How to Fix Combinations Errors

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

Fix combinations errors when start index not passed causing duplicate combinations or wrong ordering.

Quick Fix

Wrong

def comb(n,k):
    res=[]
    def dfs(cur):
        if len(cur)==k: res.append(cur.copy()); return
        for i in range(1,n+1):  # Always starts from 1 -> duplicates and wrong order
            if i not in cur: dfs(cur+[i])
    dfs([])
    return res

No start index. Generates permutations of combinations. [1,2] and [2,1] both appear.

Right

def comb(n,k):
    res=[]
    def dfs(s,cur):
        if len(cur)==k: res.append(cur.copy()); return
        for i in range(s,n+1):
            cur.append(i); dfs(i+1,cur); cur.pop()
    dfs(1,[])
    return res

comb(4,2) -> [[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]]. O(C(n,k)*k).

Prevention

Pass start index to avoid repetitions. Only consider elements after current position.

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