Leetcode Problem 903. Valid Permutations for DI Sequence

903. Valid Permutations for DI Sequence

Leetcode Solutions

Dynamic Programming with Prefix Sums

  1. Initialize a 2D array dp with dimensions (n+1) x (n+1) and set all elements to 0.
  2. Set dp[0][j] to 1 for all j because there is only one way to have a permutation of length 1.
  3. Iterate over each character in the input string s from left to right.
  4. For each character s[i], update dp[i+1][j] based on the following rules:
    • If s[i] == 'I', set dp[i+1][j] to the sum of dp[i][0] to dp[i][j-1].
    • If s[i] == 'D', set dp[i+1][j] to the sum of dp[i][j] to dp[i][n-i].
  5. Use prefix sums to optimize the computation of the sums in step 4.
  6. The answer is the sum of the last row of dp, i.e., sum(dp[n][0] to dp[n][n]).
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Backtracking with Memoization

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