lis

I have the following algorithm which works well I tried explaining it here for myself http://nemo.la/?p=943 and it is explained here http://www.geeksforgeeks.org/longest-monotonically-increasing-subsequence-size-n-log-n/ as well and on stackoverflow as well I want to modify it to produce the longest non-monotonically increasing subsequence for the sequence 30 20 20 10 10 10 10 the answer should be 4: "10 10 10 10" But the with nlgn version of the algorithm it isn't working. Initializing s to contain the first element "30" and starting at the second element = 20. This is what happens: The first

LIS:wikipedia There is one thing that I can't understand: why is X[M[i]] a non-decreasing sequence? hiddenboy Let's first look at the n^2 algorithm: dp[0] = 1; for( int i = 1; i < len; i++ ) { dp[i] = 1; for( int j = 0; j < i; j++ ) { if( array[i] > array[j] ) { if( dp[i] < dp[j]+1 ) { dp[i] = dp[j]+1; } } } } Now the improvement happens at the second loop, basically, you can improve the speed by using binary search. Besides the array dp[], let's have another array c[], c is pretty special, c[i] means: the minimum value of the last element of the longest increasing sequence whose length is i.

I'm practicing algorithms and one of my tasks is to count the number of all longest increasing sub-sequences for given 0 < n <= 10^6 numbers. Solution O(n^2) is not an option. I have already implemented finding a LIS and its length ( LIS Algorithm ), but this algorithm switches numbers to the lowest possible. Therefore, it's impossible to determine if sub-sequences with a previous number (the bigger one) would be able to achieve the longest length, otherwise I could just count those switches, I guess. Any ideas how to get this in about O(nlogn) ? I know that it should be solved using dynamic