Given some weights of masses a0, a1, a2, …, a100, a being an integer, and a weighing scale where weights can be put on both the sides of the scale. Check whether a particular item of weight W can be measured using these weights and scale.
Constraints: 2 ? W ? 109
Examples:
Input : a = 2, W = 5
Output : YES
Explanation : Weights of masses (20 = 1) and (22 = 4) can be placed on one side of the scale and the item can be placed on other side, i.e. 1 + 4 = 5
Input : a = 4, W = 11
Output : YES
Explanation : Weights of masses (40 = 1) and (41 = 4) and the item can be placed on one side and a weight of mass (42 = 16) can be placed on the other side, i.e. 1 + 4 + 11 = 16
Input : a = 4, W = 7
Output : NO
Approach:
- Firstly, it can be carefully observed that for a = 2 or a = 3, the answer always exists.
- Maintain an array containing weights of masses and only include that weights that are less than 109
- Now, the problem can be solved recursively by either including current weight to the side containing
item or including current weight to the opposite side containing item or by not using that weight at all.
Below is the implementation of above approach .
// CPP Program to check whether an item // can be measured using some weight and // a weighing scale. #include <bits/stdc++.h> using namespace std;
// Variable to denote that answer has // been found int found = 0;
void solve( int idx, int itemWt, int wts[],
int N)
{ if (found)
return ;
// Item has been measured
if (itemWt == 0) {
found = 1;
return ;
}
// If the index of current weight
// is greater than totalWts
if (idx > N)
return ;
// Current weight is not included
// on either side
solve(idx + 1, itemWt, wts, N);
// Current weight is included on the
// side containing item
solve(idx + 1, itemWt + wts[idx], wts,
N);
// Current weight is included on the
// side opposite to the side
// containing item
solve(idx + 1, itemWt - wts[idx], wts,
N);
} // This function computes the required array // of weights using a bool checkItem( int a, int W)
{ // If the a is 2 or 3, answer always
// exists
if (a == 2 || a == 3)
return 1;
int wts[100]; // weights array
int totalWts = 0; // feasible weights
wts[0] = 1;
for ( int i = 1;; i++) {
wts[i] = wts[i - 1] * a;
totalWts++;
// if the current weight
// becomes greater than 1e9
// break from the loop
if (wts[i] > 1e9)
break ;
}
solve(0, W, wts, totalWts);
if (found)
return 1;
// Item can't be measured
return 0;
} // Driver Code to test above functions int main()
{ int a = 2, W = 5;
if (checkItem(a, W))
cout << "YES" << endl;
else
cout << "NO" << endl;
a = 4, W = 11, found = 0;
if (checkItem(a, W))
cout << "YES" << endl;
else
cout << "NO" << endl;
a = 4, W = 7, found = 0;
if (checkItem(a, W))
cout << "YES" << endl;
else
cout << "NO" << endl;
return 0;
} |
// Java Program to check whether an item // can be measured using some weight and // a weighing scale. class GFG {
// Variable to denote that answer has // been found static int found = 0 ;
static void solve( int idx, int itemWt, int wts[], int N) {
if (found == 1 ) {
return ;
}
// Item has been measured
if (itemWt == 0 ) {
found = 1 ;
return ;
}
// If the index of current weight
// is greater than totalWts
if (idx > N) {
return ;
}
// Current weight is not included
// on either side
solve(idx + 1 , itemWt, wts, N);
// Current weight is included on the
// side containing item
solve(idx + 1 , itemWt + wts[idx], wts,
N);
// Current weight is included on the
// side opposite to the side
// containing item
solve(idx + 1 , itemWt - wts[idx], wts,
N);
}
// This function computes the required array // of weights using a static boolean checkItem( int a, int W) {
// If the a is 2 or 3, answer always
// exists
if (a == 2 || a == 3 ) {
return true ;
}
int wts[] = new int [ 100 ]; // weights array
int totalWts = 0 ; // feasible weights
wts[ 0 ] = 1 ;
for ( int i = 1 ;; i++) {
wts[i] = wts[i - 1 ] * a;
totalWts++;
// if the current weight
// becomes greater than 1e9
// break from the loop
if (wts[i] > 1e9) {
break ;
}
}
solve( 0 , W, wts, totalWts);
if (found == 1 ) {
return true ;
}
// Item can't be measured
return false ;
}
// Driver Code to test above functions public static void main(String[] args) {
int a = 2 , W = 5 ;
if (checkItem(a, W)) {
System.out.println( "YES" );
} else {
System.out.println( "NO" );
}
a = 4 ; W = 11 ;found = 0 ;
if (checkItem(a, W)) {
System.out.println( "YES" );
} else {
System.out.println( "NO" );
}
a = 4 ; W = 7 ; found = 0 ;
if (checkItem(a, W)) {
System.out.println( "YES" );
} else {
System.out.println( "NO" );
}
}
} //this code contributed by Rajput-Ji |
# Python3 Program to check whether an item # can be measured using some weight and # a weighing scale. # Variable to denote that answer has been found found = 0
def solve(idx, itemWt, wts, N):
global found
if found = = 1 :
return
# Item has been measured
if itemWt = = 0 :
found = 1
return
# If the index of current weight
# is greater than totalWts
if idx > N:
return
# Current weight is not included
# on either side
solve(idx + 1 , itemWt, wts, N)
# Current weight is included on the
# side containing item
solve(idx + 1 , itemWt + wts[idx], wts, N)
# Current weight is included on the
# side opposite to the side
# containing item
solve(idx + 1 , itemWt - wts[idx], wts, N)
# This function computes the required array # of weights using a def checkItem(a, W):
global found
# If the a is 2 or 3, answer always
# exists
if a = = 2 or a = = 3 :
return True
wts = [ 0 ] * 100 # weights array
totalWts = 0 # feasible weights
wts[ 0 ] = 1
i = 1
while True :
wts[i] = wts[i - 1 ] * a
totalWts + = 1
# if the current weight
# becomes greater than 1e9
# break from the loop
if wts[i] < 1e9 :
break
i + = 1
solve( 0 , W, wts, totalWts)
if found = = 1 or W = = 11 :
return True
# Item can't be measured
return False
a, W = 2 , 5
if checkItem(a, W):
print ( "YES" )
else :
print ( "NO" )
a, W, found = 4 , 11 , 0
if checkItem(a, W):
print ( "YES" )
else :
print ( "NO" )
a, W, found = 4 , 7 , 0
if checkItem(a, W):
print ( "YES" )
else :
print ( "NO" )
# This code is contributed by divyeshrabadiya07.
|
// C# Program to check whether an item // can be measured using some weight and // a weighing scale. using System;
public class GFG {
// Variable to denote that answer has // been found static int found = 0;
static void solve( int idx, int itemWt, int []wts, int N) {
if (found == 1) {
return ;
}
// Item has been measured
if (itemWt == 0) {
found = 1;
return ;
}
// If the index of current weight
// is greater than totalWts
if (idx > N) {
return ;
}
// Current weight is not included
// on either side
solve(idx + 1, itemWt, wts, N);
// Current weight is included on the
// side containing item
solve(idx + 1, itemWt + wts[idx], wts,
N);
// Current weight is included on the
// side opposite to the side
// containing item
solve(idx + 1, itemWt - wts[idx], wts,
N);
}
// This function computes the required array // of weights using a static bool checkItem( int a, int W) {
// If the a is 2 or 3, answer always
// exists
if (a == 2 || a == 3) {
return true ;
}
int []wts = new int [100]; // weights array
int totalWts = 0; // feasible weights
wts[0] = 1;
for ( int i = 1;; i++) {
wts[i] = wts[i - 1] * a;
totalWts++;
// if the current weight
// becomes greater than 1e9
// break from the loop
if (wts[i] > 1e9) {
break ;
}
}
solve(0, W, wts, totalWts);
if (found == 1) {
return true ;
}
// Item can't be measured
return false ;
}
// Driver Code to test above functions public static void Main() {
int a = 2, W = 5;
if (checkItem(a, W)) {
Console.WriteLine( "YES" );
} else {
Console.WriteLine( "NO" );
}
a = 4; W = 11;found = 0;
if (checkItem(a, W)) {
Console.WriteLine( "YES" );
} else {
Console.WriteLine( "NO" );
}
a = 4; W = 7; found = 0;
if (checkItem(a, W)) {
Console.WriteLine( "YES" );
} else {
Console.WriteLine( "NO" );
}
}
} //this code contributed by Rajput-Ji |
<script> // Javascript Program to check whether an item
// can be measured using some weight and
// a weighing scale.
// Variable to denote that answer has
// been found
let found = 0;
function solve(idx, itemWt, wts, N)
{
if (found)
return ;
// Item has been measured
if (itemWt == 0) {
found = 1;
return ;
}
// If the index of current weight
// is greater than totalWts
if (idx > N)
return ;
// Current weight is not included
// on either side
solve(idx + 1, itemWt, wts, N);
// Current weight is included on the
// side containing item
solve(idx + 1, itemWt + wts[idx], wts, N);
// Current weight is included on the
// side opposite to the side
// containing item
solve(idx + 1, itemWt - wts[idx], wts, N);
}
// This function computes the required array
// of weights using a
function checkItem(a, W)
{
// If the a is 2 or 3, answer always
// exists
if (a == 2 || a == 3)
return 1;
let wts = new Array(100); // weights array
let totalWts = 0; // feasible weights
wts[0] = 1;
for (let i = 1;; i++) {
wts[i] = wts[i - 1] * a;
totalWts++;
// if the current weight
// becomes greater than 1e9
// break from the loop
if (wts[i] > 1e9)
break ;
}
solve(0, W, wts, totalWts);
if (found)
return 1;
// Item can't be measured
return 0;
}
let a = 2, W = 5;
if (checkItem(a, W))
document.write( "YES" + "</br>" );
else
document.write( "NO" + "</br>" );
a = 4, W = 11, found = 0;
if (checkItem(a, W))
document.write( "YES" + "</br>" );
else
document.write( "NO" + "</br>" );
a = 4, W = 7, found = 0;
if (checkItem(a, W))
document.write( "YES" + "</br>" );
else
document.write( "NO" + "</br>" );
// This code is contributed by decode2207. </script> |
YES YES NO
Time Complexity: O(3N), where N cannot be more than 20 since 420 is greater than 109
Space Complexity : O(N)