Friday, September 30, 2016
Show all combinations of numbers from 1 to 9 that add up to 100 by adding subtracting and concatenating
Show all combinations of numbers from 1 to 9 that add up to 100 by adding subtracting and concatenating
So, this week I saw a blog post somewhere where the poster claimed that if you cant solve the mentioned 5 problems each in under and hour, you aint no programmer, dev or software engineer. So, I went in and read the problems. 1-4 were easy but number 5 got me a worrying a little. And expected, I failed to solve that in under 1 hour yesterday. But today morning I solved that in less than 30 minutes. But whatever, I cant call myself a programmer anymore :(
Heres my approach though, using recursion:
Each i (from 1 through 9) has 2 different ways of connecting to the sequence.
1. Add itself to the closest sum (1 + 23 + 4 + .......)
2. Or concatenate itself (1 + 234 + ......)
So if we either add an i to the sequence that has reached it or we concatenate. Examples: .......8 + 9
.......89
Now the part before 8 has the same behavior with 8
.......7 + 8
.......78
This goes all the way back to 1 and 2
1 + 2
12
So, the program works something like this
Each branch ultimately ends on the leftmost call.
Code:
Heres my approach though, using recursion:
Each i (from 1 through 9) has 2 different ways of connecting to the sequence.
1. Add itself to the closest sum (1 + 23 + 4 + .......)
2. Or concatenate itself (1 + 234 + ......)
So if we either add an i to the sequence that has reached it or we concatenate. Examples: .......8 + 9
.......89
Now the part before 8 has the same behavior with 8
.......7 + 8
.......78
This goes all the way back to 1 and 2
1 + 2
12
So, the program works something like this

Code:
#include <cstdio>
#include <iostream>
#include <sstream>
using namespace std;
string i2s(int i) {
stringstream op;
op << i;
return op.str();
}
int solveS(int i, int sum, string p) {
if (i >= 10) {
if (sum == 100) {
cout << p + " = " << sum << endl;
}
return 0;
}
int iSum = 0;
for (int j = i ; j<=9 ; j++) {
iSum = iSum * 10 + j;
if (i == 1) {
solveS(j+1, iSum, i2s(iSum));
} else {
solveS(j+1, sum+iSum, p + " + " + i2s(iSum));
solveS(j+1, sum-iSum, p + " - " + i2s(iSum));
}
}
return 0;
}
int main() {
//freopen("output.txt", "w+", stdout);
solveS(1, 0, "");
return 0;
}
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