動態規劃—組合成指定值
阿新 • • 發佈:2019-02-03
You are given coins of different denominations and a total amount of money. Write a function to compute the number of combinations that make up that amount. You may assume that you have infinite number of each kind of coin.
Note: You can assume that
- 0 <= amount <= 5000
- 1 <= coin <= 5000
- the number of coins is less than 500
- the answer is guaranteed to fit into signed 32-bit integer
Example 1:
Input: amount = 5, coins = [1, 2, 5] Output: 4 Explanation: there are four ways to make up the amount: 5=5 5=2+2+1 5=2+1+1+1 5=1+1+1+1+1
Example 2:
Input: amount = 3, coins = [2] Output: 0 Explanation: the amount of 3 cannot be made up just with coins of 2.
Example 3:
Input: amount = 10, coins = [10] Output: 1
題目:target sumclass Solution { public: int change(int amount, vector<int>& coins) { int len=coins.size(); //注意對邊界條件的判斷,len=0,amount=0,時認為方案數量為1,而非0 vector<int> dp(amount+1,0); dp[0]=1; for(int i=0;i<len;i++) { for(int j=coins[i];j<=amount;j++) { dp[j]+=dp[(j-coins[i])]; } } return dp[amount]; } };
You are given a list of non-negative integers, a1, a2, ..., an, and a target, S. Now you have 2 symbols +
and -
.
For each integer, you should choose one from +
and -
as
its new symbol.
Find out how many ways to assign symbols to make sum of integers equal to target S.
Example 1:
Input: nums is [1, 1, 1, 1, 1], S is 3. Output: 5 Explanation: -1+1+1+1+1 = 3 +1-1+1+1+1 = 3 +1+1-1+1+1 = 3 +1+1+1-1+1 = 3 +1+1+1+1-1 = 3 There are 5 ways to assign symbols to make the sum of nums be target 3.
Note:
- The length of the given array is positive and will not exceed 20.
- The sum of elements in the given array will not exceed 1000.
- Your output answer is guaranteed to be fitted in a 32-bit integer.