Integer Break问题及解法
2017-09-01 22:48
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问题描述:
Given a positive integer n, break it into the sum of at least two positive integers and maximize the product of those integers. Return the maximum product you can get.
示例:
given n = 2, return 1 (2 = 1 + 1); given n = 10, return 36 (10 = 3 + 3 + 4).
Note: You may assume that n is not less than 2 and not larger than 58.
问题分析:
通过分析发现对于n来说,它的最大乘积dp
是 dp[i] * (n - i) 或 i * (n - i) 中最大的那个, (1<= i <= n - 1).
过程详见代码:
class Solution {
public:
int integerBreak(int n) {
vector<int> dp(n + 1, 1);
for (int i = 2; i <= n; i++)
{
for (int j = 1; j < i; j++)
dp[i] = max(dp[i],max(dp[j] * (i - j), j * (i - j)));
}
return dp
;
}
};
Given a positive integer n, break it into the sum of at least two positive integers and maximize the product of those integers. Return the maximum product you can get.
示例:
given n = 2, return 1 (2 = 1 + 1); given n = 10, return 36 (10 = 3 + 3 + 4).
Note: You may assume that n is not less than 2 and not larger than 58.
问题分析:
通过分析发现对于n来说,它的最大乘积dp
是 dp[i] * (n - i) 或 i * (n - i) 中最大的那个, (1<= i <= n - 1).
过程详见代码:
class Solution {
public:
int integerBreak(int n) {
vector<int> dp(n + 1, 1);
for (int i = 2; i <= n; i++)
{
for (int j = 1; j < i; j++)
dp[i] = max(dp[i],max(dp[j] * (i - j), j * (i - j)));
}
return dp
;
}
};
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