Given a rope of length n meters, cut the rope in different parts of integer lengths in a way that maximizes product of lengths of all parts. You must make at least one cut. Assume that the length of rope is more than 2 meters.
Examples:
Input: n = 2
Output: 1 (Maximum obtainable product is 1*1)
Input: n = 3
Output: 2 (Maximum obtainable product is 1*2)
Input: n = 4
Output: 4 (Maximum obtainable product is 2*2)
Input: n = 5
Output: 6 (Maximum obtainable product is 2*3)
Input: n = 10
Output: 36 (Maximum obtainable product is 3*3*4)
class Solution {
// Given n>=2
public static int maxProd(int n) {
int dp[] = new int[n + 1];
dp[1] = 1;
dp[2] = 1;
// dp[i] -> max product we can get with length i
for (int i = 3; i <= n; i++) {
// min multiplication will be 1 ,when rod cut into peices of 1
dp[i] = 1;
for (int j = 1; j < i; j++)
dp[i] = Math.max(dp[i], Math.max(j, dp[j]) * (i - j));
}
return dp[n];
}
}