بالنظر إلى مقياس الترجيح ومجموعة من الأوزان الموجبة المختلفة حيث لدينا كمية لا حصر لها من كل وزن. مهمتنا هي وضع الأوزان على كفتي الميزان اليسرى واليمنى واحدة تلو الأخرى بطريقة تتحرك الكفات إلى الجانب الذي يتم وضع الوزن فيه، أي في كل مرة تتحرك كفات الميزان إلى جوانب بديلة.
- لقد حصلنا على عدد صحيح آخر من "الخطوات" التي نحتاجها لتنفيذ هذه العملية.
- هناك قيد آخر وهو أننا لا نستطيع وضع نفس الوزن على التوالي، أي إذا تم أخذ الوزن w ثم في الخطوة التالية أثناء وضع الوزن على المقلاة المقابلة فلا يمكننا أخذ w مرة أخرى.
أمثلة:
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.
يمكن حل هذه المشكلة عن طريق العمل DFS بين حالات الحجم.
- نحن نتنقل بين حالات DFS المختلفة للحل حيث تتوافق كل حالة DFS مع قيمة الفرق الفعلية بين المقالي اليسرى واليمنى وعدد الخطوات الحالية.
- بدلاً من تخزين أوزان كلا المقاليين، نقوم فقط بتخزين قيمة بقايا الفرق وفي كل مرة يجب أن تكون قيمة الوزن المختارة أكبر من هذا الفرق ولا يجب أن تكون مساوية لقيمة الوزن المختارة مسبقًا.
- إذا كان الأمر كذلك، فإننا نسمي طريقة DFS بشكل متكرر بقيمة فرق جديدة وخطوة أخرى.
يرجى الاطلاع على الكود أدناه لفهم أفضل
C++// C++ program to print weights for alternating // the weighting scale #include using namespace std; // DFS method to traverse among states of weighting scales 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 residueand 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; } // method prints weights for alternating scale and if // not possible prints 'not possible' void printWeightsOnScale(int arr[] int N int steps) { int wt[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++) cout << wt[i] << ' '; cout << endl; } else cout << 'Not possiblen'; } // Driver code to test above methods int main() { int arr[] = {2 3 5 6}; int N = sizeof(arr) / sizeof(int); int steps = 10; printWeightsOnScale(arr N steps); return 0; }
Java // 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 # 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# // 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); } } }
JavaScript 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
الإخراج:
2 3 2 3 5 6 5 3 2 3
إنشاء اختبار