Document adversarial temporal graph problem statement

.md

@@ -0,0 +1,77 @@
+Problem: Adversarial Temporal Graph with Stateful Encoding
+
+Problem Statement
+You are given:
+A directed graph with n nodes (0 → n-1)
+Each edge has:
+cost (energy consumption)
+time (time taken)
+label (a lowercase character 'a'–'z')
+An integer K (max energy)
+An integer T (max time)
+An integer M (modulo)
+A forbidden pattern string P
+
+Rules
+
+You start at node 0 and want to reach node n-1.
+
+You maintain:
+
+1. ⏱ Time
+Total time ≤ T
+
+3. ⚡ Energy
+Total energy ≤ K
+
+4. 🔐 Stateful Encoding
+Each path generates a value:
+𝑣𝑎𝑙𝑢𝑒=(((0⋅131+𝑐1)⋅131+𝑐2)⋯) mod 𝑀
+
+5. 🚫 Forbidden Pattern Constraint
+The concatenated labels along your path must NOT contain P as a substring.
+
+5. 🔁 Temporal Edge Activation
+Each edge (u → v) is only usable at certain times:
+You are given for each edge:
+A list of active intervals [l, r]
+You can traverse the edge only if current time ∈ any interval
+
+7. 🎭 Adversarial Twist
+At each node, an adversary can flip one outgoing edge’s label to any character (once per node visit).
+You must assume the adversary acts to minimize your final value
+You still try to maximize the final value
+
+Objective
+Return the maximum possible encoded value you can guarantee under worst-case adversarial behavior.
+If no valid path exists, return -1
+
+Constraints
+1 ≤ n ≤ 100
+1 ≤ edges ≤ 500
+1 ≤ K ≤ 5000
+1 ≤ T ≤ 5000
+|P| ≤ 50
+Active intervals per edge ≤ 10
+
+Example 1:
+n = 3
+edges:
+0 → 1 (cost=2, time=2, label='a', active=[0,10])
+1 → 2 (cost=2, time=2, label='b', active=[0,10])
+
+K = 5
+T = 5
+M = 1000
+P = "ab"
+
+Example 2:
+n = 3
+edges:
+0 → 1 (cost=1, time=1, label='a', active=[0,10])
+1 → 2 (cost=1, time=1, label='c', active=[0,10])
+
+K = 5
+T = 5
+M = 1000
+P = "ab"