diff --git a/Dynamic-Programming/MinimumCostPath.js b/Dynamic-Programming/MinimumCostPath.js index 3936f0af71..8af0e598dd 100644 --- a/Dynamic-Programming/MinimumCostPath.js +++ b/Dynamic-Programming/MinimumCostPath.js @@ -1,37 +1,46 @@ -// youtube Link -> https://www.youtube.com/watch?v=lBRtnuxg-gU +// Problem Statement => https://www.youtube.com/watch?v=lBRtnuxg-gU const minCostPath = (matrix) => { /* - Find the min cost path from top-left to bottom-right in matrix - >>> minCostPath([[2, 1], [3, 1], [4, 2]]) - 6 - */ + Find the min cost path from top-left to bottom-right in matrix + >>> minCostPath([[2, 1], [3, 1], [4, 2]]) + >>> 6 + */ + const n = matrix.length const m = matrix[0].length - // Preprocessing first row - for (let i = 1; i < m; i++) { - matrix[0][i] += matrix[0][i - 1] - } + // moves[i][j] => minimum number of moves to reach cell i, j + const moves = new Array(n) + for (let i = 0; i < moves.length; i++) moves[i] = new Array(m) - // Preprocessing first column - for (let i = 1; i < n; i++) { - matrix[i][0] += matrix[i - 1][0] - } + // base conditions + moves[0][0] = matrix[0][0] // to reach cell (0, 0) from (0, 0) is of no moves + for (let i = 1; i < m; i++) moves[0][i] = moves[0][i - 1] + matrix[0][i] + for (let i = 1; i < n; i++) moves[i][0] = moves[i - 1][0] + matrix[i][0] - // Updating cost to current position for (let i = 1; i < n; i++) { - for (let j = 1; j < m; j++) { - matrix[i][j] += Math.min(matrix[i - 1][j], matrix[i][j - 1]) - } + for (let j = 1; j < m; j++) { moves[i][j] = Math.min(moves[i - 1][j], moves[i][j - 1]) + matrix[i][j] } } - return matrix[n - 1][m - 1] + return moves[n - 1][m - 1] } const main = () => { - console.log(minCostPath([[2, 1], [3, 1], [4, 2]])) - console.log(minCostPath([[2, 1, 4], [2, 1, 3], [3, 2, 1]])) + console.log( + minCostPath([ + [2, 1], + [3, 1], + [4, 2] + ]) + ) + console.log( + minCostPath([ + [2, 1, 4], + [2, 1, 3], + [3, 2, 1] + ]) + ) } main()