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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.
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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.
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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).
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In order to reach the princess as quickly as possible, the knight decides to move only rightward or downward in each step.
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Write a function to determine the knight's minimum initial health so that he is able to rescue the princess.
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For example, given the dungeon below, 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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-2 (K) -3 3
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-5 -10 1
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10 30 -5 (P)
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Notes:
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The knight's health has no upper bound.
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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.
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Solution: ...
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*/
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publicclassSolution {
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publicintcalculateMinimumHP(int[][]dungeon) {
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intM =dungeon.length;
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if (M ==0)return0;
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intN =dungeon[0].length;
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int[][]dp =newint[M][N];
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dp[M-1][N-1] =1 -Math.min(0,dungeon[M-1][N-1]);
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for (inti =M -2;i >=0; --i) {
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if (dp[i+1][N-1] -dungeon[i][N-1] <0)dp[i][N-1] =1;
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elsedp[i][N-1] =dp[i+1][N-1] -dungeon[i][N-1];
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}
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for (intj =N -2;j >=0; --j) {
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if (dp[M-1][j+1] -dungeon[M-1][j] <0)dp[M-1][j] =1;
