# 1.07.2023 [2305. Fair Distribution of Cookies]

`Min` of the `max` distributing `n` cookies to `k` children

1.07.2023

2305. Fair Distribution of Cookies medium
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Problem TLDR

Min of the max distributing n cookies to k children

Intuition

Search all possible ways to give current cookie to one of the children. Backtrack sums and calculate the result.

Approach

Just DFS

Complexity

• Time complexity:
  O(k^n)

• Space complexity:
  O(2^n)

Code

fun distributeCookies(cookies: IntArray, k: Int): Int {
    fun dfs(pos: Int, children: IntArray): Int {
        if (pos == cookies.size) return if (children.contains(0)) -1 else children.max()!!
        var min = -1
        for (i in 0 until k) {
            children[i] += cookies[pos]
            val res = dfs(pos + 1, children)
            if (res != -1) min = if (min == -1) res else minOf(min, res)
            children[i] -= cookies[pos]
        }
        return min
    }
    return dfs(0, IntArray(k))
}