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#903 - Valid Permutations for DI Sequence

Hard • View on LeetCode • View on GitHub

String Dynamic Programming Prefix Sum

Problem Description

You are given a string s of length n where s[i] is either:

'D' means decreasing, or
'I' means increasing.

A permutation perm of n + 1 integers of all the integers in the range [0, n] is called a valid permutation if for all valid i:

If s[i] == 'D', then perm[i] > perm[i + 1], and
If s[i] == 'I', then perm[i] < perm[i + 1].

Return the number of valid permutations perm. Since the answer may be large, return it modulo 109 + 7.

Solution

/**
 * @param {string} s
 * @return {number}
 */
var numPermsDISequence = function(s) {
  const MOD = 1e9 + 7;
  const n = s.length;
  const dp = Array.from({ length: n + 1 }, () => new Array(n + 1).fill(0));

  dp[0][0] = 1;

  for (let len = 1; len <= n; len++) {
    for (let curr = 0; curr <= len; curr++) {
      if (s[len - 1] === 'D') {
        for (let prev = curr; prev < len; prev++) {
          dp[len][curr] = (dp[len][curr] + dp[len - 1][prev]) % MOD;
        }
      } else {
        for (let prev = 0; prev < curr; prev++) {
          dp[len][curr] = (dp[len][curr] + dp[len - 1][prev]) % MOD;
        }
      }
    }
  }

  let result = 0;
  for (let num = 0; num <= n; num++) {
    result = (result + dp[n][num]) % MOD;
  }

  return result;
};

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