Given three integers x, y, z, the task is to find the largest non-negative number less than or equal to z that leaves a remainder x when divided by y (Given x < y). If no such number exists then the output will be -1.
Examples:
Input: x = 1, y = 5, z = 8 Output: 6 Explanation: 6 is the largest number less than 8 which when divided by 5 leaves a remainder 1. Input: x = 4, y = 6, z = 3 Output: -1 Explanation: Since no such number exists the output is -1
Approach: To solve the problem mentioned above the very first observation is if x > z then answer will not be possible, so output will be -1.
Let the required number be p. Following are the two equations for solving the problem:
- p * y + x = 0
- p * y <= (z – x)
In order to find the answer, we need to find the value of p. So,
p = (z - x) / y
After calculating p we can simply find the answer which is
p * y + x
Below is the implementation of the above approach:
C++
// C++ implementation to Find the// largest non-negative number that// is less than or equal to integer Z// and leaves a remainder X when divided by Y#include <bits/stdc++.h>using namespace std;// Function to get the numberint get(int x, int y, int z){ // remainder can't be larger // than the largest number, // if so then answer doesn't exist. if (x > z) return -1; // reduce number by x int val = z - x; // finding the possible // number that is divisible by y int div = (z - x) / y; // this number is always <= x // as we calculated over z - x int ans = div * y + x; return ans;}// Driver Codeint main(){ // initialise the three integers int x = 1, y = 5, z = 8; cout << get(x, y, z) << "\n"; return 0;} |
Java
// Java implementation to Find the// largest non-negative number that// is less than or equal to integer Z// and leaves a remainder X when divided by Yclass GFG{ // Function to get the numberstatic int get(int x, int y, int z){ // remainder can't be larger // than the largest number, // if so then answer doesn't exist. if (x > z) return -1; // reduce number by x int val = z - x; // finding the possible // number that is divisible by y int div = (z - x) / y; // this number is always <= x // as we calculated over z - x int ans = div * y + x; return ans;} // Driver Codepublic static void main(String[] args){ // initialise the three integers int x = 1, y = 5, z = 8; System.out.print(get(x, y, z)+ "\n");}}// This code is contributed by sapnasingh4991 |
Python3
# Python implementation to Find the# largest non-negative number that# is less than or equal to integer Z# and leaves a remainder X when divided by Y# Function to get the numberdef get(x, y, z): # remainder can't be larger # than the largest number, # if so then answer doesn't exist. if (x > z): return -1 # reduce number by x val = z - x # finding the possible # number that is divisible by y div = (z - x) // y # this number is always <= x # as we calculated over z - x ans = div * y + x return ans# Driver Code# initialise the three integersx = 1y = 5z = 8print(get(x, y, z))# This code is contributed by shubhamsingh10 |
C#
// C# implementation to Find the// largest non-negative number that// is less than or equal to integer Z// and leaves a remainder X when divided by Yusing System;class GFG{ // Function to get the numberstatic int get(int x, int y, int z){ // remainder can't be larger // than the largest number, // if so then answer doesn't exist. if (x > z) return -1; // reduce number by x int val = z - x; // finding the possible // number that is divisible by y int div = (z - x) / y; // this number is always <= x // as we calculated over z - x int ans = div * y + x; return ans;} // Driver Codepublic static void Main(String[] args){ // initialise the three integers int x = 1, y = 5, z = 8; Console.Write(get(x, y, z)+ "\n");}}// This code is contributed by sapnasingh4991 |
Javascript
<script>// Javascript implementation to Find the// largest non-negative number that// is less than or equal to integer Z// and leaves a remainder X when divided by Y// Function to get the numberfunction get(x, y, z){ // remainder can't be larger // than the largest number, // if so then answer doesn't exist. if (x > z) return -1; // reduce number by x let val = z - x; // finding the possible // number that is divisible by y let div = Math.floor((z - x) / y); // this number is always <= x // as we calculated over z - x let ans = div * y + x; return ans;}// Driver Code // initialise the three integers let x = 1, y = 5, z = 8; document.write(get(x, y, z)+ "\n");</script> |
Output:
6
Time Complexity: O(1 )
Auxiliary Space: O(1)
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
