Best time to buy and sell stock

Signed-off-by: Leo Ma <begeekmyfriend@gmail.com>

Author: begeekmyfriend

188_best_time_to_buy_and_sell_stock_iv/Makefile

@@ -0,0 +1,2 @@
+all:
+	gcc -O2 -o test stock.c

188_best_time_to_buy_and_sell_stock_iv/stock.c

@@ -0,0 +1,103 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+static inline int max(int a, int b)
+{
+    return a > b ? a : b;
+}
+
+static int maxProfit(int k, int* prices, int pricesSize)
+{
+    if (pricesSize == 0) {
+        return 0;
+    }
+
+    int i, j;
+    if (k > pricesSize / 2) {
+        /* We can make transactions as many as we can */
+        int total = 0;
+        for (i = 1; i < pricesSize; i++) {
+            if (prices[i] > prices[i - 1]) {
+                total += prices[i] - prices[i - 1];
+            }
+        }
+        return total;
+    } else {
+#if 1
+        /* DP solution - O(kn) complexity
+         * dp[i, j] = max (dp[i, j-1], // same times transactions, but one days before.
+         *                 dp[i-1, t] + prices[j] - prices[t+1])  // for all of (0 <= t < j )
+         *                                                        // this means find max profit from previous any of days
+         */
+        int **dp = malloc((k + 1) * sizeof(int *));
+        for (i = 0; i <= k; i++) {
+            dp[i] = malloc((pricesSize + 1) * sizeof(int));
+            memset(dp[i], 0, (pricesSize + 1) * sizeof(int));
+        }
+
+        for (i = 1; i <= k; i++) {
+//printf("i:%d\n", i);
+//printf("\tprev_profit = %d - %d\n", dp[i - 1][0], prices[0]);
+            int prev_profit = dp[i - 1][0] - prices[0];
+            for (j = 1; j <= pricesSize; j++) {
+//printf("\tj:%d\n", j);
+                dp[i][j] = max(dp[i][j - 1], prev_profit + prices[j - 1]); /* prices[j - 1] means sell on Day j for dp[i][j] */
+//printf("\tdp[%d][%d] = max(%d, %d + %d)\n", i, j, dp[i][j - 1], prev_profit, prices[j - 1]);
+                if (j < pricesSize) {
+//printf("\tprev_profit = max(%d, %d - %d)\n", prev_profit, dp[i - 1][j], prices[j]);
+                    prev_profit = max(prev_profit, dp[i - 1][j] - prices[j]);
+                }
+            }
+        }
+#if 0
+        printf("  ");
+        for (i = 0; i < pricesSize; i++) {
+            printf("%d ", prices[i]);
+        }
+        printf("\n");
+        for (i = 0; i <= k; i++) {
+            for (j = 0; j <= pricesSize; j++) {
+                printf("%d ", dp[i][j]);
+            }
+            printf("\n");
+        }
+#endif
+
+        return dp[k][pricesSize];
+#else
+        /* local[i][j] j transactions at most and the last max profix until Day i */
+        int *local = malloc((k + 1) * sizeof(int));
+        /* global[i][j] j transactions at most until Day i */
+        int *global = malloc((k + 1) * sizeof(int));
+        memset(local, 0, (k + 1) * sizeof(int));
+        memset(global, 0, (k + 1) * sizeof(int));
+        for (i = 0; i < pricesSize - 1; i++) {
+            int diff = prices[i + 1] - prices[i];
+            for (j = k; j >= 1; j--) {
+                int tmp1 = global[j - 1] + (diff > 0 ? diff : 0);
+                int tmp2 = local[j] + diff;
+                local[j] = tmp1 > tmp2 ? tmp1 : tmp2;
+                global[j] = global[j] > local[j] ? global[j] : local[j];
+            }
+        }
+        return global[k];
+#endif
+    }
+}
+
+int main(int argc, char **argv)
+{
+    if (argc < 2) {
+        fprintf(stderr, "Usage: ./test k n1 n2...\n");
+        exit(-1);
+    }
+
+    int i, count = argc - 2;
+    int *nums = malloc(count * sizeof(int));
+    for (i = 0; i < count; i++) {
+        nums[i] = atoi(argv[i + 2]);
+    }
+    printf("%d\n", maxProfit(atoi(argv[1]), nums, count));
+    return 0;
+}