Pressure-Isolation Shutdown Order
Intuit● HardNEW GRADINTERNOAProblem statement
An offshore processing platform has n valves in a line. Valve i has signed pressure coefficient coefficients[i]. Permanent boundary regulators with coefficients leftBoundary and rightBoundary stand immediately outside the line and are never shut down.
Shut down every valve exactly once. When valve i is shut down, let x and y be the coefficients of its nearest valves or boundary regulators that are still active on its left and right. This shutdown adds x * coefficients[i] * y to the total stability score. Valve i is then removed, so later shutdowns may have different neighbors.
Return a two-element array: the maximum possible total stability score, followed by the number of distinct shutdown orders that attain that maximum. Report the number of orders modulo 10^9 + 7. Two orders are distinct when their valve-index sequences differ.
Function
maximizeStabilityAndCount(coefficients: int[], leftBoundary: int, rightBoundary: int) → long[]Examples
Example 1
coefficients = [3]leftBoundary = 2rightBoundary = 5return = [30,1]There is one shutdown order. Its only step contributes 2 * 3 * 5 = 30.
Example 2
coefficients = [1,1]leftBoundary = 1rightBoundary = 1return = [2,2]Either valve can be shut down first. Both orders score 1 + 1 = 2, so there are two maximizing orders.
Example 3
coefficients = [1,2]leftBoundary = 1rightBoundary = 1return = [4,1]Closing the first valve before the second scores 1 * 1 * 2 + 1 * 2 * 1 = 4. The other order scores 1 * 2 * 1 + 1 * 1 * 1 = 3.
Constraints
1 <= coefficients.length <= 200.-1000 <= coefficients[i], leftBoundary, rightBoundary <= 1000.- Use signed 64-bit arithmetic for stability scores and the returned score.
- The returned count is reduced modulo
10^9 + 7.