891 finish

Author: aQua

Algorithms/0891.sum-of-subsequence-widths/sum-of-subsequence-widths.go

@@ -8,14 +8,26 @@ const mod = 1e9 + 7
 
 func sumSubseqWidths(a []int) int {
 	sort.Ints(a)
-	res := 0
 
 	n := len(a)
-	c := 1
+	res := 0
+	times := 1
 	for i := 0; i < n; i++ {
-		res = (res + a[i]*c - a[n-i-1]*c) % mod
-		c = (c << 1) % mod
+		res += (a[i] - a[n-i-1]) * times
+		res %= mod
+		times = (times << 1) % mod
 	}
 
-	return res % mod
+	return res
 }
+
+/**
+ * https://leetcode.com/problems/sum-of-subsequence-widths/discuss/161267/C++Java1-line-Python-Sort-and-One-Pass
+ * For A[i]:
+ * There are i smaller numbers,
+ * so there are 2 ^ i sequences in which A[i] is maximum.
+ * we should do res += A[i] * (2 ^ i)
+ * There are n - i - 1 bigger numbers,
+ * so there are 2 ^ (n - i - 1) sequences in which A[i] is minimum.
+ * we should do res -= A[i] * 2 ^ (n - i - 1)
+ */

Algorithms/0891.sum-of-subsequence-widths/sum-of-subsequence-widths_test.go

@@ -13,6 +13,11 @@ var tcs = []struct {
 	ans int
 }{
 
+	{
+		[]int{1, 10001},
+		10000,
+	},
+
 	{
 		[]int{96, 87, 191, 197, 40, 101, 108, 35, 169, 50, 168, 182, 95, 80, 144, 43, 18, 60, 174, 13, 77, 173, 38, 46, 80, 117, 13, 19, 11, 6, 13, 118, 39, 80, 171, 36, 86, 156, 165, 190, 53, 49, 160, 192, 57, 42, 97, 35, 124, 200, 84, 70, 145, 180, 54, 141, 159, 42, 66, 66, 25, 95, 24, 136, 140, 159, 71, 131, 5, 140, 115, 76, 151, 137, 63, 47, 69, 164, 60, 172, 153, 183, 6, 70, 40, 168, 133, 45, 116, 188, 20, 52, 70, 156, 44, 27, 124, 59, 42, 172},
 		136988321,