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38 lines
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38 lines
2.0 KiB
HTML
<p>The demons had captured the princess and imprisoned her in <strong>the bottom-right corner</strong> of a <code>dungeon</code>. The <code>dungeon</code> consists of <code>m x n</code> rooms laid out in a 2D grid. Our valiant knight was initially positioned in <strong>the top-left room</strong> and must fight his way through <code>dungeon</code> to rescue the princess.</p>
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<p>The knight has an initial health point represented by a positive integer. If at any point his health point drops to <code>0</code> or below, he dies immediately.</p>
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<p>Some of the rooms are guarded by demons (represented by negative integers), so the knight loses health upon entering these rooms; other rooms are either empty (represented as 0) or contain magic orbs that increase the knight's health (represented by positive integers).</p>
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<p>To reach the princess as quickly as possible, the knight decides to move only <strong>rightward</strong> or <strong>downward</strong> in each step.</p>
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<p>Return <em>the knight's minimum initial health so that he can rescue the princess</em>.</p>
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<p><strong>Note</strong> that any room can contain threats or power-ups, even the first room the knight enters and the bottom-right room where the princess is imprisoned.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2021/03/13/dungeon-grid-1.jpg" style="width: 253px; height: 253px;" />
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<pre>
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<strong>Input:</strong> dungeon = [[-2,-3,3],[-5,-10,1],[10,30,-5]]
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<strong>Output:</strong> 7
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<strong>Explanation:</strong> The initial health of the knight must be at least 7 if he follows the optimal path: RIGHT-> RIGHT -> DOWN -> DOWN.
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> dungeon = [[0]]
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<strong>Output:</strong> 1
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>m == dungeon.length</code></li>
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<li><code>n == dungeon[i].length</code></li>
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<li><code>1 <= m, n <= 200</code></li>
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<li><code>-1000 <= dungeon[i][j] <= 1000</code></li>
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</ul>
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