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w-dp-uniquePaths-MaxProfit-leetcode62.js
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// 1. objective func: f(n) return max profit
// 2. base cases:
// f([1,1]) = 1
// f([2,2]) = 2
// 3. recurrent func:
// f(y,x) = f[y][x] + Math.max(f(y-1,x) + f(x-1,y))
// 4. order:
// bottom up
// 5. result: f(y-1,x-1)
[
[0, 2, 4, 5],
[3, 4, 5, 6],
[7, 11, 13, 13],
];
////////////////////////////////////// FIND MAX PROFIT
const traceMaxProfit = (grid) => {
// get max profit
for (y = 0; y < grid.length; y++) {
for (x = 0; x < grid[y].length; x++) {
grid[y][x] === "S" && (grid[y][x] = 0);
grid[y][x] === "E" && (grid[y][x] = 0);
if (grid[y - 1] === undefined && grid[y][x - 1] === undefined) {
continue;
} else if (grid[y - 1] === undefined) {
grid[y][x] += grid[y][x - 1];
} else if (grid[y][x - 1] === undefined) {
grid[y][x] += grid[y - 1][x];
} else {
grid[y][x] += Math.max(grid[y - 1][x], grid[y][x - 1]);
}
}
}
// trace back to find path
const stack = [[grid.length - 1, grid[0].length - 1]];
while (stack.length > 0) {
console.log(stack);
let [y, x] = stack.pop();
if (y === 0 && x === 0) {
grid[y][x] = "x";
break;
}
if (y === 0) {
grid[y][x] = "x";
stack.push([y, x - 1]);
continue;
}
if (x === 0) {
grid[y][x] = "x";
stack.push([y - 1, x]);
continue;
}
if (y > 0 && x > 0) {
grid[y - 1][x] > grid[y][x - 1] &&
(grid[y - 1][x] = "x") &&
stack.push([y - 1, x]);
grid[y - 1][x] < grid[y][x - 1] &&
(grid[y][x - 1] = "x") &&
stack.push([y, x - 1]);
continue;
}
}
console.log(stack);
console.log(grid);
// for (y = grid.length - 1; y >= 0; y--) {
// for (x = grid[y].length - 1; x >= 0; x--) {
// if (y === 0 && x === 0) {
// grid[y][x] = "x";
// } else if (y === 0) {
// // grid[y][x] = "x";
// // continue;
// } else if (x === 0) {
// // grid[y][x] = "x";
// // continue;
// } else {
// grid[y - 1][x] > grid[y][x - 1] && (grid[y - 1][x] = "x");
// grid[y - 1][x] < grid[y][x - 1] && (grid[y][x - 1] = "x");
// }
// }
// }
console.log(grid);
return grid;
};
// const gridT = [
// ["S", 2, 2, 1],
// [3, 1, 1, 1],
// [4, 4, 2, "E"],
// ];
const gridT = [
["S", 2, 2, 1],
[3, 1, 1, 1],
[4, 4, 2, "E"],
];
traceMaxProfit(gridT);
//
// ////////////////////////////////////// FIND MAX PROFIT
// const maxProfit = (grid) => {
// for (y = 0; y < grid.length; y++) {
// for (x = 0; x < grid[y].length; x++) {
// grid[y][x] === "S" && (grid[y][x] = 0);
// grid[y][x] === "E" && (grid[y][x] = 0);
// if (grid[y - 1] === undefined && grid[y][x - 1] === undefined) {
// continue;
// } else if (grid[y - 1] === undefined) {
// grid[y][x] += grid[y][x - 1];
// } else if (grid[y][x - 1] === undefined) {
// grid[y][x] += grid[y - 1][x];
// console.log("222");
// } else {
// grid[y][x] += Math.max(grid[y - 1][x], grid[y][x - 1]);
// }
// }
// }
// console.log(grid[y - 1][x - 1]);
// return grid[y - 1][x - 1];
// };
// const grid = [
// ["S", 2, 2, 1],
// [3, 1, 1, 1],
// [4, 4, 2, "E"],
// ];
// maxProfit(grid);