Understanding thee time and space completity of algoritmy ms helps in evaluating their accessiency. Merge sort and quick sort are two popular sorting algoritmy ms with different performance. This article excellains how to calculate their complexities.

Merge Sort Complexity

Merge sort divides thee array into halves recursively until each subarray conclus a single element. Thee merging process then combine these subarrays in sorted order.

Te timee complexity of merge sort is Average, and d wortt cases because it conformently divides the array and merges it accemently.

Space complexity is current 1; crcrcrcrcrcrcrcrcrcrcrcrcrccrcrcrcrcrcrcrcrcrcrcrcrccrccrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrccccccrcrcccccrccrcccccccccrcrccccccccccccccccccccccccccccccccccccccccccccccccccccc@@

Quick Sort Complexity

Quick sort selekts a pivot element and partitions thee array into subarrays that are less than or greater than thee pivot. This process is repeated recursively.

Te average timestyle is current 1; FLT: 0 Cr3; Cr3; O (n log n) current 1; Cr001; FLT: 1 Cr3; Cr3; but in the worst case, such as curn the smallett or largett element is always chosen as th te pivot, it degrades to current 1; FLT: 2 Crlend 3; O (n ^ 2) curren1; Cr1s; FLT: 3 Cr3; Cr3; Cr3;

Space complexity for quick sort is generaly consist1; CLAS1; FLT: 0 CLAS3; O (log n) consist1; CLAS1; CLAS1; CLAS1; CLASPR3; due to recursive stack space, but it can be hier consiing on thee implementation.

Summary of Complexities

  • Merge Sort - Time: CLAS1; CLAS1; CLAS3; CLAS3; O (n log n) CLAS1; CLAS1; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; O (n) CLAS1; CLAS1; CLAS1; CLAS3; CLAS3; CLAS33; CLAS3;
  • Quick Sort - Time: CLAS1; CLAS1; FLT: 0 CLAS3; CLAS3; Average O (n log n) CLAS1; CLAS1; CLAS1; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS31; CLAS1; CLAS33; CLAS33;