Auto comment: topic has been updated by pyetwi (previous revision, new revision, compare).

Problem link?

Here's an $$$O(n^22^n)$$$ solution. Try to build string b character-by-character. Let dp[mask][i] be the answer where you already took characters in mask from a, and i was the last character you took. Note you can find the prefix of b you already built by getting the number of set bits in mask. Now for every j s.t. the j'th bit of mask is off, try setting dp[mask][i] to dp[mask|(1<<j)][j] + cost[j] where $$$cost[j]$$$ is equal to $$$0$$$ if j = i+1 and $$$1$$$ otherwise. The answer is min(dp[(1<<n)-1][i]) for all $$$i \in 1...N $$$