Problem Description

This is a template problem.

Given $n$ nodes and $m$ directed edges, each edge has a specified capacity. The task is to calculate the maximum flow from node $s$ to node $t$.

Input Format

The first line contains four integers: $n, m, s, t$.
The next $m$ lines each contain three integers: $u, v, c$, representing a directed edge from node $u$ to node $v$ with a flow capacity of $c$.

Output Format

Output the maximum flow from node $s$ to node $t$.

7 14 1 7
1 2 5
1 3 6
1 4 5
2 3 2
2 5 3
3 2 2
3 4 3
3 5 3
3 6 7
4 6 5
5 6 1
6 5 1
5 7 8
6 7 7

14

10 16 1 2
1 3 2
1 4 2
5 2 2
6 2 2
3 5 1
3 6 1
4 5 1
4 6 1
1 7 2147483647
9 2 2147483647
7 8 2147483647
10 9 2147483647
8 5 2
8 6 2
3 10 2
4 10 2

8

Constraints and Hints

• $1 \leqslant n \leqslant 1200$, $1 \leqslant m \leqslant 120000$, $1 \leqslant c \leqslant 2^{31}-1$.
• The answer is guaranteed to be less than or equal to $2^{31}-1$.
• The time complexity of common maximum flow algorithms is $O(n^2 \cdot m)$. Try to optimize your algorithm.