# 25.06.2023 [1575. Count All Possible Routes]

Count paths from `start` to `finish` using `|locations[i]-locations[j]` of the `fuel`

25.06.2023

1575. Count All Possible Routes hard
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Problem TLDR

Count paths from start to finish using |locations[i]-locations[j] of the fuel

Intuition

Let’s observe the example:

//  0 1 2 3 4
//  2 3 6 8 4
//    *   *
//
//  2 3 4 6 8
//    *     *
//
//  3-2(4)-3(3)-6(0)
//  3-6(2)-8(0)
//  3-8(5)
//  3-8(5)-6(3)-8(1)
//  3-4(4)-6(2)-8(0)

At each position curr given the amount of fuel f there is a certain number of ways to finish. It is independent of all the other factors, so can be safely cached.

Approach

• as there are also paths from finish to finish, modify the code to search other paths when finish is reached

Complexity

• Time complexity:
  O(nf), f⁣ – is a max fuel

• Space complexity:
  O(nf)

Code

fun countRoutes(locations: IntArray, start: Int, finish: Int, fuel: Int): Int {
    //  0 1 2 3 4
    //  2 3 6 8 4
    //    *   *
    //
    //  2 3 4 6 8
    //    *     *
    //
    //  3-2(4)-3(3)-6(0)
    //  3-6(2)-8(0)
    //  3-8(5)
    //  3-8(5)-6(3)-8(1)
    //  3-4(4)-6(2)-8(0)

    val cache = mutableMapOf<Pair<Int, Int>, Int>()
    fun dfs(curr: Int, f: Int): Int {
        if (f < 0) return 0
        return cache.getOrPut(curr to f) {
            var sum = if (curr == finish) 1 else 0
            locations.forEachIndexed { i, n ->
                if (i != curr) {
                    sum = (sum + dfs(i, f - Math.abs(n - locations[curr]))) % 1_000_000_007
                }
            }
            return@getOrPut sum
        }
    }
    return dfs(start, fuel)
}