ابحث عن جميع التوائم الثلاثة في مصفوفة مرتبة تشكل تقدمًا هندسيًا
بالنظر إلى مجموعة مرتبة من الأعداد الصحيحة الموجبة المميزة، قم بطباعة جميع التوائم الثلاثية التي تشكل تقدمًا هندسيًا بنسبة مشتركة متكاملة.
المتتابعة الهندسية عبارة عن سلسلة من الأرقام حيث يتم العثور على كل حد بعد الأول عن طريق ضرب الحد السابق برقم ثابت غير صفري يسمى النسبة المشتركة. على سبيل المثال، التسلسل 2 6 18 54... هو متوالية هندسية بنسبة مشتركة 3.
أمثلة:
Input: arr = [1 2 6 10 18 54] Output: 2 6 18 6 18 54 Input: arr = [2 8 10 15 16 30 32 64] Output: 2 8 32 8 16 32 16 32 64 Input: arr = [ 1 2 6 18 36 54] Output: 2 6 18 1 6 36 6 18 54
الفكرة هي البدء من العنصر الثاني وتثبيت كل عنصر كعنصر وسط والبحث عن العنصرين الآخرين في ثلاثية (واحد أصغر والآخر أكبر). لكي يكون العنصر arr[j] في منتصف التقدم الهندسي، يجب أن يكون هناك عنصران arr[i] وarr[k] بحيث -
arr[j] / arr[i] = r and arr[k] / arr[j] = r where r is an positive integer and 0 <= i < j and j < k <= n - 1
وفيما يلي تنفيذ الفكرة المذكورة أعلاه
C++ // C++ program to find if there exist three elements in // Geometric Progression or not #include using namespace std ; // The function prints three elements in GP if exists // Assumption: arr[0..n-1] is sorted. void findGeometricTriplets ( int arr [] int n ) { // One by fix every element as middle element for ( int j = 1 ; j < n - 1 ; j ++ ) { // Initialize i and k for the current j int i = j - 1 k = j + 1 ; // Find all i and k such that (i j k) // forms a triplet of GP while ( i >= 0 && k <= n - 1 ) { // if arr[j]/arr[i] = r and arr[k]/arr[j] = r // and r is an integer (i j k) forms Geometric // Progression while ( arr [ j ] % arr [ i ] == 0 && arr [ k ] % arr [ j ] == 0 && arr [ j ] / arr [ i ] == arr [ k ] / arr [ j ]) { // print the triplet cout < < arr [ i ] < < ' ' < < arr [ j ] < < ' ' < < arr [ k ] < < endl ; // Since the array is sorted and elements // are distinct. k ++ i -- ; } // if arr[j] is multiple of arr[i] and arr[k] is // multiple of arr[j] then arr[j] / arr[i] != // arr[k] / arr[j]. We compare their values to // move to next k or previous i. if ( arr [ j ] % arr [ i ] == 0 && arr [ k ] % arr [ j ] == 0 ) { if ( arr [ j ] / arr [ i ] < arr [ k ] / arr [ j ]) i -- ; else k ++ ; } // else if arr[j] is multiple of arr[i] then // try next k. Else try previous i. else if ( arr [ j ] % arr [ i ] == 0 ) k ++ ; else i -- ; } } } // Driver code int main () { // int arr[] = {1 2 6 10 18 54}; // int arr[] = {2 8 10 15 16 30 32 64}; // int arr[] = {1 2 6 18 36 54}; int arr [] = { 1 2 4 16 }; // int arr[] = {1 2 3 6 18 22}; int n = sizeof ( arr ) / sizeof ( arr [ 0 ]); findGeometricTriplets ( arr n ); return 0 ; }
Java // Java program to find if there exist three elements in // Geometric Progression or not import java.util.* ; class GFG { // The function prints three elements in GP if exists // Assumption: arr[0..n-1] is sorted. static void findGeometricTriplets ( int arr [] int n ) { // One by fix every element as middle element for ( int j = 1 ; j < n - 1 ; j ++ ) { // Initialize i and k for the current j int i = j - 1 k = j + 1 ; // Find all i and k such that (i j k) // forms a triplet of GP while ( i >= 0 && k <= n - 1 ) { // if arr[j]/arr[i] = r and arr[k]/arr[j] = r // and r is an integer (i j k) forms Geometric // Progression while ( i >= 0 && arr [ j ] % arr [ i ] == 0 && arr [ k ] % arr [ j ] == 0 && arr [ j ] / arr [ i ] == arr [ k ] / arr [ j ] ) { // print the triplet System . out . println ( arr [ i ] + ' ' + arr [ j ] + ' ' + arr [ k ] ); // Since the array is sorted and elements // are distinct. k ++ ; i -- ; } // if arr[j] is multiple of arr[i] and arr[k] is // multiple of arr[j] then arr[j] / arr[i] != // arr[k] / arr[j]. We compare their values to // move to next k or previous i. if ( i >= 0 && arr [ j ] % arr [ i ] == 0 && arr [ k ] % arr [ j ] == 0 ) { if ( i >= 0 && arr [ j ] / arr [ i ] < arr [ k ] / arr [ j ] ) i -- ; else k ++ ; } // else if arr[j] is multiple of arr[i] then // try next k. Else try previous i. else if ( i >= 0 && arr [ j ] % arr [ i ] == 0 ) k ++ ; else i -- ; } } } // Driver code public static void main ( String [] args ) { // int arr[] = {1 2 6 10 18 54}; // int arr[] = {2 8 10 15 16 30 32 64}; // int arr[] = {1 2 6 18 36 54}; int arr [] = { 1 2 4 16 }; // int arr[] = {1 2 3 6 18 22}; int n = arr . length ; findGeometricTriplets ( arr n ); } } // This code is contributed by Rajput-Ji
Python 3 # Python 3 program to find if # there exist three elements in # Geometric Progression or not # The function prints three elements # in GP if exists. # Assumption: arr[0..n-1] is sorted. def findGeometricTriplets ( arr n ): # One by fix every element # as middle element for j in range ( 1 n - 1 ): # Initialize i and k for # the current j i = j - 1 k = j + 1 # Find all i and k such that # (i j k) forms a triplet of GP while ( i >= 0 and k <= n - 1 ): # if arr[j]/arr[i] = r and # arr[k]/arr[j] = r and r # is an integer (i j k) forms # Geometric Progression while ( arr [ j ] % arr [ i ] == 0 and arr [ k ] % arr [ j ] == 0 and arr [ j ] // arr [ i ] == arr [ k ] // arr [ j ]): # print the triplet print ( arr [ i ] ' ' arr [ j ] ' ' arr [ k ]) # Since the array is sorted and # elements are distinct. k += 1 i -= 1 # if arr[j] is multiple of arr[i] # and arr[k] is multiple of arr[j] # then arr[j] / arr[i] != arr[k] / arr[j]. # We compare their values to # move to next k or previous i. if ( arr [ j ] % arr [ i ] == 0 and arr [ k ] % arr [ j ] == 0 ): if ( arr [ j ] // arr [ i ] < arr [ k ] // arr [ j ]): i -= 1 else : k += 1 # else if arr[j] is multiple of # arr[i] then try next k. Else # try previous i. elif ( arr [ j ] % arr [ i ] == 0 ): k += 1 else : i -= 1 # Driver code if __name__ == '__main__' : arr = [ 1 2 4 16 ] n = len ( arr ) findGeometricTriplets ( arr n ) # This code is contributed # by ChitraNayal
C# // C# program to find if there exist three elements // in Geometric Progression or not using System ; class GFG { // The function prints three elements in GP if exists // Assumption: arr[0..n-1] is sorted. static void findGeometricTriplets ( int [] arr int n ) { // One by fix every element as middle element for ( int j = 1 ; j < n - 1 ; j ++ ) { // Initialize i and k for the current j int i = j - 1 k = j + 1 ; // Find all i and k such that (i j k) // forms a triplet of GP while ( i >= 0 && k <= n - 1 ) { // if arr[j]/arr[i] = r and arr[k]/arr[j] = r // and r is an integer (i j k) forms Geometric // Progression while ( i >= 0 && arr [ j ] % arr [ i ] == 0 && arr [ k ] % arr [ j ] == 0 && arr [ j ] / arr [ i ] == arr [ k ] / arr [ j ]) { // print the triplet Console . WriteLine ( arr [ i ] + ' ' + arr [ j ] + ' ' + arr [ k ]); // Since the array is sorted and elements // are distinct. k ++ ; i -- ; } // if arr[j] is multiple of arr[i] and arr[k] is // multiple of arr[j] then arr[j] / arr[i] != // arr[k] / arr[j]. We compare their values to // move to next k or previous i. if ( i >= 0 && arr [ j ] % arr [ i ] == 0 && arr [ k ] % arr [ j ] == 0 ) { if ( i >= 0 && arr [ j ] / arr [ i ] < arr [ k ] / arr [ j ]) i -- ; else k ++ ; } // else if arr[j] is multiple of arr[i] then // try next k. Else try previous i. else if ( i >= 0 && arr [ j ] % arr [ i ] == 0 ) k ++ ; else i -- ; } } } // Driver code static public void Main () { // int arr[] = {1 2 6 10 18 54}; // int arr[] = {2 8 10 15 16 30 32 64}; // int arr[] = {1 2 6 18 36 54}; int [] arr = { 1 2 4 16 }; // int arr[] = {1 2 3 6 18 22}; int n = arr . Length ; findGeometricTriplets ( arr n ); } } // This code is contributed by ajit.
JavaScript < script > // Javascript program to find if there exist three elements in // Geometric Progression or not // The function prints three elements in GP if exists // Assumption: arr[0..n-1] is sorted. function findGeometricTriplets ( arr n ) { // One by fix every element as middle element for ( let j = 1 ; j < n - 1 ; j ++ ) { // Initialize i and k for the current j let i = j - 1 k = j + 1 ; // Find all i and k such that (i j k) // forms a triplet of GP while ( i >= 0 && k <= n - 1 ) { // if arr[j]/arr[i] = r and arr[k]/arr[j] = r // and r is an integer (i j k) forms Geometric // Progression while ( i >= 0 && arr [ j ] % arr [ i ] == 0 && arr [ k ] % arr [ j ] == 0 && arr [ j ] / arr [ i ] == arr [ k ] / arr [ j ]) { // print the triplet document . write ( arr [ i ] + ' ' + arr [ j ] + ' ' + arr [ k ] + '
' ); // Since the array is sorted and elements // are distinct. k ++ ; i -- ; } // if arr[j] is multiple of arr[i] and arr[k] is // multiple of arr[j] then arr[j] / arr[i] != // arr[k] / arr[j]. We compare their values to // move to next k or previous i. if ( i >= 0 && arr [ j ] % arr [ i ] == 0 && arr [ k ] % arr [ j ] == 0 ) { if ( i >= 0 && arr [ j ] / arr [ i ] < arr [ k ] / arr [ j ]) i -- ; else k ++ ; } // else if arr[j] is multiple of arr[i] then // try next k. Else try previous i. else if ( i >= 0 && arr [ j ] % arr [ i ] == 0 ) k ++ ; else i -- ; } } } // Driver code // int arr[] = {1 2 6 10 18 54}; // int arr[] = {2 8 10 15 16 30 32 64}; // int arr[] = {1 2 6 18 36 54}; let arr = [ 1 2 4 16 ]; // int arr[] = {1 2 3 6 18 22}; let n = arr . length ; findGeometricTriplets ( arr n ); // This code is contributed by avanitrachhadiya2155 < /script>
الإخراج
1 2 4 1 4 16
تعقيد الوقت الحل أعلاه هو O(n 2 ) أما بالنسبة لكل j نجد i و k في الزمن الخطي.
المساحة المساعدة: O(1) لأننا لم نستخدم أي مساحة إضافية.
