Orig Description
Score : 100 points
Problem StatementThere are N blocks, numbered 1, 2, \ldots, N.
For each i (1 \leq i \leq N), Block i has a weight of w_i, a solidness of s_i and a value of v_i.
Taro has decided to build a tower by choosing some of the N blocks and stacking them vertically in some order.
Here, the tower must satisfy the following condition:
For each Block i contained in the tower, the sum of the weights of the blocks stacked above it is not greater than s_i.
Find the maximum possible sum of the values of the blocks contained in the tower.
Constraints
All values in input are integers.
1 \leq N \leq 10^3
1 \leq w_i, s_i \leq 10^4
1 \leq v_i \leq 10^9
InputInput is given from Standard Input in the following format:
N
w_1 s_1 v_1
w_2 s_2 v_2
:
w_N s_N v_N
OutputPrint the maximum possible sum of the values of the blocks contained in the tower.
Sample Input 13
2 2 20
2 1 30
3 1 40
Sample Output 150
If Blocks 2, 1 are stacked in this order from top to bottom, this tower will satisfy the condition, with the total value of 30 + 20 = 50.
Sample Input 24
1 2 10
3 1 10
2 4 10
1 6 10
Sample Output 240
Blocks 1, 2, 3, 4 should be stacked in this order from top to bottom.
Sample Input 35
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
Sample Output 35000000000
The answer may not fit into a 32-bit integer type.
Sample Input 48
9 5 7
6 2 7
5 7 3
7 8 8
1 9 6
3 3 3
4 1 7
4 5 5
Sample Output 422
We should, for example, stack Blocks 5, 6, 8, 4 in this order from top to bottom.
Extracted Specification
An integer N (1 ≤ N ≤ 10^3), representing some quantity or size.
A list of N tuples, where each tuple contains three integers (a, b, c) such that:
1 ≤ a, b ≤ 10^4
1 ≤ c ≤ 10^9
### Example Input:
```
3
2 2 20
2 1 30
3 1 40
```
### Function Signature:
Write a function f(inputs) that takes in the input.
```python
def f(inputs: List[Tuple[int, int, int]]):
'''
inputs: a list of tuples, each containing three integers
'''
```
Test Case Generator
Sure! Below is the test case generator for the given problem statement:
```python
import random
def tcgen():
# Step 1: Generate a random integer N (1 ≤ N ≤ 10^3)
N = random.randint(1, 1000)
# Step 2: Generate N blocks with random weights, solidness, and values
blocks = []
for _ in range(N):
w = random.randint(1, 10000)
s = random.randint(1, 10000)
v = random.randint(1, 1000000000)
blocks.append((w, s, v))
return N, blocks
# Example usage
N, blocks = tcgen()
print(N)
for w, s, v in blocks:
print(w, s, v)
```
### Explanation
1. **Generate N**: The first step is to generate a random integer \( N \) between 1 and 1000 inclusive, which represents the number of blocks.
2. **Generate Blocks**: For each block, we generate:
- A weight \( w \) between 1 and 10000 inclusive.
- A solidness \( s \) between 1 and 10000 inclusive.
- A value \( v \) between 1 and 1000000000 inclusive.
3. **Return Values**: The function returns \( N \) and a list of tuples, where each tuple contains the weight, solidness, and value of a block.
### Example Output
Here is an example of the output you might get from running the test case generator:
```
5
1234 5678 9101112
3456 7890 1234567
2345 6789 12345678
4567 8901 23456789
6789 1234 34567890
```
This output represents:
- \( N \) as 5, which means there are 5 blocks.
- Each subsequent line represents the weight, solidness, and value of a block respectively.
Extract Arguments
def extract_arguments(fh):
N = int(fh.readline().strip())
blocks = []
for _ in range(N):
w, s, v = map(int, fh.readline().strip().split())
blocks.append((w, s, v))
return N, blocks