// 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

*/

const n = matrix.length

const m = matrix[0].length

// 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)

// 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]

for (let i = 1; i < n; i++) {

for (let j = 1; j < m; j++) {

moves[i][j] = Math.min(moves[i - 1][j], moves[i][j - 1]) + matrix[i][j]

}

}

return moves[n - 1][m - 1]

}

export { minCostPath }

// Example

// minCostPath([

// [2, 1],

// [3, 1],

// [4, 2]

// ])

// minCostPath([

// [2, 1, 4],

// [2, 1, 3],

// [3, 2, 1]

// ])