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solution.js
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/* 2x2 = 2
0 0
0 0
*/
/* 2x3 = 3 ; s(2, 3) = s(1, 3) + s(2, 2)
0 0 0
0 0 0
*/
/* 2x4 = 4 ; s(2, 4) = s(1, 4) + s(2, 3) = 4
0 0 0 0
0 0 0 0
*/
/* 2x5 = 5 ; s(1, 5) + s(2, 4)
0 0 0 0 0
0 0 0 0 0
*/
/* 3x3 = 6; S(3,3) = S(2,3) + S(3,2)
0 0 0
0 0 0
0 0 0
*/
/* 3x4 = s(2, 4) + s(3, 3) = 10
0 0 0 0
0 0 0 0
0 0 0 0
*/
/* 3x5 = s(2, 5) + s(3, 4) = 15
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
*/
/* 4x2 = s(3, 2) + s(4, 1) = 4
0 0
0 0
0 0
0 0
*/
/* 4x4 = s(3, 4) + s(4, 3) = 20
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
*/
/* 4x5 = s(3, 5) + s(4, 4) = 35
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
*/
/* 5x5 = s(4, 5) + s(5, 4) = 70
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
*/
function numPaths(numRows, numColumns) {
const solutions = new Array(numRows);
for (i = 0; i < numRows; i++) {
solutions[i] = new Array(numColumns);
for (j = 0; j < numColumns; j++) {
if (i === 0 || j === 0) solutions[i][j] = 1;
else solutions[i][j] = solutions[i - 1][j] + solutions[i][j - 1];
}
}
return solutions[numRows - 1][numColumns - 1];
}
console.log(numPaths(5, 5)); // 70
console.log(numPaths(2, 2)); // 2
console.log(numPaths(3, 5)); // 15
console.log(numPaths(5, 3)); // 15