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Rocket Pack CodeChef Solution

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Rocket Pack CodeChef Solution

Rocket Pack CodeChef Solution

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Problem

Chef’s robot starts from the coordinate¬†(0, 0)¬†and wishes to reach to the coordinate¬†(N, M).

The initial energy of the robot is 0. There are K batteries kept at some of the coordinates such that picking up the i^{th} battery costs C_i units, and, on picking the i^{th} battery, the current energy of the robot becomes E_i.

Note that one coordinate can have multiple batteries but the robot can pick at most one battery out of those.

For example, if the robot reaches a certain coordinate with energy A and there are two batteries with energy B_1 and B_2 on that coordinate, the robot may choose at most one battery out of these. On choosing the first battery, the energy of the robot becomes B_1 (not A+B_1).

The robot can walk in all the four directions as follows:

  • Move up: Moving from coordinate¬†(X, Y)¬†to¬†(X, Y+1), the robot¬†loses¬†1¬†unit of energy.
  • Move down: Moving from coordinate¬†(X, Y)¬†to¬†(X, Y-1), the robot¬†gains¬†1¬†unit of energy.
  • Move right: Moving from coordinate¬†(X, Y)¬†to¬†(X+1, Y), the robot¬†loses¬†1¬†unit of energy.
  • Move left: Moving from coordinate¬†(X, Y)¬†to¬†(X-1, Y), the robot¬†gains¬†1¬†unit of energy.

Find the minimum cost to reach (N, M) if the robot maintains a non-negative energy throughout the journey (including the destination).

Input Format

  • The first line of input contains a single integer¬†T, the number of test cases. The description of the test cases follows.
  • Each test cases consists of two lines of input.
    • The first line contains three positive integers¬†N, M,¬†and¬†K, the coordinates of the destination and the number of batteries.
    • Next¬†K¬†lines have four space-separated integers each:¬†X_i, Y_i, C_i, E_i. The¬†i^{th}¬†line indicates that the coordinate¬†(X_i, Y_i)¬†has a¬†battery¬†with cost¬†C_i¬†and energy¬†E_i.
  • The input data guarantees that the robot can reach the destination.

Output Format

For each test case, output a single integer, the minimum cost from (0,0) to (N, M).

Constraints

  • 1 \leq T \leq 10
  • 1 \leq K \leq 10^5
  • 0 \leq X_i,Y_i \leq 2*10^9
  • 1 \leq N,M,C_i,E_i \leq 2*10^9
  • The sum of¬†K¬†over all test cases won’t exceed¬†10^5.

Sample 1:

Input

Output

2
5 5 3
0 0 10 10
0 0 2 4
2 2 1 1
5 5 4
0 0 10 10
0 0 2 4
2 2 1 1
4 1 3 5
10
6

Explanation:

Test case 1: Use the first battery with cost 10. Thus, at coordinate (0, 0), the energy of the robot becomes 10 units. The robot can traverse the path :(0,0) Р(0, 1) Р\ldots Р(0, 5) Р(1, 5) Р\ldots Р(5,5). It can be shown that the robot cannot reach the destination in less than 10 units cost.

Test case 2:

  • Use the¬†2^{nd}¬†battery: At coordinate¬†(0, 0), robot picks the¬†2^{nd}¬†battery and the energy of the robot becomes¬†4¬†units. The robot can move to coordinate¬†(2, 2)¬†using this energy. On reaching¬†(2, 2), robot’s energy is¬†0.
  • Use the¬†3^{rd}¬†battery: At coordinate¬†(2, 2), robot picks the¬†3^{rd}¬†battery and the energy of the robot becomes¬†1¬†unit. The robot can move from¬†(2, 2)¬†to¬†(2, 1)¬†and gain¬†1¬†unit of energy. Thus, it has¬†2¬†units of energy now. It can now move from¬†(2, 1)¬†to¬†(4, 1)¬†using this energy.
  • Use the¬†4^{th}¬†battery: At coordinate¬†(4, 1), robot picks the¬†4^{th}¬†battery and the energy of the robot becomes¬†5¬†units. The robot can now move from¬†(4, 1)¬†to¬†(5, 5).
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