# 20.05.2023 [399. Evaluate Division]

20.05.2023

399. Evaluate Division medium
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https://t.me/leetcode_daily_unstoppable/218

Problem TLDR

Given values for a/b and b/c find answers for a/c.

Intuition

Let’s build a graph, a -> b with weights of values[a/b]. Then answer is a path from one node to the other. The shortest path can be found with a Breadth-First Search.

Approach

• careful with corner case x/x, where x is not in a graph.

Complexity

• Time complexity:
  O(nEV)

• Space complexity:
  O(n+E+V)

Code

fun calcEquation(equations: List<List<String>>, values: DoubleArray, queries: List<List<String>>): DoubleArray {
    val fromTo = mutableMapOf<String, MutableList<Pair<String, Double>>>()
    equations.forEachIndexed { i, (from, to) ->
        fromTo.getOrPut(from) { mutableListOf() } += to to values[i]
        fromTo.getOrPut(to) { mutableListOf() } += from to (1.0 / values[i])
    }
    // a/c = a/b * b/c
    return queries.map { (from, to) ->
        with(ArrayDeque<Pair<String, Double>>()) {
            val visited = HashSet<String>()
                visited.add(from)
                if (fromTo.containsKey(to)) add(from to 1.0)
                while (isNotEmpty()) {
                    repeat(size) {
                        val (point, value) = poll()
                        if (point == to) return@map value
                        fromTo[point]?.forEach { (next, nvalue) ->
                            if (visited.add(next)) add(next to value * nvalue)
                        }
                    }
                }
                -1.0
            }
        }.toDoubleArray()
    }