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.
N lines follow, each containing three integers: the first and second between 1 and 10^4, and the third between 1 and 1e9.
### Example Input:
```
3
2 2 20
2 1 30
3 1 40
```
### Function Signature:
Write a function f(N, A) that takes in the input.
```python
def f(N: int, A: List[Tuple[int, int, int]]):
'''
N: an integer
A: a list of tuples, each containing three integers
'''
```
Test Case Generator
Sure! Below is the test case generator for the given problem statement. This generator will create random test cases which conform to the constraints provided.
```python
import random
def tcgen():
# Generate a random N between 1 and 10^3
N = random.randint(1, 1000)
# Generate N blocks with weights, solidnesses, and values
blocks = []
for _ in range(N):
w = random.randint(1, 10000)
s = random.randint(1, 10000)
v = random.randint(1, 10**9)
blocks.append((w, s, v))
return N, blocks
# Example of how to use the generator and print a test case
def print_test_case():
N, blocks = tcgen()
print(N)
for w, s, v in blocks:
print(w, s, v)
# Generate and print a test case
print_test_case()
```
### Explanation
1. **Generate Random N**: `N` is chosen randomly between 1 and 1000.
2. **Generate N Blocks**: For each block, `w`, `s`, and `v` are generated within their respective constraints:
- `w` (weight) is between 1 and 10,000.
- `s` (solidness) is between 1 and 10,000.
- `v` (value) is between 1 and 1,000,000,000.
3. **Print the Test Case**: The function `print_test_case()` demonstrates how to generate and print a test case using the `tcgen()` function.
This should provide a robust set of test cases for the problem statement.
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