Creating Strings: Algorithm for Next Permutation

Example

abcde
abced
abdce
abdec
abecd
abedc    (Replace 'b' with 'c'.)
acbde    (Then sort all characters after 'c'.)
acbed
acdbe
acdeb
acebd
acedb    (Replace 'c' with 'd'.)
adbce    (Then sort all characters after 'd'.)
adbec
adcbe
adceb
adebc
adecb
aebcd
aebdc
aecbd
aecdb
aedbc
aedcb
bacde
baced
badce
badec
baecd
baedc
bcade
bcaed
bcdae
bcdea
bcead
bceda
bdace
bdaec
bdcae
bdcea
bdeac
bdeca
beacd
beadc
becad
becda
bedac
bedca
cabde
cabed
cadbe
cadeb
caebd
caedb
cbade
cbaed
cbdae
cbdea
cbead
cbeda
cdabe
cdaeb
cdbae
cdbea
cdeab
cdeba
ceabd
ceadb
cebad
cebda
cedab
cedba
dabce
dabec
dacbe
daceb
daebc
daecb
dbace
dbaec
dbcae
dbcea
dbeac
dbeca
dcabe
dcaeb
dcbae
dcbea
dceab
dceba
deabc
deacb
debac
debca
decab
decba
eabcd
eabdc
eacbd
eacdb
eadbc
eadcb
ebacd
ebadc
ebcad
ebcda
ebdac
ebdca
ecabd
ecadb
ecbad
ecbda
ecdab
ecdba
edabc
edacb
edbac
edbca
edcab
edcba

Algorithm

• A sequence that is already reverse sorted has no next permutation.
• Scan the sequence from right to left to find the first element that violates reverse sorting. Call it the bad element. Call other elements to its right as good elements. Call the cells they are in as bad and good places, respectively.
• Find the smallest good element larger than the bad element. Call it the replacement element.
• Replace the bad element with the replacement element by swapping them.
• Sort the elements in the good places.

Equivalent Algorithm

• Find the largest i such that s[i] < s[i + 1].
• If no such i, there is no next permutation.
• Find the largest j such that s[j] > s[i].
• Swap s[i] and s[j].
• Reverse the subsequence s[i + 1] to s[length - 1].