Write code to find lexicographic minimum in a circular array, e.g. for the array BCABDADAB, the lexicographic minimum is ABBCABDAD
Input Constraint: 1 < n < 1000
Examples:
Input: GEEKSQUIZ Output: EEKSQUIZG Input: GFG Output: FGG Input : CAPABCQ Output : ABCQCAP
We have discussed a O(n2Logn) solution in Lexicographically minimum string rotation | Set 1. Here we need to find the starting index of minimum rotation and then print the rotation.
1) Initially assume 0 to be current min
starting index.
2) Loop through i = 1 to n-1.
a) For each i compare sequence starting
at i with current min starting index
b) If sequence starting at i is lexicographically
smaller, update current min starting
index.
Here is pseudo-code for algorithm
function findIndexForSmallestSequence(S, n):
result = 0
for i = 1:n-1
if (sequence beginning at i <
sequence beginning at result)
result = i
end if
end for
return result
Here is implementation of above algorithm.
Javascript
<script> // Javascript program to find lexicographically // smallest sequence with rotations. // Function to compare lexicographically // two sequence with different starting // indexes. It returns true if sequence // beginning with y is lexicographically // greater. function compareSeq(S,x,y,n) { for (let i = 0; i < n; i++) { if (S[x] < S[y]) return false; else if (S[x] > S[y]) return true; x = (x + 1) % n; y = (y + 1) % n; } return true; } // Function to find starting index // of lexicographically smallest sequence function smallestSequence(S,n) { let index = 0; for (let i = 1; i < n; i++) // if new sequence is smaller if (compareSeq(S, index, i, n)) // change index of current min index = i; return index; } // Function to print lexicographically // smallest sequence function printSmallestSequence(str,n) { let S = str.split(""); let starting_index = smallestSequence(S, n); for (let i = 0; i < n; i++) document.write(S[(starting_index + i) % n]); } // driver code let S = "DCACBCAA"; let n = 8; printSmallestSequence(S, n); // This code is contributed by avanitrachhadiya2155 </script> |
Output:
AADCACBC
Time Complexity : O(n^2)
Auxiliary Space : O(1)
Please refer complete article on Lexicographically smallest rotated sequence | Set 2 for more details!
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