Camel Train

AtCoder
IDaising2020_e
Time2000ms
Memory256MB
Difficulty
We have $N$ camels numbered $1,2,\ldots,N$. Snuke has decided to make them line up in a row. The happiness of Camel $i$ will be $L_i$ if it is among the $K_i$ frontmost camels, and $R_i$ otherwise. Snuke wants to maximize the total happiness of the camels. Find the maximum possible total happiness of the camel. Solve this problem for each of the $T$ test cases given. ## Constraints * All values in input are integers. * $1 \leq T \leq 10^5$ * $1 \leq N \leq 2 \times 10^{5}$ * $1 \leq K_i \leq N$ * $1 \leq L_i, R_i \leq 10^9$ * The sum of values of $N$ in each input file is at most $2 \times 10^5$. ## Input Input is given from Standard Input in the following format: $T$ $\mathrm{case}_1$ $\vdots$ $\mathrm{case}_T$ Each case is given in the following format: $N$ $K_1$ $L_1$ $R_1$ $\vdots$ $K_N$ $L_N$ $R_N$ [samples]
Samples
Input #1
3
2
1 5 10
2 15 5
3
2 93 78
1 71 59
3 57 96
19
19 23 16
5 90 13
12 85 70
19 67 78
12 16 60
18 48 28
5 4 24
12 97 97
4 57 87
19 91 74
18 100 76
7 86 46
9 100 57
3 76 73
6 84 93
1 6 84
11 75 94
19 15 3
12 11 34
Output #1
25
221
1354

*   In the first test case, it is optimal to line up the camels in the order $2, 1$.
    *   Camel $1$ is not the frontmost camel, so its happiness will be $10$.
    *   Camel $2$ is among the two frontmost camels, so its happiness will be $15$.
*   In the second test case, it is optimal to line up the camels in the order $2, 1, 3$.
    *   Camel $1$ is among the two frontmost camels, so its happiness will be $93$.
    *   Camel $2$ is the frontmost camel, so its happiness will be $71$.
    *   Camel $3$ is among the three frontmost camels, so its happiness will be $57$.
API Response (JSON)
{
  "problem": {
    "name": "Camel Train",
    "description": {
      "content": "We have $N$ camels numbered $1,2,\\ldots,N$. Snuke has decided to make them line up in a row. The happiness of Camel $i$ will be $L_i$ if it is among the $K_i$ frontmost camels, and $R_i$ otherwise. Sn",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "aising2020_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have $N$ camels numbered $1,2,\\ldots,N$. Snuke has decided to make them line up in a row.\nThe happiness of Camel $i$ will be $L_i$ if it is among the $K_i$ frontmost camels, and $R_i$ otherwise.\nSn...",
      "is_translate": false,
      "language": "English"
    }
  ]
}
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