How to Fix Longest Increasing Subsequence Errors

In this tutorial, you'll learn about How to Fix Longest Increasing Subsequence Errors. We cover key concepts, practical examples, and best practices.

Fix longest increasing subsequence errors when patience sorting confusion or DP O(n^2) when O(n log n) needed.

Quick Fix

Wrong

def lis(a):
    n=len(a); dp=[1]*n
    for i in range(n):
        for j in range(i):
            if a[i]>a[j]: dp[i]=max(dp[i],dp[j]+1)
    return max(dp)

O(n^2) DP works but O(n log n) patience sorting is more efficient.

Right

def lis(a):
    import bisect
    tails=[]
    for x in a:
        i=bisect.bisect_left(tails,x)
        if i==len(tails): tails.append(x)
        else: tails[i]=x
    return len(tails)

[10,9,2,5,3,7,101,18] -> 4 (LIS [2,3,7,101] or [2,5,7,101]). O(n log n).

Prevention

Patience sorting: maintain tails array of smallest possible tail for each length. Binary search.

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