notebook/notes/algorithms/sorting/merge-sort.md

title	TARGET DECK	FILE TAGS	tags
Merge Sort	Obsidian::STEM	algorithm::sorting	algorithm sorting

Overview

Property	Value
Best Case	\Omega(n\lg{n})
Worst Case	O(n\lg{n})
Avg. Case	O(n\lg{n})
Aux. Memory	O(n)
Stable	-
Adaptive	-

!

%%ANKI Basic What does the term "merge" in MERGE_SORT refer to? Back: The primary operation used to combine array halves. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

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%%ANKI Basic What is MERGE_SORT's best case runtime? Back: \Omega(n\lg{n}) Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

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%%ANKI Basic What is MERGE_SORT's worst case runtime? Back: O(n\lg{n}) Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

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%%ANKI Basic What is MERGE_SORT's average case runtime? Back: O(n\lg{n}) Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

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%%ANKI Basic How much auxiliary space does MERGE_SORT use? Back: O(n) Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

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%%ANKI Basic What is the "divide" step of MERGE_SORT? Back: Divide the input array into two subarrays of half size. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

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%%ANKI Basic What is the "conquer" step of MERGE_SORT? Back: Call MERGE_SORT on the "divide"-step's two subarrays. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

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%%ANKI Basic What is the "combine" step of MERGE_SORT? Back: Merge the sorted subarrays produced by the "conquer" step. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

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%%ANKI Basic When does MERGE_SORT "bottom out"? Back: When the sequence to be sorted has length 1 or less. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

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static void merge(int i, int mid, int j, int *A) {
  int si = mid - i + 1;
  int sj = j - (mid + 1) + 1;

  int *L = malloc(sizeof(int) * (si + 1));
  int *R = malloc(sizeof(int) * (sj + 1));

  L[si] = INT_MAX;
  R[sj] = INT_MAX;

  for (int k = 0; k < si; ++k) {
    L[k] = A[i + k];
  }
  for (int k = 0; k < sj; ++k) {
    R[k] = A[mid + 1 + k];
  }

  int topL = 0, topR = 0;
  for (int k = 0; k < j - i + 1; ++k) {
    if (L[topL] < R[topR]) {
      A[i + k] = L[topL++];
    } else {
      A[i + k] = R[topR++];
    }
  }

  free(L);
  free(R);
}

void merge_sort(int i, int j, int *A) {
  if (j <= i) {
    return;
  }
  int mid = (i + j) / 2;
  merge_sort(i, mid, A);
  merge_sort(mid + 1, j, A);
  merge(i, mid, j, A);
}

%%ANKI Basic Where in MERGE_SORT's implementation are sentinels useful? Back: As the last elements of the two arrays to combine. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

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%%ANKI Basic What sentinel values are typically used in MERGE_SORT's "merge" operation? Back: \infty or the record type's equivalent. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

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%%ANKI Basic What sorting algorithm does the following demonstrate? ! Back: MERGE_SORT Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

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Bibliography

• Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).