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Count the number of operations required to reduce the given number

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  • Difficulty Level : Medium
  • Last Updated : 09 Jun, 2022

Given an integer k and an array op[], in a single operation op[0] will be added to k and then in the second operation k = k + op[1] and so on in a circular manner until k > 0. The task is to print the operation number in which k will be reduced to ≤ 0. If it impossible to reduce k with the given operations then print -1.
Examples: 
 

Input: op[] = {-60, 10, -100}, k = 100 
Output:
Operation 1: 100 – 60 = 40 
Operation 2: 40 + 10 = 50 
Operation 3: 50 – 100 = -50
Input: op[] = {1, 1, -1}, k = 10 
Output: -1
Input: op[] = {-60, 65, -1, 14, -25}, k = 100000 
Output: 71391 
 

 

Approach: Count the number of times all the operations can be performed on the number k without actually reducing it to get the result. Then update count = times * n where n is the number of operations. Now, for the remaining operations perform each of the operation one by one and increment count. The first operation when k is reduced to ≤ 0, print the count.
Below is the implementation of the above approach: 
 

C++




// C++ implementation of the approach
 
#include <bits/stdc++.h>
using namespace std;
 
 
int operations(int op[], int n, int k)
    {
        int i, count = 0;
 
        // To store the normalized value
        // of all the operations
        int nVal = 0;
 
        // Minimum possible value for
        // a series of operations
        int minimum = INT_MAX;
        for (i = 0; i < n; i++)
        {
            nVal += op[i];
            minimum  = min(minimum , nVal);
 
            // If k can be reduced with
            // first (i + 1) operations
            if ((k + nVal) <= 0)
                return (i + 1);
        }
 
        // Impossible to reduce k
        if (nVal >= 0)
            return -1;
 
        // Number of times all the operations
        // can be performed on k without
        // reducing it to <= 0
        int times = (k - abs(minimum )) / abs(nVal);
 
        // Perform operations
        k = (k - (times * abs(nVal)));
        count = (times * n);
 
        // Final check
        while (k > 0) {
            for (i = 0; i < n; i++) {
                k = k + op[i];
                count++;
                if (k <= 0)
                    break;
            }
        }
 
        return count;
    }
 
// Driver code
int main() {
     
        int op[] = { -60, 65, -1, 14, -25 };
        int n = sizeof(op)/sizeof(op[0]);
        int k = 100000;
 
        cout << operations(op, n, k) << endl;
}
// This code is contributed by Ryuga

Java




// Java implementation of the approach
class GFG {
 
    static int operations(int op[], int n, int k)
    {
        int i, count = 0;
 
        // To store the normalized value
        // of all the operations
        int nVal = 0;
 
        // Minimum possible value for
        // a series of operations
        int min = Integer.MAX_VALUE;
        for (i = 0; i < n; i++) {
            nVal += op[i];
            min = Math.min(min, nVal);
 
            // If k can be reduced with
            // first (i + 1) operations
            if ((k + nVal) <= 0)
                return (i + 1);
        }
 
        // Impossible to reduce k
        if (nVal >= 0)
            return -1;
 
        // Number of times all the operations
        // can be performed on k without
        // reducing it to <= 0
        int times = (k - Math.abs(min)) / Math.abs(nVal);
 
        // Perform operations
        k = (k - (times * Math.abs(nVal)));
        count = (times * n);
 
        // Final check
        while (k > 0) {
            for (i = 0; i < n; i++) {
                k = k + op[i];
                count++;
                if (k <= 0)
                    break;
            }
        }
 
        return count;
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int op[] = { -60, 65, -1, 14, -25 };
        int n = op.length;
        int k = 100000;
 
        System.out.print(operations(op, n, k));
    }
}

Python3




# Python3 implementation of the approach
def operations(op, n, k):
 
    i, count = 0, 0
 
    # To store the normalized value
    # of all the operations
    nVal = 0
 
    # Minimum possible value for
    # a series of operations
    minimum = 10**9
    for i in range(n):
        nVal += op[i]
        minimum = min(minimum , nVal)
 
        # If k can be reduced with
        # first (i + 1) operations
        if ((k + nVal) <= 0):
            return (i + 1)
 
    # Impossible to reduce k
    if (nVal >= 0):
        return -1
 
    # Number of times all the operations
    # can be performed on k without
    # reducing it to <= 0
    times = (k - abs(minimum )) // abs(nVal)
 
    # Perform operations
    k = (k - (times * abs(nVal)))
    count = (times * n)
 
    # Final check
    while (k > 0):
        for i in range(n):
            k = k + op[i]
            count += 1
            if (k <= 0):
                break
 
    return count
 
# Driver code
op = [-60, 65, -1, 14, -25]
n = len(op)
k = 100000
 
print(operations(op, n, k))
 
# This code is contributed
# by mohit kumar

C#




// C# implementation of the approach
using System;
 
class GFG
{
 
    static int operations(int []op, int n, int k)
    {
        int i, count = 0;
 
        // To store the normalized value
        // of all the operations
        int nVal = 0;
 
        // Minimum possible value for
        // a series of operations
        int min = int.MaxValue;
        for (i = 0; i < n; i++)
        {
            nVal += op[i];
            min = Math.Min(min, nVal);
 
            // If k can be reduced with
            // first (i + 1) operations
            if ((k + nVal) <= 0)
                return (i + 1);
        }
 
        // Impossible to reduce k
        if (nVal >= 0)
            return -1;
 
        // Number of times all the operations
        // can be performed on k without
        // reducing it to <= 0
        int times = (k - Math.Abs(min)) / Math.Abs(nVal);
 
        // Perform operations
        k = (k - (times * Math.Abs(nVal)));
        count = (times * n);
 
        // Final check
        while (k > 0)
        {
            for (i = 0; i < n; i++)
            {
                k = k + op[i];
                count++;
                if (k <= 0)
                    break;
            }
        }
 
        return count;
    }
 
    // Driver code
    static void Main()
    {
        int []op = { -60, 65, -1, 14, -25 };
        int n = op.Length;
        int k = 100000;
 
        Console.WriteLine(operations(op, n, k));
    }
}
 
// This code is contributed by mits

PHP




<?php
// PHP implementation of the approach
function operations($op, $n, $k)
{
    $count = 0;
 
    // To store the normalized value
    // of all the operations
    $nVal = 0;
 
    // Minimum possible value for
    // a series of operations
    $minimum = PHP_INT_MAX;
    for ($i = 0; $i < $n; $i++)
    {
        $nVal += $op[$i];
        $minimum = min($minimum , $nVal);
 
        // If k can be reduced with
        // first (i + 1) operations
        if (($k + $nVal) <= 0)
            return ($i + 1);
    }
 
    // Impossible to reduce k
    if ($nVal >= 0)
        return -1;
 
    // Number of times all the operations
    // can be performed on k without
    // reducing it to <= 0
    $times = round(($k - abs($minimum )) /
                         abs($nVal));
 
    // Perform operations
    $k = ($k - ($times * abs($nVal)));
    $count = ($times * $n);
 
    // Final check
    while ($k > 0)
    {
        for ($i = 0; $i < $n; $i++)
        {
            $k = $k + $op[$i];
            $count++;
            if ($k <= 0)
                break;
        }
    }
 
    return $count;
}
 
// Driver code
$op = array(-60, 65, -1, 14, -25 );
$n = sizeof($op);
$k = 100000;
 
echo operations($op, $n, $k);
 
// This code is contributed by ihritik
?>

Javascript




<script>
// Javascript implementation of the approach
 
function operations(op,n,k)
{
    let i, count = 0;
   
        // To store the normalized value
        // of all the operations
        let nVal = 0;
   
        // Minimum possible value for
        // a series of operations
        let min = Number.MAX_VALUE;
        for (i = 0; i < n; i++) {
            nVal += op[i];
            min = Math.min(min, nVal);
   
            // If k can be reduced with
            // first (i + 1) operations
            if ((k + nVal) <= 0)
                return (i + 1);
        }
   
        // Impossible to reduce k
        if (nVal >= 0)
            return -1;
   
        // Number of times all the operations
        // can be performed on k without
        // reducing it to <= 0
        let times = Math.floor((k - Math.abs(min)) / Math.abs(nVal));
   
        // Perform operations
        k = (k - (times * Math.abs(nVal)));
        count = (times * n);
   
        // Final check
        while (k > 0) {
            for (i = 0; i < n; i++) {
                k = k + op[i];
                count++;
                if (k <= 0)
                    break;
            }
        }
   
        return count;
}
 
    // Driver code
    let op=[-60, 65, -1, 14, -25];
    let n = op.length;
    let k = 100000;
    document.write(operations(op, n, k));
     
// This code is contributed by unknown2108.
</script>

Output: 

71391

 

Time Complexity: O(n*k)

Auxiliary Space: O(1)


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