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Add N queens problem bitwise solution #15

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Aug 20, 2018
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9 changes: 9 additions & 0 deletions src/algorithms/uncategorized/n-queens-bitwise/README.md
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# N-Queens Problem with Bitwise Solution

Write a function that will find all possible solutions to the N queens problem for a given N.

## References

- [Wikipedia](https://en.wikipedia.org/wiki/Eight_queens_puzzle)
- [GREG TROWBRIDGE](http://gregtrowbridge.com/a-bitwise-solution-to-the-n-queens-problem-in-javascript/)
- [Backtracking Algorithms in MCPL using Bit Patterns and Recursion](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.51.7113&rep=rep1&type=pdf)
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import nQueensBitwise from '../nQueensBitwise';

describe('nQueensBitwise', () => {
it('should have solutions for 4 to N queens', () => {
const solutionFor4 = nQueensBitwise(4);
expect(solutionFor4).toBe(2);

const solutionFor5 = nQueensBitwise(5);
expect(solutionFor5).toBe(10);

const solutionFor6 = nQueensBitwise(6);
expect(solutionFor6).toBe(4);

const solutionFor7 = nQueensBitwise(7);
expect(solutionFor7).toBe(40);

const solutionFor8 = nQueensBitwise(8);
expect(solutionFor8).toBe(92);

const solutionFor9 = nQueensBitwise(9);
expect(solutionFor9).toBe(352);

const solutionFor10 = nQueensBitwise(10);
expect(solutionFor10).toBe(724);
});
});
33 changes: 33 additions & 0 deletions src/algorithms/uncategorized/n-queens-bitwise/nQueensBitwise.js
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export default function (n) {
// Keeps track of the # of valid solutions
let count = 0;

// Helps identify valid solutions
const done = (2 ** n) - 1;

// Checks all possible board configurations
const innerRecurse = (ld, col, rd) => {
// All columns are occupied,
// so the solution must be complete
if (col === done) {
count += 1;
return;
}

// Gets a bit sequence with "1"s
// whereever there is an open "slot"
let poss = ~(ld | rd | col);

// Loops as long as there is a valid
// place to put another queen.
while (poss & done) {
const bit = poss & -poss;
poss -= bit;
innerRecurse((ld | bit) >> 1, col | bit, (rd | bit) << 1);
}
};

innerRecurse(0, 0, 0);

return count;
}