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| 1 | +You are given K eggs, and you have access to a building with N floors from 1 to N. |
| 2 | + |
| 3 | +Each egg is identical in function, and if an egg breaks, you cannot drop it again. |
| 4 | + |
| 5 | +You know that there exists a floor F with 0 <= F <= N such that any egg dropped at a floor higher than F will break, and any egg dropped at or below floor F will not break. |
| 6 | + |
| 7 | +Each move, you may take an egg (if you have an unbroken one) and drop it from any floor X (with 1 <= X <= N). |
| 8 | + |
| 9 | +Your goal is to know with certainty what the value of F is. |
| 10 | + |
| 11 | +What is the minimum number of moves that you need to know with certainty what F is, regardless of the initial value of F? |
| 12 | + |
| 13 | + |
| 14 | + |
| 15 | +Example 1: |
| 16 | + |
| 17 | +Input: K = 1, N = 2 |
| 18 | +Output: 2 |
| 19 | +Explanation: |
| 20 | +Drop the egg from floor 1. If it breaks, we know with certainty that F = 0. |
| 21 | +Otherwise, drop the egg from floor 2. If it breaks, we know with certainty that F = 1. |
| 22 | +If it didn't break, then we know with certainty F = 2. |
| 23 | +Hence, we needed 2 moves in the worst case to know what F is with certainty. |
| 24 | +Example 2: |
| 25 | + |
| 26 | +Input: K = 2, N = 6 |
| 27 | +Output: 3 |
| 28 | +Example 3: |
| 29 | + |
| 30 | +Input: K = 3, N = 14 |
| 31 | +Output: 4 |
| 32 | + |
| 33 | + |
| 34 | +Note: |
| 35 | + |
| 36 | +1 <= K <= 100 |
| 37 | +1 <= N <= 10000 |
| 38 | + |
| 39 | + |
| 40 | + |
| 41 | + |
| 42 | + |
| 43 | + |
| 44 | +// DP (TLE) |
| 45 | + |
| 46 | +class Solution { |
| 47 | +public: |
| 48 | + // k=e=egg n=f=floor |
| 49 | + int superEggDrop(int e, int f) { |
| 50 | + int dp[e+1][f+1]; |
| 51 | + |
| 52 | + for(int i=0;i<e+1;i++){ |
| 53 | + dp[i][0]=0; // 0 floors |
| 54 | + dp[i][1]=1; // 1 floor |
| 55 | + } |
| 56 | + for(int j=1;j<f+1;j++){ |
| 57 | + dp[0][j]=0; // 0 egg |
| 58 | + dp[1][j]=j; |
| 59 | + } |
| 60 | + |
| 61 | + for(int i=2;i<e+1;i++){ |
| 62 | + for(int j=2;j<f+1;j++){ |
| 63 | + dp[i][j]=INT_MAX; |
| 64 | + for(int x=1;x<=j;x++){ |
| 65 | + int tmp=1+max(dp[i-1][x-1], dp[i][j-x]); |
| 66 | + if(tmp<dp[i][j]) dp[i][j]=tmp; |
| 67 | + } |
| 68 | + } |
| 69 | + } |
| 70 | + return dp[e][f]; |
| 71 | + } |
| 72 | +}; |
| 73 | + |
| 74 | + |
| 75 | + |
| 76 | + |
| 77 | +// Recursive (Memoized) (TLE) |
| 78 | + |
| 79 | +class Solution { |
| 80 | +public: |
| 81 | + int dp[101][10001]; // according to the constraints |
| 82 | + |
| 83 | + int eggDrop(int e, int f, int dp[][10001]){ |
| 84 | + if(e==1 || e==0) return f; |
| 85 | + if(f==0 || f==1) return f; |
| 86 | + |
| 87 | + if(dp[e][f]!=-1) return dp[e][f]; |
| 88 | + |
| 89 | + int mini=INT_MAX; |
| 90 | + int egb, egnb; |
| 91 | + for(int k=1;k<=f;k++){ |
| 92 | + if(dp[e-1][k-1]!=-1) egb=dp[e-1][k-1]; |
| 93 | + else { |
| 94 | + egb=eggDrop(e-1, k-1, dp); |
| 95 | + dp[e-1][k-1]=egb; |
| 96 | + } |
| 97 | + if(dp[e][f-k]!=-1) egnb=dp[e][f-k]; |
| 98 | + else { |
| 99 | + egnb=eggDrop(e, f-k, dp); |
| 100 | + dp[e][f-k]=egnb; |
| 101 | + } |
| 102 | + |
| 103 | + int tmp = 1 + max(egb, egnb); |
| 104 | + if(tmp<mini) mini=tmp; |
| 105 | + } |
| 106 | + return dp[e][f]=mini; |
| 107 | + } |
| 108 | + |
| 109 | + |
| 110 | + // k=e=eggs n=f=floor |
| 111 | + int superEggDrop(int e, int f) { |
| 112 | + memset(dp, -1, sizeof(dp)); |
| 113 | + return eggDrop(e, f, dp); |
| 114 | + } |
| 115 | +}; |
| 116 | + |
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