בהינתן סולם ניפוח ומערך של משקלים חיוביים שונים שבהם יש לנו היצע אינסופי של כל משקל. המשימה שלנו היא לשים משקולות על מחבתות מאזניים שמאליות וימניות אחת אחת, באופן שהמחבתות יזוזו לצד שבו שמים משקל, כלומר בכל פעם שמבניות מאזניים נעות לצדדים חלופיים.
- ניתן לנו עוד 'צעדים' של מספר שלם שאנו צריכים כדי לבצע את הפעולה הזו.
- אילוץ נוסף הוא שאנחנו לא יכולים לשים את אותו משקל ברציפות, כלומר אם לוקחים את המשקל w אז בשלב הבא תוך כדי הנחת המשקל על המחבת הנגדית לא נוכל לקחת את w שוב.
דוגמאות:
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.
ניתן לפתור בעיה זו על ידי עשייה DFS בין מצבי קנה מידה.
- אנו עוברים בין מצבי DFS שונים עבור הפתרון שבו כל מצב DFS יתאים לערך ההפרש הממשי בין תנועות שמאל וימין וספירת הצעדים הנוכחית.
- במקום לאחסן משקלים של שתי המחבתות אנו פשוט מאחסנים את ערך שאריות ההפרש וכל פעם ערך המשקל הנבחר צריך להיות גדול מההפרש הזה ולא צריך להיות שווה לערך המשקל שנבחר קודם לכן.
- אם כן, אנו קוראים לשיטת DFS באופן רקורסיבי עם ערך הבדל חדש ועוד שלב אחד.
אנא עיין בקוד למטה להבנה טובה יותר
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
תְפוּקָה:
2 3 2 3 5 6 5 3 2 3
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