<prompt> Ha u fuoa sehlopha sa linomoro, fumana sehlopha se senyenyane se seholo ka ho fetisisa seo kakaretso ea sona e leng ka tlaase ho kapa ho lekana le kakaretso e fanoeng.Beha: 3,12,2,7,8,4 Chelete e reriloeng: 15  <response>: Instruction in English: Given a set of numbers, find the largest subset whose sum is less than or equal to a given sum. . Response in English: To find the largest subset whose sum is less than or equal to the target sum, we can use a dynamic programming approach. First, we sort the set in ascending order, and then we create an n m matrix dp, where n is the size of the set, and m is the target sum 1. The values in the matrix represent whether a subset with a given sum exists or not. After that, we fill this matrix using the following rules:1. Fill the first column with True, as a subset with sum 0 is always possible.2. Fill the first row with True if the first element in the set is equal to the column index, and False otherwise.3. For all other cells, if the element in the set is less than or equal to the column index, i.e., if the element can be a part of the sum represented by the column, we check if the sum can be obtained by including the element or excluding the element. If either of the cases is True, we fill the cell with True; else, we fill it with False.After filling the matrix, we traverse the last row in reverse and look for the first True cell. This cell represents the largest subset sum that is less than or equal to the target sum. Finally, we traverse the dp matrix and follow the steps below to find the elements that make up the subset:1. Initialize the current element as the last element in the set, and the current sum as the largest subset sum we found.2. If the cell just above the current cell is True, the current element is not a part of the subset; hence, we move one row up.3. If the cell just above the current cell is False, the current element is part of the subset, and we subtract the current elements value from the current sum, and move one row up.4. We repeat the above steps until we reach the first row.In your case, the sorted set is 2, 3, 4, 7, 8,12. The dp matrix looks like below: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 --- --- --- --- --- --- --- --- --- --- . Response in Sesotho: Ho fumana subset e kholo ka ho fetisisa eo kakaretso ea eona e leng ka tlase ho kapa e lekanang le palo e reriloeng, re ka sebelisa mokhoa o matla oa ho etsa mananeo. Ntlha ea pele, re hlophisa sete ka tatellano e nyolohang, ebe re theha n m matrix dp, moo n e leng boholo ba sete, me m ke palo e lekanyelitsoeng 1. Litekanyetso tsa matrix li emela hore na subset e nang le chelete e fanoeng e teng kapa che. Ka mora moo, re tlatsa matrix ena ka ho sebelisa melao e latelang: 1. Tlatsa kholomo ea pele ka Nete, kaha karoloana e nang le kakaretso ea 0 e khoneha kamehla. 2. Tlatsa mola oa pele ka Nete haeba karolo ea pele sete e lekana le index ea kholomo, me Flse ho seng joalo. 3. Bakeng sa lisele tse ling kaofela, haeba element ka sete e ka tlaase ho kapa e lekana le index ea kholomo, ke hore, haeba element e ka ba karolo ea kakaretso e emeloang ke kholomo, re hlahloba hore na kakaretso e ka fumanoa ka ho kenyelletsa elemente kapa ho sa akarelletse elemente. Haeba e ngoe ea linyeoe e le Nete, re tlatsa sele ka Nete; ho seng joalo, re e tlatsa ka Bohata. Ka mora ho tlatsa matrix, re tšela mola oa ho qetela ka morao ebe re batla sele ea Nete ea pele. Sele ena e emela chelete e kholo ka ho fetisisa e ka tlase ho kapa e lekanang le palo e lebeletsoeng. Qetellong, re tšela dp matrix me re latela mehato e ka tlase ho fumana likarolo tse etsang karolo e nyenyane: 1. Qala karolo ea hona joale e le karolo ea ho qetela ka sete, le kakaretso ea hona joale e le kakaretso e kholo ka ho fetisisa eo re e fumaneng. 2. Haeba sele e ka hodimo ho sele ya jwale e le Nnete, elemente ya hajwale ha se karolo ya subset; ka hona, re isa mola o le mong holimo. 3. Haeba sele e kaholimo ho sele ea hajoale e le Bohata, karolo ea hajoale ke karolo ea karoloana, me re tlosa boleng ba elemente ea hajoale ho kakaretso ea hajoale, ebe re isa mola o le mong holimo. 4. Re pheta mehato e ka holimo ho fihlela re fihla mola oa pele. Tabeng ea hau, sete e hlophisitsoeng ke 2, 3, 4, 7, 8,12. dp matrix e shebahala tjena: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 --- --- --- --- --- --- --- --- --- --- 