items\": [\"A\", \"C\"]}。报告最大价值和一个最优子集。"} | |
| {"id": "f3-c1-en", "family": 3, "increment": 1, "language": "en", "items": [{"id": "A", "weight": 7, "value": 8}, {"id": "B", "weight": 3, "value": 9}, {"id": "C", "weight": 8, "value": 19}, {"id": "D", "weight": 2, "value": 5}, {"id": "E", "weight": 5, "value": 21}, {"id": "F", "weight": 6, "value": 6}], "capacity": 16, "optimum": 49, "optimal_sets": [["B", "C", "E"]], "prompt": "Select a subset of these six indivisible items. Each item may be selected at most once. Total weight must be at most 16. Maximize total value.\nID | weight | value\nA | 7 | 8\nB | 3 | 9\nC | 8 | 19\nD | 2 | 5\nE | 5 | 21\nF | 6 | 6\nExplain your calculation briefly, then give exactly one final line using this format (example only): FINAL_JSON: {\"value\": 12, \"items\": [\"A\", \"C\"]}. Report the maximum value and one optimal subset."} | |
| {"id": "f3-c1-zh", "family": 3, "increment": 1, "language": "zh", "items": [{"id": "A", "weight": 7, "value": 8}, {"id": "B", "weight": 3, "value": 9}, {"id": "C", "weight": 8, "value": 19}, {"id": "D", "weight": 2, "value": 5}, {"id": "E", "weight": 5, "value": 21}, {"id": "F", "weight": 6, "value": 6}], "capacity": 16, "optimum": 49, "optimal_sets": [["B", "C", "E"]], "prompt": "从以下六个不可分割的物品中选择一个子集。每个物品最多选一次，总重量不能超过16。请使总价值最大。\n编号 | 重量 | 价值\nA | 7 | 8\nB | 3 | 9\nC | 8 | 19\nD | 2 | 5\nE | 5 | 21\nF | 6 | 6\n简要说明计算过程，然后严格用以下格式给出唯一的最终行（仅为格式示例）：FINAL_JSON: {\"value\": 12, \"items\": [\"A\", \"C\"]}。报告最大价值和一个最优子集。"} | |
| {"id": "f4-c0-en", "family": 4, "increment": 0, "language": "en", "items": [{"id": "A", "weight": 5, "value": 23}, {"id": "B", "weight": 2, "value": 9}, {"id": "C", "weight": 2, "value": 23}, {"id": "D", "weight": 9, "value": 5}, {"id": "E", "weight": 5, "value": 22}, {"id": "F", "weight": 4, "value": 4}], "capacity": 13, "optimum": 68, "optimal_sets": [["A", "C", "E"]], "prompt": "Select a subset of these six indivisible items. Each item may be selected at most once. Total weight must be at most 13. Maximize total value.\nID | weight | value\nA | 5 | 23\nB | 2 | 9\nC | 2 | 23\nD | 9 | 5\nE | 5 | 22\nF | 4 | 4\nExplain your calculation briefly, then give exactly one final line using this format (example only): FINAL_JSON: {\"value\": 12, \"items\": [\"A\", \"C\"]}. Report the maximum value and one optimal subset."} | |
| {"id": "f4-c0-zh", "family": 4, "increment": 0, "language": "zh", "items": [{"id": "A", "weight": 5, "value": 23}, {"id": "B", "weight": 2, "value": 9}, {"id": "C", "weight": 2, "value": 23}, {"id": "D", "weight": 9, "value": 5}, {"id": "E", "weight": 5, "value": 22}, {"id": "F", "weight": 4, "value": 4}], "capacity": 13, "optimum": 68, "optimal_sets": [["A", "C", "E"]], "prompt": "从以下六个不可分割的物品中选择一个子集。每个物品最多选一次，总重量不能超过13。请使总价值最大。\n编号 | 重量 | 价值\nA | 5 | 23\nB | 2 | 9\nC | 2 | 23\nD | 9 | 5\nE | 5 | 22\nF | 4 | 4\n简要说明计算过程，然后严格用以下格式给出唯一的最终行（仅为格式示例）：FINAL_JSON: {\"value\": 12, \"items\": [\"A\", \"C\"]}。报告最大价值和一个最优子集。"} | |
| {"id": "f4-c1-en", "family": 4, "increment": 1, "language": "en", "items": [{"id": "A", "weight": 5, "value": 23}, {"id": "B", "weight": 2, "value": 9}, {"id": "C", "weight": 2, "value": 23}, {"id": "D", "weight": 9, "value": 5}, {"id": "E", "weight": 5, "value": 22}, {"id": "F", "weight": 4, "value": 4}], "capacity": 14, "optimum": 77, "optimal_sets": [["A", "B", "C", "E"]], "prompt": "Select a subset of these six indivisible items. Each item may be selected at most once. Total weight must be at most 14. Maximize total value.\nID | weight | value\nA | 5 | 23\nB | 2 | 9\nC | 2 | 23\nD | 9 | 5\nE | 5 | 22\nF | 4 | 4\nExplain your calculation briefly, then give exactly one final line using this format (example only): FINAL_JSON: {\"value\": 12, \"items\": [\"A\", \"C\"]}. Report the maximum value and one optimal subset."} | |
| {"id": "f4-c1-zh", "family": 4, "increment": 1, "language": "zh", "items": [{"id": "A", "weight": 5, "value": 23}, {"id": "B", "weight": 2, "value": 9}, {"id": "C", "weight": 2, "value": 23}, {"id": "D", "weight": 9, "value": 5}, {"id": "E", "weight": 5, "value": 22}, {"id": "F", "weight": 4, "value": 4}], "capacity": 14, "optimum": 77, "optimal_sets": [["A", "B", "C", "E"]], "prompt": "从以下六个不可分割的物品中选择一个子集。每个物品最多选一次，总重量不能超过14。请使总价值最大。\n编号 | 重量 | 价值\nA | 5 | 23\nB | 2 | 9\nC | 2 | 23\nD | 9 | 5\nE | 5 | 22\nF | 4 | 4\n简要说明计算过程，然后严格用以下格式给出唯一的最终行（仅为格式示例）：FINAL_JSON: {\"value\": 12, \"items\": [\"A\", \"C\"]}。报告最大价值和一个最优子集。"} | |