Generate All Partitions of a List
The new functions FoldPair and FoldPairList allow mapping simultaneously an output function and a state-update function.
Take a length-5 list to be partitioned.
In[1]:=
![Click for copyable input](assets.en/generate-all-partitions-of-a-list/In_59.png)
list = {a, b, c, d, e};
Use FoldPairList together with TakeDrop to generate a partition of the following lengths.
In[2]:=
![Click for copyable input](assets.en/generate-all-partitions-of-a-list/In_60.png)
lengths = {2, 2, 1};
FoldPairList[TakeDrop, list, lengths]
Out[2]=
![](assets.en/generate-all-partitions-of-a-list/O_63.png)
To construct all partitions, find all possible decompositions of the number 5.
In[3]:=
![Click for copyable input](assets.en/generate-all-partitions-of-a-list/In_61.png)
lengthsAll = Flatten[Permutations /@ IntegerPartitions[5], 1]
Out[3]=
![](assets.en/generate-all-partitions-of-a-list/O_64.png)
In[4]:=
![Click for copyable input](assets.en/generate-all-partitions-of-a-list/In_62.png)
FoldPairList[TakeDrop, list, #] & /@ lengthsAll // Column
Out[4]=
![](assets.en/generate-all-partitions-of-a-list/O_65.png)