diff --git a/.vitepress/theme/style.css b/.vitepress/theme/style.css
index 18d375e..7adac7d 100644
--- a/.vitepress/theme/style.css
+++ b/.vitepress/theme/style.css
@@ -382,3 +382,14 @@ kbd {
.vp-doc img {
border: 1px solid var(--mono-gray-300);
}
+
+/* 评分页的图表（内联 SVG，颜色取主题变量，随深浅色切换） */
+.rating-chart-figure {
+ margin: 24px 0;
+}
+
+.rating-chart-figure svg {
+ display: block;
+ width: 100%;
+ height: auto;
+}
diff --git a/features/charts/rating-accuracy.svg b/features/charts/rating-accuracy.svg
new file mode 100644
index 0000000..8212da7
--- /dev/null
+++ b/features/charts/rating-accuracy.svg
@@ -0,0 +1,4 @@
+
diff --git a/features/charts/rating-confidence.svg b/features/charts/rating-confidence.svg
new file mode 100644
index 0000000..871b22b
--- /dev/null
+++ b/features/charts/rating-confidence.svg
@@ -0,0 +1,4 @@
+
diff --git a/features/charts/rating-daily-ac.svg b/features/charts/rating-daily-ac.svg
new file mode 100644
index 0000000..1e8f03a
--- /dev/null
+++ b/features/charts/rating-daily-ac.svg
@@ -0,0 +1,4 @@
+
diff --git a/features/charts/rating-overall.svg b/features/charts/rating-overall.svg
new file mode 100644
index 0000000..ce8d939
--- /dev/null
+++ b/features/charts/rating-overall.svg
@@ -0,0 +1,4 @@
+
diff --git a/features/charts/rating-persistence.svg b/features/charts/rating-persistence.svg
new file mode 100644
index 0000000..3ce69db
--- /dev/null
+++ b/features/charts/rating-persistence.svg
@@ -0,0 +1,4 @@
+
diff --git a/features/charts/rating-volume.svg b/features/charts/rating-volume.svg
new file mode 100644
index 0000000..3b9683e
--- /dev/null
+++ b/features/charts/rating-volume.svg
@@ -0,0 +1,4 @@
+
diff --git a/features/rating.md b/features/rating.md
index 8ca4f6a..94780a6 100644
--- a/features/rating.md
+++ b/features/rating.md
@@ -1,3 +1,14 @@
+
+
+
+
# 用户评分
开启「添加用户评分和用户名颜色」后，用户名会按评分显示颜色，个人主页上也会显示具体分数。
@@ -37,8 +48,12 @@ $$g(a) = \begin{cases} a & a \le 8 \\ 8 + 8 \ln\left(1 + \dfrac{a - 8}{8}\right)
没有 AC 记录时 $B = 1$。$B$ 是一个 0–1 之间的折扣，正常练习和比赛时基本等于 1。
+
+
$$\text{做题量} = 1 - e^{-S B / 350}$$
+
+
做到几百题以后，继续刷题的收益会越来越小。要拿高分，还得靠准确度。
### 准确度
@@ -53,14 +68,20 @@ AC 之后重复提交 AC 代码既不增加 $S$ 也不增加 $X$，对评分没
$$\text{准确度} = \begin{cases} 0 & P < 0.15 \\ \dfrac{P - 0.15}{0.25} & 0.15 \le P < 0.4 \\ 1 & 0.4 \le P < 0.55 \\ \max\left(0.3,\ 1 - 2(P - 0.55)\right) & P \ge 0.55 \end{cases}$$
+
+
题做得越多，准确度越可信，所以它还要乘上可信度：
$$K = \frac{S}{S + 80}$$
+
+
### 坚持度
$$\text{坚持度} = 1 - e^{-D/250}$$
+
+
### 合在一起
$$\text{评分} = \operatorname{round}\left(3000 \times \left(0.57 \cdot \text{做题量} + 0.33 \cdot \text{准确度} \cdot K + 0.10 \cdot \text{坚持度}\right)^{0.9}\right)$$
@@ -86,6 +107,8 @@ $$\text{评分} = \operatorname{round}\left(3000 \times \left(0.57 \cdot \text{
| F | 和 D 一样，但每天 AC 50 题 | 905 |
| G | 新用户，解决 20 题，平均每题失败 3 次 | 246 |
+
+
评分在浏览器里缓存一天，所以今天的提交通常明天才会反映出来。
## 颜色
diff --git a/scripts/rating_charts.py b/scripts/rating_charts.py
new file mode 100644
index 0000000..a19c25d
--- /dev/null
+++ b/scripts/rating_charts.py
@@ -0,0 +1,202 @@
+# 生成 features/rating.md 中的图表：python3 scripts/rating_charts.py
+# 公式必须和 features/rating.md 保持一致，改动评分算法时请同步这里并重新生成。
+import math, os
+
+OUT = os.path.join(os.path.dirname(os.path.abspath(__file__)), "..", "features", "charts")
+os.makedirs(OUT, exist_ok=True)
+
+# ---------- the formula, exactly as documented ----------
+def g(a): return a if a <= 8 else 8 + 8 * math.log(1 + (a - 8) / 8)
+def acc(P):
+ if P < 0.15: return 0.0
+ if P < 0.4: return (P - 0.15) / 0.25
+ if P < 0.55: return 1.0
+ return max(0.3, 1 - 2 * (P - 0.55))
+def rating(S, X, D, B=1.0):
+ if S == 0: return 0
+ vol = 1 - math.exp(-S * B / 350)
+ P = (S + 10) / (S + X + 40)
+ K = S / (S + 80)
+ per = 1 - math.exp(-D / 250)
+ return 3000 * (0.57 * vol + 0.33 * acc(P) * K + 0.10 * per) ** 0.9
+
+# ---------- theming ----------
+# Each colour is var(--vp-…, var(--local)). Inlined into the page the --vp vars win and
+# follow the site's light/dark toggle; opened on its own the --vp vars are undefined, so
+# the local vars from """
+
+W, H = 600, 360
+
+def esc(s): return s.replace("&", "&").replace("<", "<").replace(">", ">")
+
+class Chart:
+ def __init__(self, name, label, xr, yr, xt, yt, xlab, ylab, ml=56, mr=24, mt=24, mb=52, ytick_fmt=None, xtick_fmt=None):
+ self.name, self.label = name, label
+ self.clip = f"{name}-plot" # ids must be unique: all charts share one page
+ self.x0, self.x1 = ml, W - mr
+ self.y0, self.y1 = H - mb, mt
+ self.xr, self.yr = xr, yr
+ self.parts = []
+ self.xt, self.yt = xt, yt
+ self.xlab, self.ylab = xlab, ylab
+ self.yfmt = ytick_fmt or (lambda v: f"{v:g}")
+ self.xfmt = xtick_fmt or (lambda v: f"{v:g}")
+ def X(self, v): return self.x0 + (v - self.xr[0]) / (self.xr[1] - self.xr[0]) * (self.x1 - self.x0)
+ def Y(self, v): return self.y0 - (v - self.yr[0]) / (self.yr[1] - self.yr[0]) * (self.y0 - self.y1)
+ def add(self, s): self.parts.append(s)
+ def text(self, x, y, s, fill=FG2, size=13, anchor="start", weight=400, extra=""):
+ self.add(f'{esc(s)}')
+ def frame(self):
+ out = []
+ for v in self.yt:
+ y = self.Y(v)
+ out.append(f'')
+ out.append(f'{esc(self.yfmt(v))}')
+ for v in self.xt:
+ x = self.X(v)
+ out.append(f'')
+ out.append(f'{esc(self.xfmt(v))}')
+ out.append(f'')
+ out.append(f'{esc(self.xlab)}')
+ out.append(f'{esc(self.ylab)}')
+ return out
+ def path(self, f, a, b, n=400, stroke=BR, width=2.5, dash=None, clip=True):
+ pts = []
+ for i in range(n + 1):
+ v = a + (b - a) * i / n
+ pts.append(f"{self.X(v):.2f},{self.Y(f(v)):.2f}")
+ d = f' stroke-dasharray="{dash}"' if dash else ""
+ cp = f' clip-path="url(#{self.clip})"' if clip else ""
+ self.add(f'')
+ def dot(self, xv, yv, r=4.5):
+ self.add(f'')
+ def guide(self, xv, yv):
+ x, y = self.X(xv), self.Y(yv)
+ self.add(f'')
+ def save(self, before=()):
+ body = [f'']
+ body.append(f'')
+ body += list(before)
+ body += self.frame()
+ body += self.parts
+ svg = (f'\n")
+ with open(f"{OUT}/{self.name}.svg", "w") as fh:
+ fh.write(svg)
+
+pct = lambda v: f"{v*100:.0f}%"
+
+# ---------- 1. daily AC discount g(a) ----------
+c = Chart("rating-daily-ac", "每天 AC 数与折算后计入的次数：超过 8 次后按对数增长",
+ (0, 120), (0, 60), range(0, 121, 20), range(0, 61, 10),
+ "当天的 AC 数 a", "折算后 g(a)")
+c.add(f'')
+c.text(c.X(8) + 6, c.y1 + 16, "≤ 8 次：原样计入", fill=FG2, size=12)
+c.path(lambda a: a, 0, 120, n=2, stroke=FG2, width=1.5, dash="5 4")
+c.text(c.X(44) - 6, c.Y(44) - 4, "不打折", fill=FG2, size=12, anchor="end")
+c.path(g, 0, 120)
+for a, dx, dy, anc in [(14, 10, 24, "start"), (120, -8, -14, "end")]:
+ c.dot(a, g(a))
+ c.text(c.X(a) + dx, c.Y(g(a)) + dy, f"AC {a} 次 → 约计 {g(a):.1f} 次", fill=FG, size=13, anchor=anc)
+c.save()
+
+# ---------- 2. volume ----------
+c = Chart("rating-volume", "做题量随解决题数的变化：1 − e^(−S/350)",
+ (0, 2000), (0, 1), range(0, 2001, 500), [0, .25, .5, .75, 1],
+ "解决的题数 S（B = 1 时）", "做题量", ytick_fmt=pct)
+f = lambda s: 1 - math.exp(-s / 350)
+c.path(f, 0, 2000)
+for s, dx, dy in [(350, 10, 18), (700, 10, 18), (1400, 0, 22)]:
+ c.guide(s, f(s)); c.dot(s, f(s))
+ c.text(c.X(s) + dx, c.Y(f(s)) + dy, f"{s} 题 → {f(s)*100:.0f}%", fill=FG, size=13)
+c.save()
+
+# ---------- 3. accuracy vs P ----------
+c = Chart("rating-accuracy", "准确度随 P 的变化：P 在 40%–55% 时满分，过高反而减分",
+ (0, 1), (0, 1), [0, .15, .4, .55, .9, 1], [0, .3, .5, 1],
+ "评测过的提交中解决新题的比例 P", "准确度", ytick_fmt=pct, xtick_fmt=pct, mt=60)
+c.add(f'')
+c.path(acc, 0, 1, n=1000)
+c.text((c.X(.4) + c.X(.55)) / 2, c.Y(1) + 20, "满分", fill=BR, size=13, anchor="middle", weight=600)
+c.text(c.x1, c.Y(.3) + 20, "最低 30%", fill=FG, size=13, anchor="end")
+c.text(c.X(.6), c.Y(.44), "几乎不失败，", fill=FG2, size=12)
+c.text(c.X(.6), c.Y(.44) + 16, "更像复制的代码", fill=FG2, size=12)
+# top axis: fails per solved problem when S is large (P ≈ 1 / (1 + f))
+ty = c.y1
+c.add(f'')
+for fpp in [5, 3, 2, 1, .5, 0]:
+ x = c.X(1 / (1 + fpp))
+ c.add(f'')
+ c.text(x, ty - 10, f"{fpp:g}", fill=FG2, size=12, anchor="middle")
+c.text((c.x0 + c.x1) / 2, ty - 30, "≈ 平均每道已解决的题失败几次（题数很多时）", fill=FG2, size=12, anchor="middle")
+c.save()
+
+# ---------- 4. confidence K ----------
+c = Chart("rating-confidence", "准确度的可信度 K = S / (S + 80)",
+ (0, 1000), (0, 1), range(0, 1001, 200), [0, .25, .5, .75, 1],
+ "解决的题数 S", "可信度 K", ytick_fmt=pct)
+f = lambda s: s / (s + 80)
+c.path(f, 0, 1000)
+for s, dx, dy in [(80, 10, 18), (320, 6, 22), (720, 0, 22)]:
+ c.guide(s, f(s)); c.dot(s, f(s))
+ c.text(c.X(s) + dx, c.Y(f(s)) + dy, f"{s} 题 → {f(s)*100:.0f}%", fill=FG, size=13)
+c.save()
+
+# ---------- 5. persistence ----------
+c = Chart("rating-persistence", "坚持度随有提交天数的变化：1 − e^(−D/250)",
+ (0, 1000), (0, 1), range(0, 1001, 200), [0, .25, .5, .75, 1],
+ "有提交的天数 D", "坚持度", ytick_fmt=pct)
+f = lambda d: 1 - math.exp(-d / 250)
+c.path(f, 0, 1000)
+for d, dx, dy in [(100, 10, 18), (250, 10, 18), (500, 10, 20)]:
+ c.guide(d, f(d)); c.dot(d, f(d))
+ c.text(c.X(d) + dx, c.Y(f(d)) + dy, f"{d} 天 → {f(d)*100:.0f}%", fill=FG, size=13)
+c.save()
+
+# ---------- 6. overall ----------
+BANDS = [ # (lo, hi, name, colour) — same colours as .rating.* in .vitepress/theme/style.css
+ (2400, 3000, "红", "#dc2f5a"), (2000, 2400, "橙", "#e8590c"), (1600, 2000, "蓝", "#337cf2"),
+ (1200, 1600, "绿", "#2b9f4f"), (800, 1200, "青", "#1798b0"), (0, 800, "灰", "#78828c")]
+c = Chart("rating-overall", "评分随解决题数的变化，按每题平均失败次数分四条线，背景为用户名颜色",
+ (0, 2000), (0, 3000), range(0, 2001, 500), [0, 800, 1200, 1600, 2000, 2400, 3000],
+ "解决的题数 S", "评分", mr=132, ml=64)
+bg = []
+for lo, hi, name, col in BANDS:
+ y_hi, y_lo = c.Y(hi), c.Y(lo)
+ bg.append(f'')
+ bg.append(f'')
+ bg.append(f'{name}')
+# y tick labels sit on the band boundaries; nudge them so they don't collide with band names
+c.yfmt = lambda v: ""
+for v in [0, 800, 1200, 1600, 2000, 2400, 3000]:
+ bg.append(f'{v}')
+LINES = [(1, "每题失败 1 次", None, 2.75), (3, "每题失败 3 次", "8 4", 2.25), (7, "每题失败 7 次", "2 4", 2.25), (0, "从不失败", "10 3 2 3", 2.25)]
+ends = []
+for fpp, lab, dash, w in LINES:
+ fn = lambda s, fpp=fpp: rating(s, fpp * s, s / 3)
+ c.path(fn, 1, 2000, n=600, stroke=FG, width=w, dash=dash)
+ ends.append([c.Y(fn(2000)), lab, dash, w])
+ends.sort()
+for i in range(1, len(ends)): # spread labels at least 17px apart
+ ends[i][0] = max(ends[i][0], ends[i - 1][0] + 17)
+for y, lab, dash, w in ends:
+ d = f' stroke-dasharray="{dash}"' if dash else ""
+ c.add(f'')
+ c.text(c.x1 + 36, y + 4.5, lab, fill=FG, size=12)
+c.text(c.x1 - 8, c.y0 - 28, "假设每天 AC 不超过 8 次，", fill=FG2, size=11, anchor="end")
+c.text(c.x1 - 8, c.y0 - 12, "平均每天解决 3 题（D = S/3）", fill=FG2, size=11, anchor="end")
+c.save(before=bg)