Reporting Reduces to Decision

Assume that subset-sum ({a1,…,an},b) is true X := the empty set;

for i = 1 to n do

if subset-sum({ai+1,…,an},b - ai) then

add i to X;

b := b - ai;

Example: 3, 5, 2, 7, 4, 2, b = 11

5, 2, 7, 4, 2, b = 11-3 --> yes, X = {3}, b = 8

2, 7, 4, 2, b = 8-5 --> no

7, 4, 2, b = 8-2 --> yes, X = {3,2}, b = 6

4, 2, b = 6-7 --> no

2, b = 6-4 --> yes, X = {3,2,4}, b = 2

b = 4 -2 --> yes, X ={3,2,4,2}

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