Daily Coding Sixty Two

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Dearest Corinthia, twas’t been a fortnite ‘til eyes lain upon. I yurn once more for to gaze upon your coding solution to a rando email. Ever yours, Dwayne Wyatt Evernly VI, Esq. 

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/*
There is an N by M matrix of zeroes. Given N and M, write a function to count the number of ways of starting at the top-left corner and getting to the bottom-right corner. You can only move right or down.

For example, given a 2 by 2 matrix, you should return 2, since there are two ways to get to the bottom-right:

Right, then down
Down, then right
Given a 5 by 5 matrix, there are 70 ways to get to the bottom-right.
*/

function countWays(N, M) {
    // create a zero'd out 2D array 'matrix' with dimensions N x M 
    const matrix = Array.from({ length: N }, () => Array(M).fill(0));
    
    matrix[0][0] = 1;

    // fill the Matrix...*whoa*
    for (let i = 0; i < N; i++) {
        for (let j = 0; j < M; j++) {
            // If moving right is possible
            if (j > 0) {
                matrix[i][j] += matrix[i][j - 1];
            }
            // If moving down is possible
            if (i > 0) {
                matrix[i][j] += matrix[i - 1][j];
            }
        }
    }

    // the bottom-right corner will have the number of ways to reach it
    return matrix[N - 1][M - 1];
}

Running this a few times netted:

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console.log(countWays(2, 2)); // Output: 2
console.log(countWays(5, 5)); // Output: 70
console.log(countWays(10,3)); // Output: 55
console.log(countWays(18,10)); // Output 3124550