188. Best Time to Buy and Sell Stock IV


dp
time: O(nk)
space: O(nk)
注意 n/2 這件事

class Solution {
public int maxProfit(int k, int[] prices) {
/*
dp[i][k][0] = max(dp[i-1][k][0], dp[i-1][k][1] + prices[i])
dp[i][k][1] = max(dp[i-1][k][1], dp[i-1][k-1][0] - prices[i])
*/
if (prices == null || prices.length == 0 || prices.length < 2 || k == 0) return 0;
int n = prices.length;
if (k >= n/2) return maxProfit(prices);
int dp[][][] = new int[n][k+1][2];
for (int i = 0; i <= k; i++) {
dp[0][i][0] = 0;
dp[0][i][1] = -prices[0];
}
for (int i = 1; i < n; i++) {
for (int j = 1; j <= k; j++) {
dp[i][j][0] = Math.max(dp[i-1][j][0], dp[i-1][j][1] + prices[i]);
dp[i][j][1] = Math.max(dp[i-1][j][1], dp[i-1][j-1][0] - prices[i]);
}
}
return dp[n-1][k][0];
}
private int maxProfit(int[] prices) {
int res = 0;
for (int i = 1; i < prices.length; i++) {
if (prices[i] > prices[i - 1]) {
res += prices[i] - prices[i - 1];
}
}
return res;
}
}
more simple
因為其實只用到 i 天和 i-1 的資料, 所以第一維可以去掉
time: O(nk)
space: O(nk)
class Solution {
public int maxProfit(int k, int[] prices) {
/*
dp[i][k][0] = max(dp[i-1][k][0], dp[i-1][k][1] + prices[i])
dp[i][k][1] = max(dp[i-1][k][1], dp[i-1][k-1][0] - prices[i])
*/
if (prices == null || prices.length == 0 || prices.length < 2 || k == 0) return 0;
int n = prices.length;
if (k >= n/2) return maxProfit(prices);
int dp[][] = new int[k+1][2];
for (int i = 0; i <= k; i++) {
dp[i][0] = 0;
dp[i][1] = -prices[0];
}
int res = Integer.MIN_VALUE;
for (int i = 1; i < n; i++) {
for (int j = 1; j <= k; j++) {
dp[j][0] = Math.max(dp[j][0], dp[j][1] + prices[i]);
dp[j][1] = Math.max(dp[j][1], dp[j-1][0] - prices[i]);
}
}
for (int i = 1; i < n; i++) {
for (int j = 0; j <= k; j++) {
res = Math.max(res, dp[j][0]);
}
}
return dp[k][0];
}
private int maxProfit(int[] prices) {
int res = 0;
for (int i = 1; i < prices.length; i++) {
if (prices[i] > prices[i - 1]) {
res += prices[i] - prices[i - 1];
}
}
return res;
}
}
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