Portfolio Balances and Difference Array Range Updates

A quantitative asset allocation engine at Citadel manages capital across $N$ distinct asset classes indexed from $1$ to $N$. Initially, each asset class holds an allocation balance of $0$.

The fund receives a batch of $M$ bulk allocation rebalancing orders. Each order is specified as a 3-tuple $[l, r, v]$, representing an instruction to inject $v$ dollars of capital into every asset class in the contiguous index range $[l, r]$ inclusive ($1 \le l \le r \le N$).

Your Task

Implement the function max_portfolio_balance(n: int, updates: list[list[int]]) -> int that determines the maximum capital balance allocated to any single asset class after all $M$ rebalancing instructions have been executed.

Constraints

• $1 \le n \le 10^7$
• $1 \le \text{len}(updates) \le 2 \times 10^5$
• $1 \le l \le r \le n$
• $0 \le v \le 10^9$

Examples

n = 5
updates = [[1, 2, 100], [2, 5, 100], [3, 4, 100]]
# Asset balances after updates: [100, 200, 200, 200, 100]
# Output: 200