LintCode 440 · Backpack III.java

Backpack with Value array:
note that now you can take k times, or "infinite times"
function:
dp[i][j] = Math.max(dp[i - 1][j - A[i - 1] * k] + V[i - 1] * k, dp[i][j]); (when you take that ith item)
or
dp[i][j] += dp[i - 1][j]; (when you don't take that ith item)

	public class Solution {
	/**
	* @param A: an integer array
	* @param V: an integer array
	* @param m: An integer
	* @return: an array
	*/
	public int backPackIII(int[] A, int[] V, int m) {
	// write your code here
	if (A == null || A.length == 0) {
	return 0;
	}
	int n = A.length;
	// init
	int[][] dp = new int[n+1][m+1];
	dp[0][0] = 0;
	for (int j = 1; j <= m; j++) {
	dp[0][j] = 0;
	}
	// dp: functions
	int maximumJ = Integer.MIN_VALUE;
	for (int i = 1; i <= n; i++) {
	dp[i][0] = 0;
	for (int j = 1; j <= m; j++) {
	dp[i][j] = dp[i - 1][j];
	int k = 1;
	while (j - A[i-1] * k >= 0) {
	dp[i][j] = Math.max(dp[i - 1][j - A[i - 1] * k] + V[i - 1] * k, dp[i][j]);
	k++;
	}
	}
	}
	// dp: answer
	return dp[n][m];
	}
	}

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