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142 lines (128 loc) · 66.3 KB
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/**
* Difficulty:
* Hard
*
* Desc:
* The demons had captured the princess (P) and imprisoned her in the bottom-right corner of a dungeon.
* The dungeon consists of M x N rooms laid out in a 2D grid. Our valiant knight (K) was initially positioned in the top-left room and must fight his way through the dungeon to rescue the princess.
* The knight has an initial health point represented by a positive integer.
* If at any point his health point drops to 0 or below, he dies immediately.
* Some of the rooms are guarded by demons,
* so the knight loses health (negative integers) upon entering these rooms;
* other rooms are either empty (0's) or contain magic orbs that increase the knight's health (positive integers).
* In order to reach the princess as quickly as possible,
* the knight decides to move only rightward or downward in each step.
* Write a function to determine the knight's minimum initial health so that he is able to rescue the princess.
*
* Example:
* given the dungeon below,
* [
* [-2(K), -3, 3],
* [-5, -10, 1],
* [10, 30, -5(P)]
* ]
* the initial health of the knight must be at least 7 if he follows the optimal path RIGHT-> RIGHT -> DOWN -> DOWN.
*
* 考察 DP。注意，递归方法会超时；循环的方法可以成功通过
*/
let calculateMinimumHP;
/* ====================== 递归版本，会超时！ ====================== */
/**
* @param {number[][]} dungeon
* @return {number}
*/
calculateMinimumHP = (dungeon) => {
const cache = [];
const healthNeeded = [];
const maxY = dungeon.length - 1;
const maxX = dungeon[0].length - 1;
let minHealth = Infinity;
// nextNeeded: 走过当前格后所剩下的最少血量
const goNext = (x, y, nextNeeded) => {
const point = dungeon[y][x];
// preNeeded: 能够成功走到当前格所需的最少血量
let preNeeded;
if (nextNeeded > point) {
preNeeded = nextNeeded - point;
} else {
preNeeded = 1;
}
if (!healthNeeded[y]) {
healthNeeded[y] = [];
healthNeeded[y][x] = preNeeded;
} else if (healthNeeded[y][x] === undefined) {
healthNeeded[y][x] = preNeeded;
} else if (healthNeeded[y][x] > preNeeded) {
healthNeeded[y][x] = preNeeded;
} else {
return;
}
if (y === 0 && x === 0) return;
if (x > 0) goNext(x - 1, y, preNeeded);
if (y > 0) goNext(x, y - 1, preNeeded);
};
goNext(maxX, maxY, 1);
console.log(healthNeeded[0][0])
return healthNeeded[0][0];
};
/* ====================== 循环版本，成功通过 ====================== */
const getPoint = (point, needed) => {
let result;
if (needed > point) {
result = needed - point;
} else {
result = 1;
}
return result;
};
/**
* @param {number[][]} dungeon
* @return {number}
*/
calculateMinimumHP = (dungeon) => {
const healthNeeded = [];
const maxY = dungeon.length - 1;
const maxX = dungeon[0].length - 1;
for (let i = maxY; i >= 0; i -= 1) {
healthNeeded[i] = [];
for (let j = maxX; j >= 0; j -= 1) {
const point = dungeon[i][j];
if (i === maxY && j === maxX) {
healthNeeded[i][j] = getPoint(point, 1);
} else if (j === maxX) {
healthNeeded[i][j] = getPoint(point, healthNeeded[i + 1][j]);
} else if (i === maxY) {
healthNeeded[i][j] = getPoint(point, healthNeeded[i][j + 1]);
} else {
healthNeeded[i][j] = Math.min(
getPoint(point, healthNeeded[i + 1][j]),
getPoint(point, healthNeeded[i][j + 1])
);
}
}
}
return healthNeeded[0][0];
};
// Test case
calculateMinimumHP([
[-2, -3, 3],
[-5, -10, 1],
[10, 30, -5]
]);
calculateMinimumHP([[-3,5]]);
calculateMinimumHP([
[0,-5],
[0,0]
]);
calculateMinimumHP([
[3,0,-3],
[-3,-2,-2],
[3,1,-3]
]);
calculateMinimumHP([
[3,-20,30],
[-3,4,0]
]);
calculateMinimumHP(
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