## algorithm to reverse words of a string

June 14, 2013 1 Comment

This is a bit tricky algorithm and most frequently asked question in interviews. I will now show how to do it in the best time complexity of [O(2n)]. Complete source code can be downloaded from here.

Here we will make use of algorithm to reverse the string which is explained in our previous posts at O(n/2) complexity.

Steps to solve this algorithm

- take two pointers, one pointing to the start of the array and another to the end of the array and swap the values at respective pointers.
- While traversing the array increment starting pointer and decrement ending pointer and continue swap the values at respective pointers
- continue this till we reach the middle of the array which will result in reversed string
- from above generated reversed string take a pointer which runs through this string and stops at spaces which indicates the occurance of a word
- go back to first three steps to reverse a word within this reversed string and go back to fourth step till the sentence is completed
- by end of this algorithm, last word will not be reversed because there is no space after it and hence reverse the last word at the end

Source Code

/** * Algorithm to reverse word of a string * @return reversed words array */ public char[] reverseWords(char[] arr) { // reverse the string reverse(arr, 0, arr.length / 2, arr.length); // reverse words of a string int wordIdx = 0; int wordMidIdx = 0; int prevWordLastIdx = 0; // outer loop to track spaces for (int sentenceIdx = 0; sentenceIdx < arr.length; sentenceIdx++) { if (arr[sentenceIdx] != ' ') continue; wordIdx = prevWordLastIdx; int wordLastIdx = sentenceIdx; wordMidIdx = (sentenceIdx + wordIdx) / 2; // reverse each word in a string reverse(arr, wordIdx, wordMidIdx, wordLastIdx); prevWordLastIdx = sentenceIdx + 1; } // reverse last word wordIdx = prevWordLastIdx; wordMidIdx = (arr.length + wordIdx) / 2; reverse(arr, wordIdx, wordMidIdx, arr.length); return arr; }

**How to arrive at the time complexity? **

**Step #1:** reverse the complete string which is explained in our previous algorithm at O(n/2) complexity. https://tekmarathon.wordpress.com/2012/10/05/algorithm-to-reverse-a-string/

**Step #2:** keep a pointer which traverses through the string looking for spaces which takes O(n)

**Step #3:** using the above spaces reverse words within the string at O(n/2). Let us see why this is O(n/2)

'welcome to coding algorithms' would become 'smhtirogla gnidoc ot emoclew' Now take the string 'smhtirogla gnidoc ot emoclew' and reverse each word within it with same logic explained in reversing the string. This will take O(n) iterations, let us see how is it O(n) At first iteration 'smhtirogla gnidoc ot emoclew' would become 'algorithms gnidoc ot emoclew' at 5 iterations i.e (length of 'smhtirogla')/2) At second iteration 'algorithms gnidoc ot emoclew' would become 'algorithms coding ot emoclew' at 3 iterations i.e (length of 'gnidoc')/2) At third iteration 'algorithms coding ot emoclew' would become 'algorithms coding to emoclew' at 1 iterations i.e (length of 'ot')/2) At fourth iteration 'algorithms coding to emoclew' would become 'algorithms coding to welcome' at 3 iterations i.e (length of 'emoclew')/2) total length of the string = 29 total iterations = 12 + spaces = 15 (approximately half the length of the total string)

**Total complexity from Step #1, Step #2 and Step #3 = O(n/2) + O(n) + O(n/2) = O(2n)**

Complete source code can be downloaded from here.

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