Objective: Given a sorted array of positive integers, find out the smallest integer which cannot be represented as the sum of any subset of the array
Input: A Sorted Array
Output: The smallest number which cannot be represented as the sum of any subset of the given array
Examples :
Array {1,1,3,4,6,7,9} smallest Number : 32
Array {1,1,1,1,1} smallest Number : 6
Array {2,3,6,7} smallest Number : 1
Array {1,2,6,7,9} smallest Number : 4
Approach:
- If 1 is not present in the array, our answer is 1.
- So take a variable “smlNumber” and assign 1 to it.
- Now we need to find the gap between the array elements which cannot be represented as sum of any subset of array.
- To find that keep adding the array elements to smlNumber and check it current array element and if at any point smlNumber<current array element that means we have found the gap. return smlNumber.
- See figure
Complete Code:
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| public class SmallestIntegerInSortedArray { | |
| public int find(int [] arrA){ | |
| int smlNumber = 1; | |
| for(int i = 0;i<arrA.length;i++){ | |
| if(arrA[i]<=smlNumber){ | |
| smlNumber += arrA[i]; | |
| }else{ | |
| break; | |
| } | |
| } | |
| return smlNumber; | |
| } | |
| public static void main(String arg[]){ | |
| SmallestIntegerInSortedArray i = new SmallestIntegerInSortedArray(); | |
| System.out.println("Smallest Positive Integer that cant be represented by the sum of any subset of following arrays are : "); | |
| int [] arrA = { 1,1,3,4,6,7,9}; | |
| System.out.println("{1,1,3,4,6,7,9} –" + i.find(arrA)); | |
| int [] arrB = {1,1,1,1,1}; | |
| System.out.println("{1,1,1,1,1} –" + i.find(arrB)); | |
| int [] arrC = {2,3,6,7}; | |
| System.out.println("{2,3,6,7} –" + i.find(arrC)); | |
| int [] arrD = {1,2,6,7,9}; | |
| System.out.println("{1,2,6,7,9} –"+ i.find(arrD)); | |
| } | |
| } |
Output:
Smallest Positive Integer that cant be represented by the sum of any subset of following arrays are :
{1,1,3,4,6,7,9} - 32
{1,1,1,1,1} -> 6
{2,3,6,7} -> 1
{1,2,6,7,9} -> 4
http://stackoverflow.com/questions/21060873/minimum-sum-that-cant-be-obtained-from-a-set
Implementation may be simple. but to understand how it works. the above link is helpful