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Bubble Sort Time Complexity Calculation . Also suggest improvements which will improve the best case running time of algorithm to o(n). The below tables depicts the time and space complexity of bubble sort. Bubble Sort Algorithm, Source Code, Time Complexity from www.happycoders.eu The best case of o (n) occurs when the provided array is already sorted. Each element of the array moves to the end in each iteration, much to the movement of air bubbles in the water that rise to the surface. When analyzing time complexity, we would say that this is “on the order of n 2 ” time.