Givet en viktningsskala och en rad olika positiva vikter där vi har ett oändligt utbud av varje vikt. Vår uppgift är att sätta vikter på vänster och höger skala en efter en på ett sådant sätt att kastruller flyttas till den sida där vikten läggs, dvs varje gång vågen flyttas till alternativa sidor.
- Vi får ytterligare ett heltals "steg" gånger som vi behöver för att utföra denna operation.
- En annan begränsning är att vi inte kan lägga samma vikt i följd, det vill säga om vikten w tas kan vi inte ta w igen i nästa steg medan vi lägger vikten på motsatt panna.
Exempel:
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.
Detta problem kan lösas genom att göra DFS bland skaltillstånd.
- Vi går mellan olika DFS-tillstånd för lösningen där varje DFS-tillstånd kommer att motsvara det faktiska skillnadsvärdet mellan vänster och höger panorering och aktuellt stegräkning.
- Istället för att lagra vikterna för båda kastrullerna lagrar vi bara skillnadsrestvärdet och varje gång valt viktvärde bör vara större än denna skillnad och bör inte vara lika med tidigare valt viktvärde.
- Om det är så kallar vi DFS-metoden rekursivt med nytt differensvärde och ett steg till.
Se koden nedan för bättre förståelse
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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