Filling Bookcase Shelves LeetCode solution in Java

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class Solution {
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  public int minHeightShelves(int[][] books, int shelfWidth) {
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    int memo[] = new int[books.length];
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    return recur(books, shelfWidth, 0, memo);
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  }
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  private int recur(int[][] books, int shelfWidth, int index, int[] memo) {
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    if (index == books.length) {
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      return 0;
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    }
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    if (memo[index] > 0) {
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      return memo[index];
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    }
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    int ans = Integer.MAX_VALUE;
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    int height = 0;
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    int width = 0;
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    for (int i = index; i < books.length; i++) {
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      width += books[i][0];
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      if (width > shelfWidth) {
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        break;
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      }
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      height = Math.max(height, books[i][1]);
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      ans = Math.min(ans, height + recur(books, shelfWidth, i + 1, memo));
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    }
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    return memo[index] = ans;
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  }
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}