Standard Algorithms

Using the traversals that we have learned in the previous two topics, we can make many useful algorithms. Here, we will have a snippet for each algorithm you are expected to know with annotations for each.

You should come up with an example array to use as you trace through the code below. This will help you gain a better understanding of how the algorithms work by allowing you to see the loops in action and what they are manipulating. 

Finding the Minimum and Maximum

/** Finds the maximum
*/
public static int maximum(int[] array) {
  int maxValue = array[0];
  for (int number: array) {
    if (number > maxValue) {
      //if new max value found, replace current maxValue
      maxValue = number;
    }
  }
  return maxValue;
}

/** Finds the minimum
*/
public static int minimum(int[] array) {
  int minValue = array[0];
  for (int number: array) {
    if (number < minValue) { 
     //if new min value found, replace current minValue
     minValue = number;
    }
  }
  return minValue;
}

Initializing the maxValue and minValue to 0 is a common mistake. 

• If all the values in the array are positive, it would incorrectly keep minValue at 0 (all the values are greater than 0, leaving 0 as the minimum).
• If all the values in the array are negative, it would incorrectly keep maxValue at 0 (all the values are less than 0, leaving 0 as the maximum). To counter these errors, initialize these to the first value in the array.

Finding a Sum

/** Sums up all elements in the array
*/
public static int sum(int[] array) {
  int sum = 0;
  for (int number: array) {
    sum += number; //adds every element to sum
  }
  return sum;
}

Finding a Mean

/** Finds the mean/average of the array
*/
public static int mean(int[] array) {
  // find the sum of the array, can be replaced with sum algorithm from above
  int sum = sum(array);
  // then divide by number of items
  return (double) sum / (array.length);
}                                     

Finding a Mode

/** Finds the mode of an array
    **Prerequisite:** The array must have a mode
*/
public static int mode(int[] array) {
  int mostCommon = 0;
  int mostCommonFrequency = 0;
  //traverse through the first n-1 elements of the array
  for (int i = 0; i < array.length - 1; i++) { 
    int currentFrequency = 1;
    //traverse through the array starting from the next element
    for (int j = i + 1; j < array.length; j++) { 
      if (array[j] == array[i]) {
        // if any element matches current element being checked, add 1 to frequency
        currentFrequency++; 
      }
    }
    if (currentFrequency > mostCommonFrequency) {
      // replaces current mode if new most common element
      mostCommon = array[i];      
      mostCommonFrequency = currentFrequency;
    }
  }
  return mostCommon;  // can also be modified to return the frequency
}

Determining If All Values Have a Certain Property

/** Determines whether all values are even
*/
public static boolean isEven(int[] array) {
//Assume all values are positive first
  for (int number: array) {
   if (number % 2 == 1) {
      //If there is one value that is not positive, return false
      return false;
    }
  }
  return true; //No odd numbers were found
}

Accessing All Consecutive Pairs/Triplets/Sequences of Length n of Elements

/** Returns all consecutive sequences of length n in the array
*/
public static void returnAllConsecutiveSequences(int[] array, int length) {
  for (int i = 0; i <= array.length - length; i++) {
    for (int j = 0; j < length; j++) {
      //2 loops, one to get the starting number, the other to go through the sequences
      System.out.print(array[i+j] + " "); 
    }                                    
    System.out.println();
  }
}

Checking if There are Duplicate Elements

/** Checks to see if there are duplicate elements
*/
public static boolean duplicates(int[] array) {
  for (int i = 0; i < array.length - 1; i++) { //traverse through the array
    for (int j = i + 1; j < array.length; j++) { //traverse through rest of array
      if (array[j] == array[i]) {
        // if any element matches current element being checked, return true
        return true; 
      }
    }
  }
  return false;        // if this point reached, no duplicates found
}

Determining How Many Elements Fit a Criteria

/** Returns how many even numbers there are
*/
public static int evenFrequency(int[] array) {
  int numberEven = 0;
  for (int number: array) {
    if (number % 2 == 0) {
      // increments every time an even integer is found
      numberEven++; 
    }
  }
  return numberEven;
}

Shifting Elements One Index Left

/** Shifts Elements One Index to the Left
*/
public static int[] shiftLeft(int[] array) {
  int firstItem = array[0]
  for (int i = 0; i < array.length - 1; i++) {
    // Does the shifting
    array[i] = array[i+1]; 
  }
  array[array.length - 1] = firstItem;
  return array;
}

Shifting Elements One Index Right

/** Shifts Elements One Index to the Right
*/
public static int[] shiftRight(int[] array) {
  int lastItem = array[array.length - 1]
  for (int i = array.length - 1; i > 0; i--) {
    // Does the shifting
    array[i] = array[i-1]; 
  }
  array[0] = lastItem;
  return array;
}

Reversing an Array

/** Reverses the array
*/
public static int[] reverse(int[] array) {
  int[] newArray = new int[array.length];
  for (int i = 0; i < array.length; i++) {
    // places the items in the new array in opposite order of the original
    newArray[i] = array[array.length - i - 1]; 
  }
  return newArray;
}