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Commit b73ddec

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Add Pascal's Triangle based solution for Unique Paths problem.
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‎README.md‎

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* `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
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* `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - in-place algorithm
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* `B` [Jump Game](src/algorithms/uncategorized/jump-game) - backtracking, dynamic programming (top-down + bottom-up) and greedy examples
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* `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) - backtracking and dynamic programming examples
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* `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) - backtracking, dynamic programming and Pascal's Triangle based examples
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* `A` [N-Queens Problem](src/algorithms/uncategorized/n-queens)
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* `A` [Knight's Tour](src/algorithms/uncategorized/knight-tour)
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‎src/algorithms/uncategorized/unique-paths/README.md‎

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**Auxiliary Space Complexity**: `O(m * n)` - since we need to have DP matrix.
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### Pascal's Triangle Based
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This question is actually another form of Pascal Triangle.
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The corner of this rectangle is at `m + n - 2` line, and
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at `min(m, n) - 1` position of the Pascal's Triangle.
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## References
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- [LeetCode](https://leetcode.com/problems/unique-paths/description/)
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import uniquePaths from '../uniquePaths';
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describe('uniquePaths', () => {
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it('should find the number of unique paths on board', () => {
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expect(uniquePaths(3, 2)).toBe(3);
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expect(uniquePaths(7, 3)).toBe(28);
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expect(uniquePaths(3, 7)).toBe(28);
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expect(uniquePaths(10, 10)).toBe(48620);
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expect(uniquePaths(100, 1)).toBe(1);
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expect(uniquePaths(1, 100)).toBe(1);
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});
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});
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import pascalTriangle from '../../math/pascal-triangle/pascalTriangle';
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/**
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* @param {number} width
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* @param {number} height
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* @return {number}
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*/
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export default function uniquePaths(width, height) {
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const pascalLine = width + height - 2;
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const pascalLinePosition = Math.min(width, height) - 1;
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return pascalTriangle(pascalLine)[pascalLinePosition];
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}

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