# 13.05.2023 [2466. Count Ways To Build Good Strings]

13.05.2023

2466. Count Ways To Build Good Strings medium
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https://t.me/leetcode_daily_unstoppable/211

Problem

Count distinct strings, length low to high, appending ‘0’ zero or ‘1’ one times. Return count % 1,000,000,007.

Intuition

Let’s add zero's or one's one by one. For each current length, the resulting count is independent of all the previous additions. We can cache the result by the current size of the string.

Approach

Let’s write a DFS solution, adding zero or one and count the good strings.
Then we can rewrite it to the iterative DP.

Complexity

• Time complexity:
  
  O(n)

• Space complexity:
  
  O(n)

Code

top-down:

fun countGoodStrings(low: Int, high: Int, zero: Int, one: Int): Int {
    val m = 1_000_000_007
    val cache = mutableMapOf<Int, Int>()
    fun dfs(currSize: Int): Int {
        if (currSize > high) return 0
        return cache.getOrPut(currSize) {
            val curr = if (currSize in low..high) 1 else 0
            val addZeros = if (zero > 0) dfs(currSize + zero) else 0
            val addOnes = if (one > 0) dfs(currSize + one) else 0
            (curr + addZeros + addOnes) % m
        }
    }
    return dfs(0)
}

bottom-up

fun countGoodStrings(low: Int, high: Int, zero: Int, one: Int): Int {
    val cache = mutableMapOf<Int, Int>()
    for (sz in high downTo 0)
    cache[sz] = ((if (sz >= low) 1 else 0)
    + (cache[sz + zero]?:0)
    + (cache[sz + one]?:0)) % 1_000_000_007
    return cache[0]!!
}