The Stock Span Problem

The stock span problem is a financial problem where we have a series of n daily price quotes for a stock and we need to calculate span of stock’s price for all n days.
The span Si of the stock’s price on a given day i is defined as the maximum number of consecutive days just before the given day, for which the price of the stock on the current day is less than or equal to its price on the given day.
For example, if an array of 7 days prices is given as {100, 80, 60, 70, 60, 75, 85}, then the span values for corresponding 7 days are {1, 1, 1, 2, 1, 4, 6}

A Simple but inefficient method
Traverse the input price array. For every element being visited, traverse elements on left of it and increment the span value of it while elements on the left side are smaller.

Following is implementation of this method.

C

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// C program for brute force method to calculate stock span values
#include <stdio.h>
  
// Fills array S[] with span values
void calculateSpan(int price[], int n, int S[])
{
   // Span value of first day is always 1
   S[0] = 1;
  
   // Calculate span value of remaining days by linearly checking
   // previous days
   for (int i = 1; i < n; i++)
   {
      S[i] = 1; // Initialize span value
  
      // Traverse left while the next element on left is smaller
      // than price[i]
      for (int j = i-1; (j>=0)&&(price[i]>=price[j]); j--)
          S[i]++;
   }
}
  
// A utility function to print elements of array
void printArray(int arr[], int n)
{
    for (int i = 0; i < n; i++)
      printf("%d ", arr[i]);
}
  
// Driver program to test above function
int main()
{
    int price[] = {10, 4, 5, 90, 120, 80};
    int n = sizeof(price)/sizeof(price[0]);
    int S[n];
  
    // Fill the span values in array S[]
    calculateSpan(price, n, S);
  
    // print the calculated span values
    printArray(S, n);
  
    return 0;
}

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Java

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// Java implementation for brute force method to calculate stock span values
  
import java.util.Arrays;
  
class GFG
{
    //  method to calculate stock span values
    static void calculateSpan(int price[], int n, int S[])
    {
        // Span value of first day is always 1
        S[0] = 1;
          
        // Calculate span value of remaining days by linearly checking
        // previous days
        for (int i = 1; i < n; i++)
        {
            S[i] = 1; // Initialize span value
              
            // Traverse left while the next element on left is smaller
            // than price[i]
            for (int j = i-1; (j>=0)&&(price[i]>=price[j]); j--)
                S[i]++;
        }
    }
      
    // A utility function to print elements of array
    static void printArray(int arr[])
    {
        System.out.print(Arrays.toString(arr));
    }
      
    // Driver program to test above functions
    public static void main(String[] args) 
    {
        int price[] = {10, 4, 5, 90, 120, 80};
        int n = price.length;
        int S[]= new int[n];
          
        // Fill the span values in array S[]
        calculateSpan(price, n, S); 
          
        // print the calculated span values
        printArray(S);
    }
}
// This code is contributed by Sumit Ghosh 

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Python

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# Python program for brute force method to calculate stock span values
  
# Fills list S[] with span values
def calculateSpan(price, n, S):
      
    # Span value of first day is always 1
    S[0] = 1
  
    # Calculate span value of remaining days by linearly 
    # checking previous days
    for i in range(1, n, 1):
        S[i] = 1   # Initialize span value
  
        # Traverse left while the next element on left is
        # smaller than price[i]
        j = i - 1
        while (j>=0) and (price[i] >= price[j]) :
                       S[i] += 1
                       j -= 1
                         
# A utility function to print elements of array
def printArray(arr, n):
  
    for i in range(n):
        print(arr[i], end = " ")
  
# Driver program to test above function    
price = [10, 4, 5, 90, 120, 80]
n = len(price)
S = [None] * n
  
# Fill the span values in list S[]
calculateSpan(price, n, S)
  
# print the calculated span values
printArray(S, n)
  
  
# This code is contributed by Sunny Karira

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C#

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// C# implementation for brute force method 
// to calculate stock span values
using System;
  
class GFG {
      
    // method to calculate stock span values
    static void calculateSpan(int []price, 
                             int n, int []S)
    {
          
        // Span value of first day is always 1
        S[0] = 1;
          
        // Calculate span value of remaining 
        // days by linearly checking previous
        // days
        for (int i = 1; i < n; i++)
        {
            S[i] = 1; // Initialize span value
              
            // Traverse left while the next 
            // element on left is smaller
            // than price[i]
            for (int j = i-1; (j >= 0) && 
                 (price[i] >= price[j]); j--)
                S[i]++;
        }
    }
      
    // A utility function to print elements 
    // of array
    static void printArray(int []arr)
    {
        string result = string.Join(" ", arr);
        Console.WriteLine(result);
    }
      
    // Driver function
    public static void Main()
    {
        int []price = {10, 4, 5, 90, 120, 80};
        int n = price.Length;
        int []S= new int[n];
          
        // Fill the span values in array S[]
        calculateSpan(price, n, S); 
          
        // print the calculated span values
        printArray(S);
    }
  
}
  
// This code is contributed by Sam007.

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PHP

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<?php
// PHP program for brute force method
// to calculate stock span values
  
// Fills array S[] with span values
function calculateSpan($price, $n, $S)
{
      
    // Span value of first
    // day is always 1
    $S[0] = 1;
      
    // Calculate span value of 
    // remaining days by linearly 
    // checking previous days
    for ($i = 1; $i < $n; $i++)
    {
          
        // Initialize span value
        $S[$i] = 1; 
      
        // Traverse left while the next
        // element on left is smaller
        // than price[i]
        for ($j = $i - 1; ($j >= 0) && 
            ($price[$i] >= $price[$j]); $j--)
            $S[$i]++;
    }
      
        // print the calculated 
        // span values
        for ($i = 0; $i < $n; $i++)
        echo $S[$i] . " ";;
      
          
}
  
    // Driver Code
    $price = array(10, 4, 5, 90, 120, 80);
    $n = count($price);
    $S = array($n);
  
    // Fill the span values in array S[]
    calculateSpan($price, $n, $S);
  
// This code is contributed by Sam007
?>

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Output :

1 1 2 4 5 1

Time Complexity of the above method is O(n^2). We can calculate stock span values in O(n) time.



A Linear Time Complexity Method
We see that S[i] on day i can be easily computed if we know the closest day preceding i, such that the price is greater than on that day than the price on day i. If such a day exists, let’s call it h(i), otherwise, we define h(i) = -1.
The span is now computed as S[i] = i – h(i). See the following diagram.

To implement this logic, we use a stack as an abstract data type to store the days i, h(i), h(h(i)) and so on. When we go from day i-1 to i, we pop the days when the price of the stock was less than or equal to price[i] and then push the value of day i back into the stack.

Following is C++ implementation of this method.

C++

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// a linear time solution for stock span problem
#include <iostream>
#include <stack>
using namespace std;
  
// A stack based efficient method to calculate
// stock span values
void calculateSpan(int price[], int n, int S[])
{
   // Create a stack and push index of first
   // element to it
   stack<int> st;
   st.push(0);
  
   // Span value of first element is always 1
   S[0] = 1;
  
   // Calculate span values for rest of the elements
   for (int i = 1; i < n; i++)
   {
      // Pop elements from stack while stack is not 
      // empty and top of stack is smaller than 
      // price[i]
      while (!st.empty() && price[st.top()] <= price[i])
         st.pop();
  
      // If stack becomes empty, then price[i] is
      // greater than all elements on left of it,
      // i.e., price[0], price[1],..price[i-1].  Else
      // price[i] is greater than elements after 
      // top of stack
      S[i] = (st.empty())? (i + 1) : (i - st.top());
  
      // Push this element to stack
      st.push(i);
   }
}
  
// A utility function to print elements of array
void printArray(int arr[], int n)
{
    for (int i = 0; i < n; i++)
      cout << arr[i] << " ";
}
  
// Driver program to test above function
int main()
{
    int price[] = {10, 4, 5, 90, 120, 80};
    int n = sizeof(price)/sizeof(price[0]);
    int S[n];
  
    // Fill the span values in array S[]
    calculateSpan(price, n, S);
  
    // print the calculated span values
    printArray(S, n);
  
    return 0;
}

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Java

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// Java linear time solution for stock span problem
  
import java.util.Stack;
import java.util.Arrays;
  
public class GFG
{
    // a linear time solution for stock span problem
    // A stack based efficient method to calculate 
    // stock span values
    static void calculateSpan(int price[], int n, int S[])
    {
        // Create a stack and push index of first element
        // to it
        Stack<Integer> st= new Stack<>();
        st.push(0); 
          
        // Span value of first element is always 1
        S[0] = 1;
          
        // Calculate span values for rest of the elements
        for (int i = 1; i < n; i++)
        {
  
            // Pop elements from stack while stack is not 
            // empty and top of stack is smaller than 
            // price[i]
            while (!st.empty() && price[st.peek()] <= price[i])
                st.pop();
      
            // If stack becomes empty, then price[i] is 
            // greater than all elements on left of it, i.e., 
            // price[0], price[1],..price[i-1]. Else price[i]
            // is greater than elements after top of stack
            S[i] = (st.empty())? (i + 1) : (i - st.peek());
      
            // Push this element to stack
            st.push(i);
        }
    }
      
    // A utility function to print elements of array
    static void printArray(int arr[])
    {
        System.out.print(Arrays.toString(arr));
    }
      
    // Driver method
    public static void main(String[] args) 
    {
        int price[] = {10, 4, 5, 90, 120, 80};
        int n = price.length;
        int S[]=new int[n];
          
        // Fill the span values in array S[]
        calculateSpan(price, n, S);
  
        // print the calculated span values
        printArray(S);
    }
}
// This code is contributed by Sumit Ghosh 

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Python3

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# A linear time solution for stack stock problem
  
# A stack based efficient method to calculate s
def calculateSpan(price, S):
      
    n = len(price)
    # Create a stack and push index of fist element to it
    st = [] 
    st.append(0)
  
    # Span value of first element is always 1
    S[0] = 1
  
    # Calculate span values for rest of the elements
    for i in range(1, n):
          
        # Pop elements from stack whlie stack is not
        # empty and top of stack is smaller than price[i]
        while( len(st) > 0 and price[st[0]] <= price[i]):
            st.pop()
  
        # If stack becomes empty, then price[i] is greater
        # than all elements on left of it, i.e. price[0],
        # price[1], ..price[i-1]. Else the price[i] is
        # greater than elements after top of stack
        S[i] = i+1 if len(st) <= 0 else (i - st[0])
  
        # Push this element to stack
        st.append(i)
  
  
# A utility function to print elements of array
def printArray(arr, n):
    for i in range(0,n):
        print (arr[i], end=" ")
  
  
# Driver program to test above function
price = [10, 4, 5, 90, 120, 80]
S = [0 for i in range(len(price)+1)]
  
# Fill the span values in array S[]
calculateSpan(price, S)
  
# Print the calculated span values
printArray(S, len(price))
  
# This code is contributed by Nikhil Kumar Singh (nickzuck_007)

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Output:

1 1 2 4 5 1

Time Complexity: O(n). It seems more than O(n) at first look. If we take a closer look, we can observe that every element of array is added and removed from stack at most once. So there are total 2n operations at most. Assuming that a stack operation takes O(1) time, we can say that the time complexity is O(n).

Auxiliary Space: O(n) in worst case when all elements are sorted in decreasing order.

Another approach: (without using stack)

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// C++ program for a linear time solution for stock
// span problem without using stack
#include <iostream> 
#include <stack> 
using namespace std; 
  
// An efficient method to calculate stock span values 
// implementing the same idea without using stack
void calculateSpan(int A[], int n, int ans[]) 
    // Span value of first element is always 1 
    ans[0] = 1; 
  
    // Calculate span values for rest of the elements 
    for (int i = 1; i < n; i++) 
    
        int counter = 1;
        while ((i - counter) >= 0 && 
               A[i] > A[i - counter]){
            counter += ans[i-counter];
        }
        ans[i]=counter;
    
  
// A utility function to print elements of array 
void printArray(int arr[], int n) 
    for (int i = 0; i < n; i++) 
    cout << arr[i] << " "
  
// Driver program to test above function 
int main() 
    int price[] = {10, 4, 5, 90, 120, 80}; 
    int n = sizeof(price)/sizeof(price[0]); 
    int S[n]; 
  
    // Fill the span values in array S[] 
    calculateSpan(price, n, S); 
  
    // print the calculated span values 
    printArray(S, n); 
  
    return 0; 

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Output:

1 1 2 4 5 1

References:
http://en.wikipedia.org/wiki/Stack_(abstract_data_type)#The_Stock_Span_Problem
http://crypto.cs.mcgill.ca/~crepeau/CS250/2004/Stack-I.pdf

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