From ea1b09b1e41139a6769d54a23612d39e61c14d88 Mon Sep 17 00:00:00 2001 From: Siddharth Singh <102693720+siddharthsingh250304@users.noreply.github.com> Date: Sun, 16 Nov 2025 09:15:35 +0530 Subject: [PATCH 1/6] Add files via upload --- coin_change.typ | 93 ++++++++++++++++++++++++++++++++++++++++++++ lis.typ | 101 ++++++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 194 insertions(+) create mode 100644 coin_change.typ create mode 100644 lis.typ diff --git a/coin_change.typ b/coin_change.typ new file mode 100644 index 0000000..ae53009 --- /dev/null +++ b/coin_change.typ @@ -0,0 +1,93 @@ +#import "../lib/style.typ": * +#import "../lib/mapcode.typ": * + +== Coin Change (Minimum Coins) +#set math.equation(numbering: none) + +Compute the minimum number of coins needed to make a target amount. + +Formal definition: +$ +"CC"(0) &= 0\ +"CC"(n) &= min_(c in "coins", c <= n) (1 + "CC"(n-c)) quad "for" n > 0 +$ + +Example: coins = [1,3,4], amount = 6 +Minimum coins = 2 (using 3+3) + +*As mapcode:* + +_primitives_: `min` and `add`($+$) are strict. i.e min and add on $bot$ is undefined. + +$ +I = "amount": NN quad quad quad X &= [0.."amount"] -> NN_bot quad quad quad A = NN\ +rho("amount") &= {i -> bot | i in [0.."amount"], i > 0} union {0 -> 0}\ +F(x)[i] &= cases( + 0 & "if" i = 0, + min_(c in "coins", c <= i) {1 + x[i - c]} & "if" i > 0 "and deps defined", + bot & "otherwise" +)\ +pi(x) &= x["amount"] +$ + +#let coins = (1, 3, 4); +#let amount = 6; +#figure( + caption: [Coin Change computation using mapcode for amount = #amount, coins = #coins], +$ +#{ + let rho = (amount) => { + let x = () + for i in range(0, amount + 1) { + if i == 0 { + x.push(0) + } else { + x.push(none) + } + } + x + } + + let F_i = (x) => ((i,)) => { + if i == 0 { + 0 + } else { + let candidates = () + for c in coins { + if c <= i and x.at(i - c) != none { + candidates.push(x.at(i - c) + 1) + } + } + if candidates.len() > 0 { + calc.min(..candidates) + } else { + none + } + } + } + let F = map_tensor(F_i, dim: 1) + + let pi = (i) => (x) => x.at(i) + + let X_h = (x, diff_mask: none) => { + let cells = x.enumerate().map(((i, x_i)) => { + let val = if x_i != none {[$#x_i$]} else {[$bot$]} + if diff_mask != none and diff_mask.at(i) { + rect(fill: yellow.transparentize(70%), inset: 2pt)[$#val$] + } else { + rect(stroke: none, inset: 2pt)[$#val$] + } + }) + $vec(delim: "[", ..cells)$ + } + + mapcode-viz( + rho, F, pi(amount), + X_h: X_h, + pi_name: [$pi (#amount)$], + group-size: calc.min(7, amount + 1), + cell-size: 10mm, scale-fig: 85% + )(amount) +} +$ +) diff --git a/lis.typ b/lis.typ new file mode 100644 index 0000000..a207daa --- /dev/null +++ b/lis.typ @@ -0,0 +1,101 @@ +#import "../lib/style.typ": * +#import "../lib/mapcode.typ": * + +== Longest Increasing Subsequence (LIS) +#set math.equation(numbering: none) + +Compute the length of the longest increasing subsequence in an array. + +Formal definition: +$ +"LIS"(i) = cases( + 1 & "if" i = 0, + 1 + max_(j < i, A[j] < A[i]) "LIS"(j) & "if" i > 0 "and valid j exists", + 1 & "otherwise" +) +$ + +Example: A = [10, 9, 2, 5, 3, 7, 101] +LIS length = 4 (subsequence: [2, 3, 7, 101] or [2, 5, 7, 101]) + +*As mapcode:* + +_primitives_: `max` and `add`($+$) are strict. i.e max and add on $bot$ is undefined. + +$ +I = (n: NN, A: "array") quad quad quad X &= [0..n-1] -> NN_bot quad quad quad A = NN\ +rho(n, A) &= {i -> 1 | i in [0..n-1]}\ +F(x)[i] &= cases( + 1 & "if" i = 0, + 1 + max_(j < i, A[j] < A[i]) {x[j]} & "if valid j and deps defined", + 1 & "otherwise" +)\ +pi(x) &= max_(i) x[i] +$ + +#let arr = (10, 9, 2, 5, 3, 7, 101); +#let n = arr.len(); +#figure( + caption: [LIS computation using mapcode for array = #arr], +$ +#{ + let rho = (n) => { + let x = () + for i in range(0, n) { + x.push(1) + } + x + } + + let F_i = (x) => ((i,)) => { + if i == 0 { + 1 + } else { + let max_len = 1 + for j in range(0, i) { + if arr.at(j) < arr.at(i) and x.at(j) != none { + max_len = calc.max(max_len, x.at(j) + 1) + } + } + max_len + } + } + let F = map_tensor(F_i, dim: 1) + + let pi = (n) => (x) => { + let max_val = 0 + for val in x { + if val != none { + max_val = calc.max(max_val, val) + } + } + max_val + } + + let X_h = (x, diff_mask: none) => { + let cells = x.enumerate().map(((i, x_i)) => { + let val = if x_i != none {[$#x_i$]} else {[$bot$]} + let arr_val = arr.at(i) + if diff_mask != none and diff_mask.at(i) { + rect(fill: yellow.transparentize(70%), inset: 2pt)[ + $#arr_val: #val$ + ] + } else { + rect(stroke: none, inset: 2pt)[ + $#arr_val: #val$ + ] + } + }) + $vec(delim: "[", ..cells)$ + } + + mapcode-viz( + rho, F, pi(n), + X_h: X_h, + pi_name: [$max_i x[i]$], + group-size: calc.min(7, n), + cell-size: 12mm, scale-fig: 80% + )(n) +} +$ +) From 67b229461ae4e786775c745128128e84bb925e91 Mon Sep 17 00:00:00 2001 From: Siddharth Singh <102693720+siddharthsingh250304@users.noreply.github.com> Date: Sun, 16 Nov 2025 09:18:00 +0530 Subject: [PATCH 2/6] Update and rename coin_change.typ to slgorithms/coin_change.typ --- coin_change.typ => slgorithms/coin_change.typ | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename coin_change.typ => slgorithms/coin_change.typ (100%) diff --git a/coin_change.typ b/slgorithms/coin_change.typ similarity index 100% rename from coin_change.typ rename to slgorithms/coin_change.typ From d06ab481abb13356648de3e423a0473b500e9b1f Mon Sep 17 00:00:00 2001 From: Siddharth Singh <102693720+siddharthsingh250304@users.noreply.github.com> Date: Sun, 16 Nov 2025 09:18:27 +0530 Subject: [PATCH 3/6] Update and rename lis.typ to algorithms/lis.typ --- lis.typ => algorithms/lis.typ | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename lis.typ => algorithms/lis.typ (100%) diff --git a/lis.typ b/algorithms/lis.typ similarity index 100% rename from lis.typ rename to algorithms/lis.typ From 2f9c42d5967a597a2a30099da79e3179e88b4e45 Mon Sep 17 00:00:00 2001 From: Siddharth Singh <102693720+siddharthsingh250304@users.noreply.github.com> Date: Sun, 16 Nov 2025 09:18:58 +0530 Subject: [PATCH 4/6] Update and rename coin_change.typ to coin_change.typ --- {slgorithms => algorithms}/coin_change.typ | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename {slgorithms => algorithms}/coin_change.typ (100%) diff --git a/slgorithms/coin_change.typ b/algorithms/coin_change.typ similarity index 100% rename from slgorithms/coin_change.typ rename to algorithms/coin_change.typ From af5e21aa878be2525b9769365a23b2451eb75c64 Mon Sep 17 00:00:00 2001 From: Siddharth Singh <102693720+siddharthsingh250304@users.noreply.github.com> Date: Sun, 16 Nov 2025 09:19:46 +0530 Subject: [PATCH 5/6] Add new includes for LIS and coin change algorithms --- main.typ | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/main.typ b/main.typ index 9952d9b..ad742c1 100644 --- a/main.typ +++ b/main.typ @@ -52,3 +52,7 @@ All primitives are _strict_ meaning they do not allow for undefined values (i.e. #include "algorithms/LongestCommonSubsequence.typ" #pagebreak() #include "algorithms/leetcode/P2_add-two-numbers.typ" +#pagebreak() +#include "algorithms/lis.typ" +#pagebreak() +#include "algorithms/coin_change.typ" From b8a8adde60e419e174c393c46202e422b3aa31ec Mon Sep 17 00:00:00 2001 From: Siddharth Singh <102693720+siddharthsingh250304@users.noreply.github.com> Date: Sun, 16 Nov 2025 09:20:19 +0530 Subject: [PATCH 6/6] Add files via upload --- main.pdf | Bin 0 -> 578796 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 main.pdf diff --git a/main.pdf b/main.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c24eeb4e0624211e9534d9a47c3f6b5650bf9047 GIT binary patch literal 578796 zcmeFaU9T)RawYn%Ur{du*bn30Sy`2p1sDSCwvFpMvMs3lJ{f*cOULaqBc0QukD2MW z`RO;vh*edLiV6l9vd8co0m9DBorlSlK`t&bS4RG)FaPRq{`2x@m(Tvw|EB*w`)oP9 z9X|foPe{=whB`(F?L{I~Ca`tIG~ zPnN^qfBfm|pWc7`@Z;g@58obs{qe*9pnp|<|I_l1{_0(6!LnAQkJl>gczvxee|Yyl z?hR)g^^V+dEF~ge-GTh)OF5QS9S?u~zrOzd58u6O8gZ)k{jm|H%BM!$?ob8H|K_3U 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