3ms C++ bit manipulation solution beat 100%

  • 3

    Inspired by @topcoder007 and @StefanPochmann

    Please refer @topcoder007's post about the basic idea of bit manipulation.

    The idea is to find all valid masks with minimum bits set first, and then find the minimum abbreviation recursively.
    For each bit in a key built from diff of target and word, there could be below cases:

    • If a bit is 0, which means the char in word is same as the corresponding char in target, the bit has no effect to the final result on this word
    • If a bit is 1 and it is the only bit set, i.e. the only difference from target, then that char is required, i.e. the bit must be set in final result
    • If there are 2 or more bits set, all the bits are optional, i.e. as long as one of them is set in final result, it will make the abbreviation distinct between target and this word.
    • If a bit is optional for word1 but required for word2, we can ignore word1 because it is already covered by word2. For example "apple" ["xpple", "xpplx"] => [10000, 10001] => [10000] => "a4
    • if a bit is optional for both word1 and word2, we can take that bit to cover both words and at same time, minimize the number of set bits. For example "apple" ["xppze", "xpplx"] => [10010, 10001] => [10000] => "a4

    Therefore, a valid abbreviation key will be [required bits] | [ a mask with minimum number of '1' which ensure at least one optional bit set for each word], steps as below:

    1. Generate keys for each word dictionary, if required (only 1 bit set), put it to required mask. If optional, put to the distinct list.
    2. Check all keys in distinct list, if covered by required , remove from the list
    3. Make all keys distinct, i.e. distinct[i] & distinct[j] == 0 if i != j
    4. For remaining keys in distinct, take required as base mask and then pick up 1 optional bit from each key recursively, and check the length of the abbreviation.

    Refer inline comments for more details. Please correct me if I am wrong. Thanks

    class Solution {
        string minAbbreviation(string target, vector<string>& dictionary) {
            int n = target.size();
            vector<int> distinct;
            int required = 0;
            for (auto word : dictionary) {
                if (word.size() != n) continue;
                int key = getKey(target, word);
                if ((key & (key-1)) == 0) required |= key; // only 1 distinct char, so it is requried
                else distinct.push_back(key);
            // check if the required bits can cover any keys
            if (required) { 
                vector<int> tmp;
                for (auto x : distinct) {
                    // if no overlapped bits, it is not covered
                    // need to handle them later
                    if ((x & required) == 0) tmp.push_back(x);
            // make all remaining keys distinct each other
            vector<int> tmp;
            for (auto x : distinct) {
                bool merged = false;
                for (int i = 0; i < tmp.size(); i++) {
                    if (tmp[i] & x) {
                        tmp[i] &= x;
                        merged = true;
                if (!merged) tmp.push_back(x);
            // now only distinct keys left, recursively check the length of each valid key 
            int res = pow(2, n) - 1;
            solve(distinct, 0, required, n, res);
            return getAbbre(target, res);
        void solve(vector<int>& v, int idx, int key, int len, int& out) {
            // all keys combined, check length
            if (idx == v.size()) {
                if (getLen(key, len) < getLen(out, len)) {
                    out = key;
            else { // append remaining keys
                int cand = v[idx];
                while(cand) {
                    int mask = cand;
                    cand &= cand-1;
                    mask ^= cand;
                    solve(v, idx+1, key | mask, len, out);
        string getAbbre(string& target, int key) {
            int n = target.size();
            string res;
            int count = 0;
            for (int i = 0; i < n; i++) {
                if ((key & (1 << (n-1-i)))) {
                    if (count) res += to_string(count);
                    count = 0;
                else count++;
            if (count) res += to_string(count);
            return res;
        int getLen(int key, int len) {
            int count = len;
            int n = 1 << len;
            for (int i = 3; i < n; i <<= 1) {
                if ((key & i) == 0) count--;
            return count;
        int getKey(string& s1, string& s2) {
            int key = 0;
            for (int i = 0; i < s1.size(); i++) {
                key <<= 1;
                key += s1[i] == s2[i] ? 0 : 1;
            return key;

  • 0

    very concise and clear explanation. Thank you !

  • 0

    I'm afraid this greedy approximation method is not correct, despite efficient (see set cover problem and it's similarity to this problem. Try this test case:


    correct answer should be 3DE.

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