Restore The Array

Description

A program was supposed to print an array of integers. The program forgot to print whitespaces and the array is printed as a string of digits and all we know is that all integers in the array were in the range [1, k] and there are no leading zeros in the array.

Given the string s and the integer k. There can be multiple ways to restore the array.

Return the number of possible array that can be printed as a string s using the mentioned program.

The number of ways could be very large so return it modulo 10^9 + 7

 

Example 1:

Input: s = "1000", k = 10000
Output: 1
Explanation: The only possible array is [1000]

Example 2:

Input: s = "1000", k = 10
Output: 0
Explanation: There cannot be an array that was printed this way and has all integer >= 1 and <= 10.

Example 3:

Input: s = "1317", k = 2000
Output: 8
Explanation: Possible arrays are [1317],[131,7],[13,17],[1,317],[13,1,7],[1,31,7],[1,3,17],[1,3,1,7]

Example 4:

Input: s = "2020", k = 30
Output: 1
Explanation: The only possible array is [20,20]. [2020] is invalid because 2020 > 30. [2,020] is ivalid because 020 contains leading zeros.

Example 5:

Input: s = "1234567890", k = 90
Output: 34

 

Constraints:

• 1 <= s.length <= 10^5.
• s consists of only digits and doesn't contain leading zeros.
• 1 <= k <= 10^9.

Solution(javascript)

// /** 1: Top-down Maximum call stack size exceed
//  * @param {string} s
//  * @param {number} k
//  * @return {number}
//  */
// const numberOfArrays = function (s, k) {
//   const memo = {}
//   const base = (10 ** 9) + 7
//   const aux = (start) => {
//     if (memo[start] !== undefined) {
//       return memo[start]
//     }
//     if (start > s.length - 1) {
//       return 1
//     }
//     if (s[start] === '0') {
//       return 0
//     }
//     let count = 0
//     let num = 0
//     for (let i = start; i < s.length; i++) {
//       num = num * 10 + parseInt(s[i], 10)
//       if (num <= k) {
//         count += aux(i + 1)
//         count %= base
//       } else {
//         break
//       }
//     }
//     memo[start] = count
//     return count
//   }
//   return aux(0)
// }

/** 1: Bottom-up
 * @param {string} s
 * @param {number} k
 * @return {number}
 */
const numberOfArrays = function (s, k) {
  const memo = new Array(s.length).fill(0)
  const base = (10 ** 9) + 7

  for (let i = s.length - 1; i >= 0; i--) {
    let num = 0
    let count = 0
    if (s[i] === '0') {
      continue
    }
    for (let j = i; j < s.length; j++) {
      num = num * 10 + parseInt(s[j], 10)
      if (num <= k) {
        count += (memo[j + 1] === undefined ? 1 : memo[j + 1])
        count %= base
      } else {
        break
      }
    }
    memo[i] = count
  }
  return memo[0]
}