Question

1977. Number of Ways to Separate Numbers

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Description

You wrote down many positive integers in a string called num. However, you realized that you forgot to add commas to seperate the different numbers. You remember that the list of integers was non-decreasing and that no integer had leading zeros.

Return _the number of possible lists of integers that you could have written down to get the string _num. Since the answer may be large, return it modulo 109 + 7.

 

Example 1:

Input: num = "327"
Output: 2
Explanation: You could have written down the numbers:
3, 27
327

Example 2:

Input: num = "094"
Output: 0
Explanation: No numbers can have leading zeros and all numbers must be positive.

Example 3:

Input: num = "0"
Output: 0
Explanation: No numbers can have leading zeros and all numbers must be positive.

 

Constraints:

• 1 <= num.length <= 3500
• num consists of digits '0' through '9'.

Solutions

Solution 1

class Solution:
  def numberOfCombinations(self, num: str) -> int:
    def cmp(i, j, k):
      x = lcp[i][j]
      return x >= k or num[i + x] >= num[j + x]

    mod = 10**9 + 7
    n = len(num)
    lcp = [[0] * (n + 1) for _ in range(n + 1)]
    for i in range(n - 1, -1, -1):
      for j in range(n - 1, -1, -1):
        if num[i] == num[j]:
          lcp[i][j] = 1 + lcp[i + 1][j + 1]

    dp = [[0] * (n + 1) for _ in range(n + 1)]
    dp[0][0] = 1
    for i in range(1, n + 1):
      for j in range(1, i + 1):
        v = 0
        if num[i - j] != '0':
          if i - j - j >= 0 and cmp(i - j, i - j - j, j):
            v = dp[i - j][j]
          else:
            v = dp[i - j][min(j - 1, i - j)]
        dp[i][j] = (dp[i][j - 1] + v) % mod
    return dp[n][n]

class Solution {
  private static final int MOD = (int) 1e9 + 7;

  public int numberOfCombinations(String num) {
    int n = num.length();
    int[][] lcp = new int[n + 1][n + 1];
    for (int i = n - 1; i >= 0; --i) {
      for (int j = n - 1; j >= 0; --j) {
        if (num.charAt(i) == num.charAt(j)) {
          lcp[i][j] = 1 + lcp[i + 1][j + 1];
        }
      }
    }
    int[][] dp = new int[n + 1][n + 1];
    dp[0][0] = 1;
    for (int i = 1; i <= n; ++i) {
      for (int j = 1; j <= i; ++j) {
        int v = 0;
        if (num.charAt(i - j) != '0') {
          if (i - j - j >= 0) {
            int x = lcp[i - j][i - j - j];
            if (x >= j || num.charAt(i - j + x) >= num.charAt(i - j - j + x)) {
              v = dp[i - j][j];
            }
          }
          if (v == 0) {
            v = dp[i - j][Math.min(j - 1, i - j)];
          }
        }
        dp[i][j] = (dp[i][j - 1] + v) % MOD;
      }
    }
    return dp[n][n];
  }
}

class Solution {
public:
  const int mod = 1e9 + 7;

  int numberOfCombinations(string num) {
    int n = num.size();
    vector<vector<int>> lcp(n + 1, vector<int>(n + 1));
    for (int i = n - 1; i >= 0; --i) {
      for (int j = n - 1; j >= 0; --j) {
        if (num[i] == num[j]) {
          lcp[i][j] = 1 + lcp[i + 1][j + 1];
        }
      }
    }
    auto cmp = [&](int i, int j, int k) {
      int x = lcp[i][j];
      return x >= k || num[i + x] >= num[j + x];
    };
    vector<vector<int>> dp(n + 1, vector<int>(n + 1));
    dp[0][0] = 1;
    for (int i = 1; i <= n; ++i) {
      for (int j = 1; j <= i; ++j) {
        int v = 0;
        if (num[i - j] != '0') {
          if (i - j - j >= 0 && cmp(i - j, i - j - j, j)) {
            v = dp[i - j][j];
          } else {
            v = dp[i - j][min(j - 1, i - j)];
          }
        }
        dp[i][j] = (dp[i][j - 1] + v) % mod;
      }
    }
    return dp[n][n];
  }
};

func numberOfCombinations(num string) int {
  n := len(num)
  lcp := make([][]int, n+1)
  dp := make([][]int, n+1)
  for i := range lcp {
    lcp[i] = make([]int, n+1)
    dp[i] = make([]int, n+1)
  }
  for i := n - 1; i >= 0; i-- {
    for j := n - 1; j >= 0; j-- {
      if num[i] == num[j] {
        lcp[i][j] = 1 + lcp[i+1][j+1]
      }
    }
  }
  cmp := func(i, j, k int) bool {
    x := lcp[i][j]
    return x >= k || num[i+x] >= num[j+x]
  }
  dp[0][0] = 1
  var mod int = 1e9 + 7
  for i := 1; i <= n; i++ {
    for j := 1; j <= i; j++ {
      v := 0
      if num[i-j] != '0' {
        if i-j-j >= 0 && cmp(i-j, i-j-j, j) {
          v = dp[i-j][j]
        } else {
          v = dp[i-j][min(j-1, i-j)]
        }
      }
      dp[i][j] = (dp[i][j-1] + v) % mod
    }
  }
  return dp[n][n]
}