Write a C function to return minimum and maximum in an array. Your program should make the minimum number of comparisons.
First of all, how do we return multiple values from a C function? We can do it either using structures or pointers.
We have created a structure named pair (which contains min and max) to return multiple values.
c
struct pair { int min; int max; }; |
And the function declaration becomes: struct pair getMinMax(int arr[], int n) where arr[] is the array of size n whose minimum and maximum are needed.
METHOD 1 (Simple Linear Search)
Initialize values of min and max as minimum and maximum of the first two elements respectively. Starting from 3rd, compare each element with max and min, and change max and min accordingly (i.e., if the element is smaller than min then change min, else if the element is greater than max then change max, else ignore the element)
C++
// C++ program of above implementation #include<iostream> using namespace std; // Pair struct is used to return // two values from getMinMax() struct Pair { int min; int max; }; struct Pair getMinMax( int arr[], int n) { struct Pair minmax; int i; // If there is only one element // then return it as min and max both if (n == 1) { minmax.max = arr[0]; minmax.min = arr[0]; return minmax; } // If there are more than one elements, // then initialize min and max if (arr[0] > arr[1]) { minmax.max = arr[0]; minmax.min = arr[1]; } else { minmax.max = arr[1]; minmax.min = arr[0]; } for (i = 2; i < n; i++) { if (arr[i] > minmax.max) minmax.max = arr[i]; else if (arr[i] < minmax.min) minmax.min = arr[i]; } return minmax; } // Driver code int main() { int arr[] = { 1000, 11, 445, 1, 330, 3000 }; int arr_size = 6; struct Pair minmax = getMinMax(arr, arr_size); cout << "Minimum element is " << minmax.min << endl; cout << "Maximum element is " << minmax.max; return 0; } // This code is contributed by nik_3112 |
C
/* structure is used to return two values from minMax() */ #include<stdio.h> struct pair { int min; int max; }; struct pair getMinMax( int arr[], int n) { struct pair minmax; int i; /*If there is only one element then return it as min and max both*/ if (n == 1) { minmax.max = arr[0]; minmax.min = arr[0]; return minmax; } /* If there are more than one elements, then initialize min and max*/ if (arr[0] > arr[1]) { minmax.max = arr[0]; minmax.min = arr[1]; } else { minmax.max = arr[1]; minmax.min = arr[0]; } for (i = 2; i<n; i++) { if (arr[i] > minmax.max) minmax.max = arr[i]; else if (arr[i] < minmax.min) minmax.min = arr[i]; } return minmax; } /* Driver program to test above function */ int main() { int arr[] = {1000, 11, 445, 1, 330, 3000}; int arr_size = 6; struct pair minmax = getMinMax (arr, arr_size); printf ( "nMinimum element is %d" , minmax.min); printf ( "nMaximum element is %d" , minmax.max); getchar (); } |
Java
// Java program of above implementation public class GFG { /* Class Pair is used to return two values from getMinMax() */ static class Pair { int min; int max; } static Pair getMinMax( int arr[], int n) { Pair minmax = new Pair(); int i; /*If there is only one element then return it as min and max both*/ if (n == 1 ) { minmax.max = arr[ 0 ]; minmax.min = arr[ 0 ]; return minmax; } /* If there are more than one elements, then initialize min and max*/ if (arr[ 0 ] > arr[ 1 ]) { minmax.max = arr[ 0 ]; minmax.min = arr[ 1 ]; } else { minmax.max = arr[ 1 ]; minmax.min = arr[ 0 ]; } for (i = 2 ; i < n; i++) { if (arr[i] > minmax.max) { minmax.max = arr[i]; } else if (arr[i] < minmax.min) { minmax.min = arr[i]; } } return minmax; } /* Driver program to test above function */ public static void main(String args[]) { int arr[] = { 1000 , 11 , 445 , 1 , 330 , 3000 }; int arr_size = 6 ; Pair minmax = getMinMax(arr, arr_size); System.out.printf( "\nMinimum element is %d" , minmax.min); System.out.printf( "\nMaximum element is %d" , minmax.max); } } |
Python3
# Python program of above implementation # structure is used to return two values from minMax() class pair: def __init__( self ): self . min = 0 self . max = 0 def getMinMax(arr: list , n: int ) - > pair: minmax = pair() # If there is only one element then return it as min and max both if n = = 1 : minmax. max = arr[ 0 ] minmax. min = arr[ 0 ] return minmax # If there are more than one elements, then initialize min # and max if arr[ 0 ] > arr[ 1 ]: minmax. max = arr[ 0 ] minmax. min = arr[ 1 ] else : minmax. max = arr[ 1 ] minmax. min = arr[ 0 ] for i in range ( 2 , n): if arr[i] > minmax. max : minmax. max = arr[i] elif arr[i] < minmax. min : minmax. min = arr[i] return minmax # Driver Code if __name__ = = "__main__" : arr = [ 1000 , 11 , 445 , 1 , 330 , 3000 ] arr_size = 6 minmax = getMinMax(arr, arr_size) print ( "Minimum element is" , minmax. min ) print ( "Maximum element is" , minmax. max ) # This code is contributed by # sanjeev2552 |
C#
// C# program of above implementation using System; class GFG { /* Class Pair is used to return two values from getMinMax() */ class Pair { public int min; public int max; } static Pair getMinMax( int []arr, int n) { Pair minmax = new Pair(); int i; /* If there is only one element then return it as min and max both*/ if (n == 1) { minmax.max = arr[0]; minmax.min = arr[0]; return minmax; } /* If there are more than one elements, then initialize min and max*/ if (arr[0] > arr[1]) { minmax.max = arr[0]; minmax.min = arr[1]; } else { minmax.max = arr[1]; minmax.min = arr[0]; } for (i = 2; i < n; i++) { if (arr[i] > minmax.max) { minmax.max = arr[i]; } else if (arr[i] < minmax.min) { minmax.min = arr[i]; } } return minmax; } // Driver Code public static void Main(String []args) { int []arr = {1000, 11, 445, 1, 330, 3000}; int arr_size = 6; Pair minmax = getMinMax(arr, arr_size); Console.Write( "Minimum element is {0}" , minmax.min); Console.Write( "\nMaximum element is {0}" , minmax.max); } } // This code is contributed by PrinciRaj1992 |
Output:
Minimum element is 1 Maximum element is 3000
Time Complexity: O(n)
In this method, the total number of comparisons is 1 + 2(n-2) in the worst case and 1 + n – 2 in the best case.
In the above implementation, the worst case occurs when elements are sorted in descending order and the best case occurs when elements are sorted in ascending order.
METHOD 2 (Tournament Method)
Divide the array into two parts and compare the maximums and minimums of the two parts to get the maximum and the minimum of the whole array.
Pair MaxMin(array, array_size) if array_size = 1 return element as both max and min else if arry_size = 2 one comparison to determine max and min return that pair else /* array_size > 2 */ recur for max and min of left half recur for max and min of right half one comparison determines true max of the two candidates one comparison determines true min of the two candidates return the pair of max and min
Implementation
C++
// C++ program of above implementation #include<iostream> using namespace std; // structure is used to return // two values from minMax() struct Pair { int min; int max; }; struct Pair getMinMax( int arr[], int low, int high) { struct Pair minmax, mml, mmr; int mid; // If there is only one element if (low == high) { minmax.max = arr[low]; minmax.min = arr[low]; return minmax; } // If there are two elements if (high == low + 1) { if (arr[low] > arr[high]) { minmax.max = arr[low]; minmax.min = arr[high]; } else { minmax.max = arr[high]; minmax.min = arr[low]; } return minmax; } // If there are more than 2 elements mid = (low + high) / 2; mml = getMinMax(arr, low, mid); mmr = getMinMax(arr, mid + 1, high); // Compare minimums of two parts if (mml.min < mmr.min) minmax.min = mml.min; else minmax.min = mmr.min; // Compare maximums of two parts if (mml.max > mmr.max) minmax.max = mml.max; else minmax.max = mmr.max; return minmax; } // Driver code int main() { int arr[] = { 1000, 11, 445, 1, 330, 3000 }; int arr_size = 6; struct Pair minmax = getMinMax(arr, 0, arr_size - 1); cout << "Minimum element is " << minmax.min << endl; cout << "Maximum element is " << minmax.max; return 0; } // This code is contributed by nik_3112 |
C
/* structure is used to return two values from minMax() */ #include<stdio.h> struct pair { int min; int max; }; struct pair getMinMax( int arr[], int low, int high) { struct pair minmax, mml, mmr; int mid; // If there is only one element if (low == high) { minmax.max = arr[low]; minmax.min = arr[low]; return minmax; } /* If there are two elements */ if (high == low + 1) { if (arr[low] > arr[high]) { minmax.max = arr[low]; minmax.min = arr[high]; } else { minmax.max = arr[high]; minmax.min = arr[low]; } return minmax; } /* If there are more than 2 elements */ mid = (low + high)/2; mml = getMinMax(arr, low, mid); mmr = getMinMax(arr, mid+1, high); /* compare minimums of two parts*/ if (mml.min < mmr.min) minmax.min = mml.min; else minmax.min = mmr.min; /* compare maximums of two parts*/ if (mml.max > mmr.max) minmax.max = mml.max; else minmax.max = mmr.max; return minmax; } /* Driver program to test above function */ int main() { int arr[] = {1000, 11, 445, 1, 330, 3000}; int arr_size = 6; struct pair minmax = getMinMax(arr, 0, arr_size-1); printf ( "nMinimum element is %d" , minmax.min); printf ( "nMaximum element is %d" , minmax.max); getchar (); } |
Java
// Java program of above implementation public class GFG { /* Class Pair is used to return two values from getMinMax() */ static class Pair { int min; int max; } static Pair getMinMax( int arr[], int low, int high) { Pair minmax = new Pair(); Pair mml = new Pair(); Pair mmr = new Pair(); int mid; // If there is only one element if (low == high) { minmax.max = arr[low]; minmax.min = arr[low]; return minmax; } /* If there are two elements */ if (high == low + 1 ) { if (arr[low] > arr[high]) { minmax.max = arr[low]; minmax.min = arr[high]; } else { minmax.max = arr[high]; minmax.min = arr[low]; } return minmax; } /* If there are more than 2 elements */ mid = (low + high) / 2 ; mml = getMinMax(arr, low, mid); mmr = getMinMax(arr, mid + 1 , high); /* compare minimums of two parts*/ if (mml.min < mmr.min) { minmax.min = mml.min; } else { minmax.min = mmr.min; } /* compare maximums of two parts*/ if (mml.max > mmr.max) { minmax.max = mml.max; } else { minmax.max = mmr.max; } return minmax; } /* Driver program to test above function */ public static void main(String args[]) { int arr[] = { 1000 , 11 , 445 , 1 , 330 , 3000 }; int arr_size = 6 ; Pair minmax = getMinMax(arr, 0 , arr_size - 1 ); System.out.printf( "\nMinimum element is %d" , minmax.min); System.out.printf( "\nMaximum element is %d" , minmax.max); } } |
Python3
# Python program of above implementation def getMinMax(low, high, arr): arr_max = arr[low] arr_min = arr[low] # If there is only one element if low = = high: arr_max = arr[low] arr_min = arr[low] return (arr_max, arr_min) # If there is only two element elif high = = low + 1 : if arr[low] > arr[high]: arr_max = arr[low] arr_min = arr[high] else : arr_max = arr[high] arr_min = arr[low] return (arr_max, arr_min) else : # If there are more than 2 elements mid = int ((low + high) / 2 ) arr_max1, arr_min1 = getMinMax(low, mid, arr) arr_max2, arr_min2 = getMinMax(mid + 1 , high, arr) return ( max (arr_max1, arr_max2), min (arr_min1, arr_min2)) # Driver code arr = [ 1000 , 11 , 445 , 1 , 330 , 3000 ] high = len (arr) - 1 low = 0 arr_max, arr_min = getMinMax(low, high, arr) print ( 'Minimum element is ' , arr_min) print ( 'nMaximum element is ' , arr_max) # This code is contributed by DeepakChhitarka |
C#
// C# implementation of the approach using System; public class GFG { /* Class Pair is used to return two values from getMinMax() */ public class Pair { public int min; public int max; } static Pair getMinMax( int []arr, int low, int high) { Pair minmax = new Pair(); Pair mml = new Pair(); Pair mmr = new Pair(); int mid; // If there is only one element if (low == high) { minmax.max = arr[low]; minmax.min = arr[low]; return minmax; } /* If there are two elements */ if (high == low + 1) { if (arr[low] > arr[high]) { minmax.max = arr[low]; minmax.min = arr[high]; } else { minmax.max = arr[high]; minmax.min = arr[low]; } return minmax; } /* If there are more than 2 elements */ mid = (low + high) / 2; mml = getMinMax(arr, low, mid); mmr = getMinMax(arr, mid + 1, high); /* compare minimums of two parts*/ if (mml.min < mmr.min) { minmax.min = mml.min; } else { minmax.min = mmr.min; } /* compare maximums of two parts*/ if (mml.max > mmr.max) { minmax.max = mml.max; } else { minmax.max = mmr.max; } return minmax; } /* Driver program to test above function */ public static void Main(String []args) { int []arr = {1000, 11, 445, 1, 330, 3000}; int arr_size = 6; Pair minmax = getMinMax(arr, 0, arr_size - 1); Console.Write( "\nMinimum element is {0}" , minmax.min); Console.Write( "\nMaximum element is {0}" , minmax.max); } } // This code contributed by Rajput-Ji |
Output:
Minimum element is 1 Maximum element is 3000
Time Complexity: O(n)
Total number of comparisons: let the number of comparisons be T(n). T(n) can be written as follows:
Algorithmic Paradigm: Divide and Conquer
T(n) = T(floor(n/2)) + T(ceil(n/2)) + 2 T(2) = 1 T(1) = 0
If n is a power of 2, then we can write T(n) as:
T(n) = 2T(n/2) + 2
After solving the above recursion, we get
T(n) = 3n/2 -2
Thus, the approach does 3n/2 -2 comparisons if n is a power of 2. And it does more than 3n/2 -2 comparisons if n is not a power of 2.
METHOD 3 (Compare in Pairs)
If n is odd then initialize min and max as first element.
If n is even then initialize min and max as minimum and maximum of the first two elements respectively.
For rest of the elements, pick them in pairs and compare their
maximum and minimum with max and min respectively.
C++
// C++ program of above implementation #include<iostream> using namespace std; // Structure is used to return // two values from minMax() struct Pair { int min; int max; }; struct Pair getMinMax( int arr[], int n) { struct Pair minmax; int i; // If array has even number of elements // then initialize the first two elements // as minimum and maximum if (n % 2 == 0) { if (arr[0] > arr[1]) { minmax.max = arr[0]; minmax.min = arr[1]; } else { minmax.min = arr[0]; minmax.max = arr[1]; } // Set the starting index for loop i = 2; } // If array has odd number of elements // then initialize the first element as // minimum and maximum else { minmax.min = arr[0]; minmax.max = arr[0]; // Set the starting index for loop i = 1; } // In the while loop, pick elements in // pair and compare the pair with max // and min so far while (i < n - 1) { if (arr[i] > arr[i + 1]) { if (arr[i] > minmax.max) minmax.max = arr[i]; if (arr[i + 1] < minmax.min) minmax.min = arr[i + 1]; } else { if (arr[i + 1] > minmax.max) minmax.max = arr[i + 1]; if (arr[i] < minmax.min) minmax.min = arr[i]; } // Increment the index by 2 as // two elements are processed in loop i += 2; } return minmax; } // Driver code int main() { int arr[] = { 1000, 11, 445, 1, 330, 3000 }; int arr_size = 6; Pair minmax = getMinMax(arr, arr_size); cout << "nMinimum element is " << minmax.min << endl; cout << "nMaximum element is " << minmax.max; return 0; } // This code is contributed by nik_3112 |
C
#include<stdio.h> /* structure is used to return two values from minMax() */ struct pair { int min; int max; }; struct pair getMinMax( int arr[], int n) { struct pair minmax; int i; /* If array has even number of elements then initialize the first two elements as minimum and maximum */ if (n%2 == 0) { if (arr[0] > arr[1]) { minmax.max = arr[0]; minmax.min = arr[1]; } else { minmax.min = arr[0]; minmax.max = arr[1]; } i = 2; /* set the starting index for loop */ } /* If array has odd number of elements then initialize the first element as minimum and maximum */ else { minmax.min = arr[0]; minmax.max = arr[0]; i = 1; /* set the starting index for loop */ } /* In the while loop, pick elements in pair and compare the pair with max and min so far */ while (i < n-1) { if (arr[i] > arr[i+1]) { if (arr[i] > minmax.max) minmax.max = arr[i]; if (arr[i+1] < minmax.min) minmax.min = arr[i+1]; } else { if (arr[i+1] > minmax.max) minmax.max = arr[i+1]; if (arr[i] < minmax.min) minmax.min = arr[i]; } i += 2; /* Increment the index by 2 as two elements are processed in loop */ } return minmax; } /* Driver program to test above function */ int main() { int arr[] = {1000, 11, 445, 1, 330, 3000}; int arr_size = 6; struct pair minmax = getMinMax (arr, arr_size); printf ( "nMinimum element is %d" , minmax.min); printf ( "nMaximum element is %d" , minmax.max); getchar (); } |
Java
// Java program of above implementation public class GFG { /* Class Pair is used to return two values from getMinMax() */ static class Pair { int min; int max; } static Pair getMinMax( int arr[], int n) { Pair minmax = new Pair(); int i; /* If array has even number of elements then initialize the first two elements as minimum and maximum */ if (n % 2 == 0 ) { if (arr[ 0 ] > arr[ 1 ]) { minmax.max = arr[ 0 ]; minmax.min = arr[ 1 ]; } else { minmax.min = arr[ 0 ]; minmax.max = arr[ 1 ]; } i = 2 ; /* set the starting index for loop */ } /* If array has odd number of elements then initialize the first element as minimum and maximum */ else { minmax.min = arr[ 0 ]; minmax.max = arr[ 0 ]; i = 1 ; /* set the starting index for loop */ } /* In the while loop, pick elements in pair and compare the pair with max and min so far */ while (i < n - 1 ) { if (arr[i] > arr[i + 1 ]) { if (arr[i] > minmax.max) { minmax.max = arr[i]; } if (arr[i + 1 ] < minmax.min) { minmax.min = arr[i + 1 ]; } } else { if (arr[i + 1 ] > minmax.max) { minmax.max = arr[i + 1 ]; } if (arr[i] < minmax.min) { minmax.min = arr[i]; } } i += 2 ; /* Increment the index by 2 as two elements are processed in loop */ } return minmax; } /* Driver program to test above function */ public static void main(String args[]) { int arr[] = { 1000 , 11 , 445 , 1 , 330 , 3000 }; int arr_size = 6 ; Pair minmax = getMinMax(arr, arr_size); System.out.printf( "\nMinimum element is %d" , minmax.min); System.out.printf( "\nMaximum element is %d" , minmax.max); } } |
Python3
# Python3 program of above implementation def getMinMax(arr): n = len (arr) # If array has even number of elements then # initialize the first two elements as minimum # and maximum if (n % 2 = = 0 ): mx = max (arr[ 0 ], arr[ 1 ]) mn = min (arr[ 0 ], arr[ 1 ]) # set the starting index for loop i = 2 # If array has odd number of elements then # initialize the first element as minimum # and maximum else : mx = mn = arr[ 0 ] # set the starting index for loop i = 1 # In the while loop, pick elements in pair and # compare the pair with max and min so far while (i < n - 1 ): if arr[i] < arr[i + 1 ]: mx = max (mx, arr[i + 1 ]) mn = min (mn, arr[i]) else : mx = max (mx, arr[i]) mn = min (mn, arr[i + 1 ]) # Increment the index by 2 as two # elements are processed in loop i + = 2 return (mx, mn) # Driver Code if __name__ = = '__main__' : arr = [ 1000 , 11 , 445 , 1 , 330 , 3000 ] mx, mn = getMinMax(arr) print ( "Minimum element is" , mn) print ( "Maximum element is" , mx) # This code is contributed by Kaustav |
C#
// C# program of above implementation using System; class GFG { /* Class Pair is used to return two values from getMinMax() */ public class Pair { public int min; public int max; } static Pair getMinMax( int []arr, int n) { Pair minmax = new Pair(); int i; /* If array has even number of elements then initialize the first two elements as minimum and maximum */ if (n % 2 == 0) { if (arr[0] > arr[1]) { minmax.max = arr[0]; minmax.min = arr[1]; } else { minmax.min = arr[0]; minmax.max = arr[1]; } i = 2; } /* set the starting index for loop */ /* If array has odd number of elements then initialize the first element as minimum and maximum */ else { minmax.min = arr[0]; minmax.max = arr[0]; i = 1; /* set the starting index for loop */ } /* In the while loop, pick elements in pair and compare the pair with max and min so far */ while (i < n - 1) { if (arr[i] > arr[i + 1]) { if (arr[i] > minmax.max) { minmax.max = arr[i]; } if (arr[i + 1] < minmax.min) { minmax.min = arr[i + 1]; } } else { if (arr[i + 1] > minmax.max) { minmax.max = arr[i + 1]; } if (arr[i] < minmax.min) { minmax.min = arr[i]; } } i += 2; /* Increment the index by 2 as two elements are processed in loop */ } return minmax; } // Driver Code public static void Main(String []args) { int []arr = {1000, 11, 445, 1, 330, 3000}; int arr_size = 6; Pair minmax = getMinMax(arr, arr_size); Console.Write( "Minimum element is {0}" , minmax.min); Console.Write( "\nMaximum element is {0}" , minmax.max); } } // This code is contributed by 29AjayKumar |
Output:
Minimum element is 1 Maximum element is 3000
Time Complexity: O(n)
Total number of comparisons: Different for even and odd n, see below:
If n is odd: 3*(n-1)/2 If n is even: 1 Initial comparison for initializing min and max, and 3(n-2)/2 comparisons for rest of the elements = 1 + 3*(n-2)/2 = 3n/2 -2
Second and third approaches make the equal number of comparisons when n is a power of 2.
In general, method 3 seems to be the best.
Please write comments if you find any bug in the above programs/algorithms or a better way to solve the same problem.
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