From 71692af8c42bc6fd47497744ae505e5d10dcecfe Mon Sep 17 00:00:00 2001 From: krahets Date: Sun, 27 Aug 2023 19:22:02 +0800 Subject: [PATCH] Fix a figure. --- .../knapsack_problem.md | 8 ++++---- .../fractional_knapsack_example.png | Bin 78915 -> 79822 bytes 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/docs/chapter_dynamic_programming/knapsack_problem.md b/docs/chapter_dynamic_programming/knapsack_problem.md index 21bb326b8..31c67324f 100644 --- a/docs/chapter_dynamic_programming/knapsack_problem.md +++ b/docs/chapter_dynamic_programming/knapsack_problem.md @@ -26,12 +26,12 @@ **第二步:找出最优子结构,进而推导出状态转移方程** -当我们做出物品 $i$ 的决策后,剩余的是前 $i-1$ 个物品的决策。因此,状态转移分为两种情况: +当我们做出物品 $i$ 的决策后,剩余的是前 $i-1$ 个物品的决策,可分为以下两种情况。 -- **不放入物品 $i$** :背包容量不变,状态转移至 $[i-1, c]$ 。 -- **放入物品 $i$** :背包容量减小 $wgt[i-1]$ ,价值增加 $val[i-1]$ ,状态转移至 $[i-1, c-wgt[i-1]]$ 。 +- **不放入物品 $i$** :背包容量不变,状态变化为 $[i-1, c]$ 。 +- **放入物品 $i$** :背包容量减小 $wgt[i-1]$ ,价值增加 $val[i-1]$ ,状态变化为 $[i-1, c-wgt[i-1]]$ 。 -上述的状态转移向我们揭示了本题的最优子结构:**最大价值 $dp[i, c]$ 等于不放入物品 $i$ 和放入物品 $i$ 两种方案中的价值更大的那一个**。由此可推出状态转移方程: +上述分析向我们揭示了本题的最优子结构:**最大价值 $dp[i, c]$ 等于不放入物品 $i$ 和放入物品 $i$ 两种方案中的价值更大的那一个**。由此可推出状态转移方程: $$ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1]) diff --git a/docs/chapter_greedy/fractional_knapsack_problem.assets/fractional_knapsack_example.png b/docs/chapter_greedy/fractional_knapsack_problem.assets/fractional_knapsack_example.png index 74ce89b486ab30b2d19df58e65eda6bcc27ed597..11ffef563a729470d7c93d850a3366967688c64a 100644 GIT binary patch delta 25447 zcmX_{1yCGK*QkNu?jGDBxVuAw2X}XOXK)Cf;2t12!QI^@xVyW%-A&%_ztq$gLoq$Q zr@N0nr{@52{2a1!brPVU9Tw!Tx$M>xWOVB6`bbFl6BafwQ2aAI)hIk{I7uKxHY6IV z2qfe;2s#KO$X+m-&uEmiJm%aRXB&-#oMGpSzV}B*CEi}$O-G>nqe5@9 zXZ>?+`#$XPgvIO95fwJ~X-58f|MPn^ZIX&nLZypnwhsTcJ79_a$ey@1MSXK)MYe^L zHZzZ(bI^dwE8%^~EVW$Xk&Fa_EDix2ZbOHrI0`mgI2N|@C*!_x->v{k-RCl`(zBA% za#1igJaqjr4b$*~ZrVwl&ek-H) zb(1aOY-r0i@L^4=W%7t$52WJPr-;R5WzHLoL;_nJRvZVKWYZI)KQJo|=ul0jzp^q4 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