Givet en vægtningsskala og en række forskellige positive vægte, hvor vi har et uendeligt udbud af hver vægt. Vores opgave er at lægge vægte på venstre og højre skalaer én efter én på en sådan måde, at pander flytter til den side, hvor vægten lægges, dvs. hver gang vægten flytter sig til alternative sider.
- Vi får endnu et heltals 'trin' gange, som vi skal bruge for at udføre denne operation.
- En anden begrænsning er, at vi ikke kan lægge samme vægt fortløbende, dvs. hvis vægten tages, kan vi i næste trin ikke tage w igen, mens vi lægger vægten på den modsatte plade.
Eksempler:
Let weight array is [7 11] and steps = 3 then 7 11 7 is the sequence in which weights should be kept in order to move scale alternatively. Let another weight array is [2 3 5 6] and steps = 10 then 3 2 3 5 6 5 3 2 3 is the sequence in which weights should be kept in order to move scale alternatively.
Dette problem kan løses ved at gøre DFS blandt skalatilstande.
- Vi krydser mellem forskellige DFS-tilstande for løsningen, hvor hver DFS-tilstand svarer til den faktiske forskelsværdi mellem venstre og højre panorering og det aktuelle trinantal.
- I stedet for at gemme vægten af begge pander gemmer vi blot forskellens restværdi, og hver gang den valgte vægtværdi skal være større end denne forskel og bør ikke være lig med den tidligere valgte vægtværdi.
- Hvis det er det, så kalder vi DFS-metoden rekursivt med ny differensværdi og et trin mere.
Se venligst nedenstående kode for bedre forståelse
C++// C++ program to print weights for alternating // the weighting scale #include
// Java program to print weights for alternating // the weighting scale class GFG { // DFS method to traverse among // states of weighting scales static boolean dfs(int residue int curStep int[] wt int[] arr int N int steps) { // If we reach to more than required steps // return true if (curStep >= steps) return true; // Try all possible weights and // choose one which returns 1 afterwards for (int i = 0; i < N; i++) { /* * Try this weight only if it is * greater than current residue * and not same as previous chosen weight */ if (curStep - 1 < 0 || (arr[i] > residue && arr[i] != wt[curStep - 1])) { // assign this weight to array and // recur for next state wt[curStep] = arr[i]; if (dfs(arr[i] - residue curStep + 1 wt arr N steps)) return true; } } // if any weight is not possible // return false return false; } // method prints weights for alternating scale // and if not possible prints 'not possible' static void printWeightOnScale(int[] arr int N int steps) { int[] wt = new int[steps]; // call dfs with current residue as 0 // and current steps as 0 if (dfs(0 0 wt arr N steps)) { for (int i = 0; i < steps; i++) System.out.print(wt[i] + ' '); System.out.println(); } else System.out.println('Not Possible'); } // Driver Code public static void main(String[] args) { int[] arr = { 2 3 5 6 }; int N = arr.length; int steps = 10; printWeightOnScale(arr N steps); } } // This code is contributed by // sanjeev2552
# Python3 program to print weights for # alternating the weighting scale # DFS method to traverse among states # of weighting scales def dfs(residue curStep wt arr N steps): # If we reach to more than required # steps return true if (curStep >= steps): return True # Try all possible weights and choose # one which returns 1 afterwards for i in range(N): # Try this weight only if it is greater # than current residueand not same as # previous chosen weight if (arr[i] > residue and arr[i] != wt[curStep - 1]): # assign this weight to array and # recur for next state wt[curStep] = arr[i] if (dfs(arr[i] - residue curStep + 1 wt arr N steps)): return True # if any weight is not possible # return false return False # method prints weights for alternating scale # and if not possible prints 'not possible' def printWeightsOnScale(arr N steps): wt = [0] * (steps) # call dfs with current residue as 0 # and current steps as 0 if (dfs(0 0 wt arr N steps)): for i in range(steps): print(wt[i] end = ' ') else: print('Not possible') # Driver Code if __name__ == '__main__': arr = [2 3 5 6] N = len(arr) steps = 10 printWeightsOnScale(arr N steps) # This code is contributed by PranchalK
// C# program to print weights for alternating // the weighting scale using System; namespace GFG { class Program { // DFS method to traverse among states of weighting scales static bool dfs(int residue int curStep int[] wt int[] arr int N int steps) { // If we reach to more than required steps return true if (curStep >= steps) return true; // Try all possible weights and choose one which returns 1 afterwards for (int i = 0; i < N; i++) { /* * Try this weight only if it is greater than current residue * and not same as previous chosen weight */ if (curStep - 1 < 0 || (arr[i] > residue && arr[i] != wt[curStep - 1])) { // assign this weight to array and recur for next state wt[curStep] = arr[i]; if (dfs(arr[i] - residue curStep + 1 wt arr N steps)) return true; } } // if any weight is not possible return false return false; } // method prints weights for alternating scale and // if not possible prints 'not possible' static void printWeightOnScale(int[] arr int N int steps) { int[] wt = new int[steps]; // call dfs with current residue as 0 and current steps as 0 if (dfs(0 0 wt arr N steps)) { for (int i = 0; i < steps; i++) Console.Write(wt[i] + ' '); Console.WriteLine(); } else Console.WriteLine('Not Possible'); } static void Main(string[] args) { int[] arr = { 2 3 5 6 }; int N = arr.Length; int steps = 10; printWeightOnScale(arr N steps); } } }
function dfs(residue curStep wt arr N steps) { // If we reach to more than required steps // return true if (curStep > steps) { return true; } // Try all possible weights and choose one which // returns 1 afterwards for (let i = 0; i < N; i++) { /* Try this weight only if it is greater than current residue and not same as previous chosen weight */ if (arr[i] > residue && arr[i] !== wt[curStep - 1]) { // assign this weight to array and recur for // next state wt[curStep] = arr[i]; if (dfs(arr[i] - residue curStep + 1 wt arr N steps)) { return true; } } } // if any weight is not possible return false return false; } function printWeightsOnScale(arr N steps) { const wt = new Array(steps); // call dfs with current residue as 0 and current // steps as 0 if (dfs(0 1 wt arr N steps)) { for (let i = 1; i <= steps; i++) { process.stdout.write(`${wt[i]} `); } console.log(); } else { console.log('Not possible'); } } const arr = [2 3 5 6]; const N = arr.length; const steps = 10; printWeightsOnScale(arr N steps); // This code is contributed by divyansh2212
Produktion:
2 3 2 3 5 6 5 3 2 3
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