C程式的蛋掉落謎題 - DP-11

這是一個著名的難題。假設有一棟 n 層樓的建築，如果我們有 m 個雞蛋，那麼我們如何找到可以安全地將雞蛋掉落而不打破雞蛋的樓層所需的最少掉落次數。

有一些重要的要點需要記住 -

• 當雞蛋沒有從給定的樓層破裂時，那麼它在任何較低的樓層也不會破裂。
• 如果一個雞蛋從給定的樓層破裂，那麼它也會在所有上面的樓層破裂。
• 當雞蛋破裂時，它必須被丟棄，否則我們可以再次使用它。

輸入- 雞蛋數量和最大樓層。假設雞蛋數量為 4，最大樓層為 10。

輸出- 最小試驗次數 4。

演算法

eggTrialCount(雞蛋，樓層)

#輸入− 雞蛋數量、最大樓層。

輸出 − 取得雞蛋的最小數量試驗。

Begin
   define matrix of size [eggs+1, floors+1]
   for i:= 1 to eggs, do
      minTrial[i, 1] := 1
      minTrial[i, 0] := 0
   done
   for j := 1 to floors, do
      minTrial[1, j] := j
   done
   for i := 2 to eggs, do
      for j := 2 to floors, do
         minTrial[i, j] := ∞
         for k := 1 to j, do
            res := 1 + max of minTrial[i-1, k-1] and minTrial[i, j-k]
            if res < minTrial[i, j], then minTrial[i,j] := res
         done
      done
   done
   return minTrial[eggs, floors]
End

範例

 即時示範

#include<stdio.h>
#define MAX_VAL 9999
int max(int a, int b) {
   return (a > b)? a: b;
}
int eggTrialCount(int eggs, int floors) { //minimum trials for worst case
   int minTrial[eggs+1][floors+1]; //to store minimum trials for i-th egg
   and jth floor
   int res, i, j, k;
   for (i = 1; i <= eggs; i++) { //one trial to check from first floor, and
      no trial for 0th floor
      minTrial[i][1] = 1;
      minTrial[i][0] = 0;
   }
   for (j = 1; j <= floors; j++) //when egg is 1, we need 1 trials for
      each floor
      minTrial[1][j] = j;
   for (i = 2; i <= eggs; i++){ //for 2 or more than 2 eggs
      for (j = 2; j <= floors; j++) { //for second or more than second
         floor
         minTrial[i][j] = MAX_VAL;
         for (k = 1; k <= j; k++) {
            res = 1 + max(minTrial[i-1][k-1], minTrial[i][j-k]);
            if (res < minTrial[i][j])
               minTrial[i][j] = res;
         }
      }
   }
   return minTrial[eggs][floors]; //number of trials for asked egg and
   floor
}
int main () {
   int egg, maxFloor;
   printf("Enter number of eggs: ");
   scanf("%d", &egg);
   printf("Enter max Floor: ");
   scanf("%d", &maxFloor);
   printf("Minimum number of trials: %d", eggTrialCount(egg, maxFloor));
}

輸出

Enter number of eggs: 4
Enter max Floor: 10
Minimum number of trials: 4

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